Identifier
Images
=>
Cc0005;cc-rep-1
[]=>[]
[1]=>[1,0]
[1,2]=>[1,0,1,0]
[2,1]=>[1,1,0,0]
[1,2,3]=>[1,0,1,0,1,0]
[1,3,2]=>[1,0,1,1,0,0]
[2,1,3]=>[1,1,0,0,1,0]
[2,3,1]=>[1,1,0,1,0,0]
[3,1,2]=>[1,1,1,0,0,0]
[3,2,1]=>[1,1,1,0,0,0]
[1,2,3,4]=>[1,0,1,0,1,0,1,0]
[1,2,4,3]=>[1,0,1,0,1,1,0,0]
[1,3,2,4]=>[1,0,1,1,0,0,1,0]
[1,3,4,2]=>[1,0,1,1,0,1,0,0]
[1,4,2,3]=>[1,0,1,1,1,0,0,0]
[1,4,3,2]=>[1,0,1,1,1,0,0,0]
[2,1,3,4]=>[1,1,0,0,1,0,1,0]
[2,1,4,3]=>[1,1,0,0,1,1,0,0]
[2,3,1,4]=>[1,1,0,1,0,0,1,0]
[2,3,4,1]=>[1,1,0,1,0,1,0,0]
[2,4,1,3]=>[1,1,0,1,1,0,0,0]
[2,4,3,1]=>[1,1,0,1,1,0,0,0]
[3,1,2,4]=>[1,1,1,0,0,0,1,0]
[3,1,4,2]=>[1,1,1,0,0,1,0,0]
[3,2,1,4]=>[1,1,1,0,0,0,1,0]
[3,2,4,1]=>[1,1,1,0,0,1,0,0]
[3,4,1,2]=>[1,1,1,0,1,0,0,0]
[3,4,2,1]=>[1,1,1,0,1,0,0,0]
[4,1,2,3]=>[1,1,1,1,0,0,0,0]
[4,1,3,2]=>[1,1,1,1,0,0,0,0]
[4,2,1,3]=>[1,1,1,1,0,0,0,0]
[4,2,3,1]=>[1,1,1,1,0,0,0,0]
[4,3,1,2]=>[1,1,1,1,0,0,0,0]
[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]
[1,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,0]
[1,2,4,3,5]=>[1,0,1,0,1,1,0,0,1,0]
[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]
[1,2,5,3,4]=>[1,0,1,0,1,1,1,0,0,0]
[1,2,5,4,3]=>[1,0,1,0,1,1,1,0,0,0]
[1,3,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]
[1,3,2,5,4]=>[1,0,1,1,0,0,1,1,0,0]
[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]
[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]
[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]
[1,3,5,4,2]=>[1,0,1,1,0,1,1,0,0,0]
[1,4,2,3,5]=>[1,0,1,1,1,0,0,0,1,0]
[1,4,2,5,3]=>[1,0,1,1,1,0,0,1,0,0]
[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]
[1,4,3,5,2]=>[1,0,1,1,1,0,0,1,0,0]
[1,4,5,2,3]=>[1,0,1,1,1,0,1,0,0,0]
[1,4,5,3,2]=>[1,0,1,1,1,0,1,0,0,0]
[1,5,2,3,4]=>[1,0,1,1,1,1,0,0,0,0]
[1,5,2,4,3]=>[1,0,1,1,1,1,0,0,0,0]
[1,5,3,2,4]=>[1,0,1,1,1,1,0,0,0,0]
[1,5,3,4,2]=>[1,0,1,1,1,1,0,0,0,0]
[1,5,4,2,3]=>[1,0,1,1,1,1,0,0,0,0]
[1,5,4,3,2]=>[1,0,1,1,1,1,0,0,0,0]
[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]
[2,1,3,5,4]=>[1,1,0,0,1,0,1,1,0,0]
[2,1,4,3,5]=>[1,1,0,0,1,1,0,0,1,0]
[2,1,4,5,3]=>[1,1,0,0,1,1,0,1,0,0]
[2,1,5,3,4]=>[1,1,0,0,1,1,1,0,0,0]
[2,1,5,4,3]=>[1,1,0,0,1,1,1,0,0,0]
[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]
[2,3,1,5,4]=>[1,1,0,1,0,0,1,1,0,0]
[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]
[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]
[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]
[2,3,5,4,1]=>[1,1,0,1,0,1,1,0,0,0]
[2,4,1,3,5]=>[1,1,0,1,1,0,0,0,1,0]
[2,4,1,5,3]=>[1,1,0,1,1,0,0,1,0,0]
[2,4,3,1,5]=>[1,1,0,1,1,0,0,0,1,0]
[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]
[2,4,5,1,3]=>[1,1,0,1,1,0,1,0,0,0]
[2,4,5,3,1]=>[1,1,0,1,1,0,1,0,0,0]
[2,5,1,3,4]=>[1,1,0,1,1,1,0,0,0,0]
[2,5,1,4,3]=>[1,1,0,1,1,1,0,0,0,0]
[2,5,3,1,4]=>[1,1,0,1,1,1,0,0,0,0]
[2,5,3,4,1]=>[1,1,0,1,1,1,0,0,0,0]
[2,5,4,1,3]=>[1,1,0,1,1,1,0,0,0,0]
[2,5,4,3,1]=>[1,1,0,1,1,1,0,0,0,0]
[3,1,2,4,5]=>[1,1,1,0,0,0,1,0,1,0]
[3,1,2,5,4]=>[1,1,1,0,0,0,1,1,0,0]
[3,1,4,2,5]=>[1,1,1,0,0,1,0,0,1,0]
[3,1,4,5,2]=>[1,1,1,0,0,1,0,1,0,0]
[3,1,5,2,4]=>[1,1,1,0,0,1,1,0,0,0]
[3,1,5,4,2]=>[1,1,1,0,0,1,1,0,0,0]
[3,2,1,4,5]=>[1,1,1,0,0,0,1,0,1,0]
[3,2,1,5,4]=>[1,1,1,0,0,0,1,1,0,0]
[3,2,4,1,5]=>[1,1,1,0,0,1,0,0,1,0]
[3,2,4,5,1]=>[1,1,1,0,0,1,0,1,0,0]
[3,2,5,1,4]=>[1,1,1,0,0,1,1,0,0,0]
[3,2,5,4,1]=>[1,1,1,0,0,1,1,0,0,0]
[3,4,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]
[3,4,1,5,2]=>[1,1,1,0,1,0,0,1,0,0]
[3,4,2,1,5]=>[1,1,1,0,1,0,0,0,1,0]
[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]
[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]
[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]
[3,5,1,2,4]=>[1,1,1,0,1,1,0,0,0,0]
[3,5,1,4,2]=>[1,1,1,0,1,1,0,0,0,0]
[3,5,2,1,4]=>[1,1,1,0,1,1,0,0,0,0]
[3,5,2,4,1]=>[1,1,1,0,1,1,0,0,0,0]
[3,5,4,1,2]=>[1,1,1,0,1,1,0,0,0,0]
[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]
[4,1,2,3,5]=>[1,1,1,1,0,0,0,0,1,0]
[4,1,2,5,3]=>[1,1,1,1,0,0,0,1,0,0]
[4,1,3,2,5]=>[1,1,1,1,0,0,0,0,1,0]
[4,1,3,5,2]=>[1,1,1,1,0,0,0,1,0,0]
[4,1,5,2,3]=>[1,1,1,1,0,0,1,0,0,0]
[4,1,5,3,2]=>[1,1,1,1,0,0,1,0,0,0]
[4,2,1,3,5]=>[1,1,1,1,0,0,0,0,1,0]
[4,2,1,5,3]=>[1,1,1,1,0,0,0,1,0,0]
[4,2,3,1,5]=>[1,1,1,1,0,0,0,0,1,0]
[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]
[4,2,5,1,3]=>[1,1,1,1,0,0,1,0,0,0]
[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]
[4,3,1,2,5]=>[1,1,1,1,0,0,0,0,1,0]
[4,3,1,5,2]=>[1,1,1,1,0,0,0,1,0,0]
[4,3,2,1,5]=>[1,1,1,1,0,0,0,0,1,0]
[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]
[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]
[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]
[4,5,1,2,3]=>[1,1,1,1,0,1,0,0,0,0]
[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]
[4,5,2,1,3]=>[1,1,1,1,0,1,0,0,0,0]
[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]
[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]
[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]
[5,1,2,3,4]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,2,4,3]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,3,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,3,4,2]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,4,2,3]=>[1,1,1,1,1,0,0,0,0,0]
[5,1,4,3,2]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,1,3,4]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,3,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,3,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,4,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,1,4,2]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,4,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,1,2,3]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,1,3,2]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,3,6,4,5]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,3,6,5,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,4,3,6,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,4,6,5,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,5,3,4,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,5,3,6,4]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,2,5,4,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,5,4,6,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,2,5,6,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,5,6,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,6,3,4,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,6,3,5,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,6,4,3,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,6,4,5,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,6,5,3,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,6,5,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,3,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,2,4,6,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,3,2,5,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,2,5,6,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,3,2,6,4,5]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,3,2,6,5,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,3,4,2,6,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,4,6,5,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,5,2,6,4]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,5,4,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,5,4,6,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,5,6,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,5,6,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,6,2,4,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,3,6,2,5,4]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,3,6,4,2,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,3,6,4,5,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,3,6,5,2,4]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,3,6,5,4,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,4,2,3,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,4,2,3,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,4,2,5,3,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,4,2,5,6,3]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,4,2,6,3,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,4,2,6,5,3]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,4,3,2,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,4,3,2,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,4,3,5,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,4,3,5,6,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,4,3,6,2,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,4,3,6,5,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,4,5,2,3,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,4,5,2,6,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,4,5,3,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,4,5,3,6,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,4,5,6,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,4,6,2,3,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,4,6,2,5,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,4,6,3,2,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,4,6,3,5,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,4,6,5,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,4,6,5,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,5,2,3,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,5,2,3,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,5,2,4,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,5,2,4,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,5,2,6,3,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,5,2,6,4,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,5,3,2,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,5,3,2,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,5,3,4,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,5,3,4,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,5,3,6,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,5,3,6,4,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,5,4,2,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,5,4,2,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,5,4,6,3,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,5,6,2,3,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,5,6,2,4,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,5,6,3,4,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,5,6,4,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,5,6,4,3,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,6,2,3,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,2,3,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,2,4,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,2,4,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,2,5,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,2,5,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,3,2,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,3,2,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,3,4,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,3,4,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,3,5,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,3,5,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,4,2,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,4,2,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,4,3,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,4,5,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,4,5,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,5,2,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,5,2,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,5,3,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,5,3,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,5,4,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,5,4,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,3,4,6,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,1,3,5,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,1,3,5,6,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,3,6,4,5]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,1,3,6,5,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,1,4,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,1,4,3,6,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,4,5,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,1,4,5,6,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,4,6,3,5]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,4,6,5,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,5,3,4,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,1,5,3,6,4]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[2,1,5,4,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,1,5,4,6,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[2,1,5,6,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,5,6,4,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,6,3,4,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,6,3,5,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,6,4,3,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,6,4,5,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,6,5,3,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,6,5,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,1,4,6,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,3,1,5,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,3,1,5,6,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,3,1,6,4,5]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,3,1,6,5,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,3,4,1,6,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,4,6,5,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,5,1,4,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,3,5,1,6,4]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,3,5,4,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,3,5,4,6,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,3,5,6,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,3,5,6,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,3,6,1,4,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,3,6,1,5,4]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,3,6,4,1,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,3,6,4,5,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,3,6,5,1,4]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,3,6,5,4,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,4,1,3,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,4,1,3,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,4,1,5,3,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,4,1,5,6,3]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,4,1,6,3,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,4,1,6,5,3]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,4,3,1,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,4,3,1,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,4,3,5,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,4,3,5,6,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,4,3,6,1,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,4,3,6,5,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,4,5,1,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,4,5,1,6,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,4,5,3,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,4,5,3,6,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,4,5,6,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,4,6,1,3,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,4,6,1,5,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,4,6,3,1,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,4,6,3,5,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,4,6,5,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,4,6,5,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,5,1,3,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,5,1,3,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,5,1,4,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,5,1,4,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,5,1,6,3,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,5,1,6,4,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,5,3,1,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,5,3,1,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,5,3,4,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,5,3,4,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,5,3,6,1,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,5,3,6,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,5,4,1,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,5,4,1,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,5,4,6,1,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,5,6,1,3,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,5,6,1,4,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,5,6,3,1,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,5,6,4,1,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,5,6,4,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,6,1,3,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,1,3,5,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,1,4,3,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,1,4,5,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,1,5,3,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,1,5,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,3,1,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,3,1,5,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,3,4,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,3,4,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,3,5,1,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,3,5,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,4,1,3,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,4,1,5,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,4,3,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,4,5,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,4,5,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,5,1,3,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,5,1,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,5,3,1,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,5,3,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,5,4,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,5,4,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[3,1,2,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,1,2,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[3,1,2,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[3,1,2,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,1,2,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[3,1,2,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[3,1,4,2,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,1,4,2,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[3,1,4,5,2,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,1,4,5,6,2]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,1,4,6,2,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,1,4,6,5,2]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,1,5,2,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,1,5,2,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,5,4,2,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,1,5,4,6,2]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,5,6,2,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,5,6,4,2]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,6,2,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,1,6,2,5,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,1,6,4,2,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,1,6,4,5,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,1,6,5,2,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,1,6,5,4,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,2,1,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,2,1,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[3,2,1,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[3,2,1,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,2,1,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[3,2,1,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[3,2,4,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,2,4,1,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[3,2,4,5,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,2,4,6,1,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,2,4,6,5,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,2,5,1,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,2,5,1,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,2,5,4,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,2,5,4,6,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,2,5,6,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,2,5,6,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,2,6,1,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,2,6,1,5,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,2,6,4,1,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,2,6,4,5,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,2,6,5,1,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,2,6,5,4,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,4,1,2,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,4,1,2,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,4,1,5,2,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,4,1,5,6,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[3,4,1,6,2,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[3,4,1,6,5,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[3,4,2,1,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,4,2,1,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,4,2,5,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,4,2,5,6,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[3,4,2,6,1,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[3,4,2,6,5,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[3,4,5,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,4,5,1,6,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,4,5,2,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,4,5,2,6,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,4,5,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[3,4,6,1,5,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[3,4,6,2,1,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[3,4,6,2,5,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[3,4,6,5,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[3,5,1,2,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,5,1,2,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,5,1,4,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,5,1,4,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,5,1,6,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,5,1,6,4,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,5,2,1,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,5,2,1,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,5,2,4,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,5,2,4,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,5,2,6,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,5,2,6,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,5,4,1,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,5,4,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,5,4,6,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,5,6,1,2,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,5,6,1,4,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,5,6,2,1,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,5,6,4,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,6,1,2,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,1,2,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,1,4,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,1,4,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,1,5,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,1,5,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,2,1,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,2,1,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,2,4,1,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,2,4,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,2,5,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,2,5,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,4,1,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,4,1,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,4,2,1,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,4,2,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,4,5,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,5,1,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,5,1,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,5,2,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,5,2,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,5,4,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[4,1,2,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[4,1,2,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[4,1,2,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,1,2,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[4,1,2,6,3,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,1,2,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,1,3,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[4,1,3,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[4,1,3,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,1,3,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[4,1,3,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,1,3,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,1,5,2,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[4,1,5,2,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[4,1,5,3,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[4,1,5,3,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[4,1,5,6,2,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[4,1,5,6,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[4,1,6,2,3,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,1,6,2,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,1,6,3,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,1,6,3,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,1,6,5,2,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,1,6,5,3,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,2,1,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[4,2,1,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[4,2,1,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,2,1,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[4,2,1,6,3,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,2,1,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,2,3,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[4,2,3,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[4,2,3,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,2,3,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[4,2,3,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,2,3,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,2,5,1,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[4,2,5,1,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[4,2,5,3,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[4,2,5,3,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[4,2,5,6,1,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[4,2,5,6,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[4,2,6,1,3,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,2,6,1,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,2,6,3,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,2,6,3,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,2,6,5,1,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,3,1,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[4,3,1,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[4,3,1,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,3,1,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[4,3,1,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,3,1,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,3,2,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[4,3,2,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[4,3,2,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,3,2,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[4,3,2,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,3,2,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,3,5,1,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[4,3,5,1,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[4,3,5,2,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[4,3,5,2,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[4,3,6,1,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,3,6,1,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,3,6,2,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,3,6,2,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,3,6,5,1,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,5,1,2,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[4,5,1,2,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[4,5,1,3,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[4,5,1,6,2,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[4,5,1,6,3,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[4,5,2,1,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[4,5,2,1,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[4,5,2,3,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[4,5,2,6,1,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[4,5,3,1,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[4,5,3,1,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[4,5,3,2,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[4,5,3,2,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[4,6,1,2,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,1,2,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,1,3,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,1,3,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,1,5,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,1,5,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,2,1,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,2,1,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,2,3,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,2,5,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,3,1,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,3,1,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,3,2,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,3,2,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,3,5,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,5,1,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,5,2,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[5,1,2,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,1,2,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,1,2,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,1,2,4,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,1,2,6,3,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,1,2,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,1,3,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,1,3,2,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,1,3,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,1,3,4,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,1,3,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,1,3,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,1,4,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,1,4,2,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,1,4,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,1,4,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,1,4,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,1,6,2,3,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,1,6,2,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,1,6,3,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,1,6,3,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,1,6,4,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,1,6,4,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,2,1,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,2,1,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,2,1,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,2,1,4,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,2,1,6,3,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,2,1,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,2,3,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,2,3,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,2,3,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,2,3,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,2,3,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,2,3,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,2,4,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,2,4,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,2,4,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,2,4,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,2,4,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,2,6,1,3,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,2,6,1,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,2,6,3,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,2,6,4,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,3,1,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,3,1,2,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,3,1,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,3,1,4,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,3,1,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,3,1,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,3,2,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,3,2,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,3,2,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,3,2,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,3,2,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,3,4,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,3,4,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,3,4,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,3,4,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,3,6,1,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,3,6,2,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,4,1,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,4,1,2,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,4,1,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,4,1,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,4,1,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,4,1,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,4,2,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,4,2,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,4,2,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,4,2,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,4,3,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,4,3,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,4,3,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[5,6,1,2,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,1,2,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,1,3,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,1,4,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,2,1,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,2,3,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,2,4,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,3,1,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,3,2,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[6,1,2,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,4,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,5,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,4,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,4,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,2,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,5,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,2,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,3,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,3,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,4,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,4,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,5,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,4,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,1,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,3,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,3,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,4,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,4,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,1,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,4,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,4,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,2,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,5,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,1,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,2,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,3,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,3,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,4,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,1,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,3,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,3,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,1,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,4,5,6,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,3,4,5,7,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,3,4,6,5,7]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,3,4,6,7,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,3,4,7,5,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,3,4,7,6,5]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,3,5,4,6,7]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,3,5,4,7,6]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,2,3,5,6,4,7]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,3,5,6,7,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,3,5,7,4,6]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,3,5,7,6,4]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,3,6,4,5,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,3,6,4,7,5]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,2,3,6,5,4,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,3,6,5,7,4]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,2,3,6,7,4,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,3,6,7,5,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,3,7,4,5,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,7,4,6,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,7,5,4,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,7,5,6,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,7,6,4,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,7,6,5,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,4,3,5,6,7]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,4,3,5,7,6]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,4,3,6,5,7]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,2,4,3,6,7,5]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,2,4,3,7,5,6]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,4,3,7,6,5]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,4,5,3,6,7]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,4,5,3,7,6]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,4,5,6,3,7]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,4,5,6,7,3]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,4,5,7,3,6]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,4,5,7,6,3]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,4,6,3,5,7]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,4,6,3,7,5]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,4,6,5,3,7]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,4,6,5,7,3]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,4,6,7,3,5]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,4,6,7,5,3]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,4,7,3,5,6]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,4,7,3,6,5]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,4,7,5,3,6]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,4,7,5,6,3]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,4,7,6,3,5]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,4,7,6,5,3]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,5,3,4,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,5,3,4,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,5,3,6,4,7]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,2,5,3,6,7,4]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,2,5,3,7,4,6]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,2,5,3,7,6,4]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,2,5,4,3,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,5,4,3,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,5,4,6,3,7]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,2,5,4,6,7,3]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,2,5,4,7,3,6]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,2,5,4,7,6,3]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,2,5,6,3,4,7]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,5,6,3,7,4]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,5,6,4,3,7]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,5,6,4,7,3]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,5,6,7,3,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,5,6,7,4,3]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,5,7,3,4,6]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,5,7,3,6,4]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,5,7,4,3,6]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,5,7,4,6,3]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,5,7,6,3,4]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,5,7,6,4,3]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,6,3,4,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,6,3,4,7,5]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,2,6,3,5,4,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,6,3,5,7,4]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,2,6,3,7,4,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,2,6,3,7,5,4]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,2,6,4,3,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,6,4,3,7,5]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,2,6,4,5,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,6,4,5,7,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,2,6,4,7,3,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,2,6,4,7,5,3]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,2,6,5,3,4,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,6,5,3,7,4]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,2,6,5,4,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,6,5,4,7,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,2,6,5,7,3,4]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,2,6,5,7,4,3]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,2,6,7,3,4,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,6,7,3,5,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,6,7,4,3,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,6,7,4,5,3]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,6,7,5,3,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,6,7,5,4,3]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,7,3,4,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,3,4,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,3,5,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,3,5,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,3,6,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,3,6,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,4,3,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,4,3,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,4,5,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,4,5,6,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,4,6,3,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,4,6,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,5,3,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,5,3,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,5,4,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,5,4,6,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,5,6,3,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,5,6,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,6,3,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,6,3,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,6,4,3,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,6,4,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,6,5,3,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,3,2,4,5,6,7]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,2,4,5,7,6]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,3,2,4,6,5,7]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,2,4,6,7,5]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,3,2,4,7,5,6]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,3,2,4,7,6,5]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,3,2,5,4,6,7]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,2,5,4,7,6]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,2,5,6,4,7]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,2,5,6,7,4]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,2,5,7,4,6]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,3,2,5,7,6,4]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,3,2,6,4,5,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,3,2,6,4,7,5]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,3,2,6,5,4,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,3,2,6,5,7,4]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,3,2,6,7,4,5]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,3,2,6,7,5,4]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,3,2,7,4,5,6]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,3,2,7,4,6,5]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,3,2,7,5,4,6]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,3,2,7,5,6,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,3,2,7,6,4,5]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,3,2,7,6,5,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,3,4,2,5,6,7]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,4,2,5,7,6]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,3,4,2,6,5,7]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,3,4,2,6,7,5]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,3,4,2,7,5,6]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,3,4,2,7,6,5]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,3,4,5,2,6,7]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,4,5,2,7,6]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,4,5,6,2,7]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,4,5,6,7,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,4,5,7,2,6]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,3,4,5,7,6,2]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,3,4,6,2,5,7]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,3,4,6,2,7,5]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,4,6,5,2,7]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,3,4,6,5,7,2]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,4,6,7,2,5]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,3,4,6,7,5,2]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,3,4,7,2,5,6]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,3,4,7,2,6,5]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,3,4,7,5,2,6]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,3,4,7,5,6,2]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,3,4,7,6,2,5]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,3,4,7,6,5,2]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,3,5,2,4,6,7]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,3,5,2,4,7,6]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,3,5,2,6,4,7]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,5,2,6,7,4]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,3,5,2,7,4,6]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,5,2,7,6,4]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,5,4,2,6,7]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,3,5,4,2,7,6]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,3,5,4,6,2,7]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,5,4,6,7,2]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,3,5,4,7,2,6]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,5,4,7,6,2]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,5,6,2,4,7]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,3,5,6,2,7,4]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,3,5,6,4,2,7]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,3,5,6,4,7,2]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,3,5,6,7,2,4]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,3,5,6,7,4,2]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,3,5,7,2,4,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,5,7,2,6,4]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,5,7,4,2,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,5,7,4,6,2]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,5,7,6,2,4]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,5,7,6,4,2]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,6,2,4,5,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,3,6,2,4,7,5]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,3,6,2,5,4,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,3,6,2,5,7,4]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,3,6,2,7,4,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,3,6,2,7,5,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,3,6,4,2,5,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,3,6,4,2,7,5]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,3,6,4,5,2,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,3,6,4,5,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,3,6,4,7,2,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,3,6,4,7,5,2]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,3,6,5,2,4,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,3,6,5,2,7,4]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,3,6,5,4,2,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,3,6,5,4,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,3,6,5,7,2,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,3,6,5,7,4,2]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,3,6,7,2,4,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,3,6,7,2,5,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,3,6,7,4,2,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,3,6,7,4,5,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,3,6,7,5,2,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,3,6,7,5,4,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,3,7,2,4,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,2,4,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,2,5,4,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,2,5,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,2,6,4,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,2,6,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,4,2,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,4,2,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,4,5,2,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,4,5,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,4,6,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,4,6,5,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,5,2,4,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,5,2,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,5,4,2,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,5,4,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,5,6,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,5,6,4,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,6,2,4,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,6,2,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,6,4,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,6,4,5,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,6,5,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,6,5,4,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,4,2,3,5,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,4,2,3,5,7,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,4,2,3,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,4,2,3,6,7,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,4,2,3,7,5,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,4,2,3,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,4,2,5,3,6,7]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,4,2,5,3,7,6]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,4,2,5,6,3,7]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,4,2,5,6,7,3]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,4,2,5,7,3,6]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,4,2,5,7,6,3]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,4,2,6,3,5,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,4,2,6,3,7,5]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,4,2,6,5,3,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,4,2,6,5,7,3]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,4,2,6,7,3,5]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,4,2,6,7,5,3]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,4,2,7,3,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,4,2,7,3,6,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,4,2,7,5,3,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,4,2,7,5,6,3]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,4,2,7,6,3,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,4,2,7,6,5,3]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,4,3,2,5,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,4,3,2,5,7,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,4,3,2,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,4,3,2,6,7,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,4,3,2,7,5,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,4,3,2,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,4,3,5,2,6,7]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,4,3,5,2,7,6]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,4,3,5,6,2,7]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,4,3,5,6,7,2]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,4,3,5,7,2,6]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,4,3,5,7,6,2]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,4,3,6,2,5,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,4,3,6,2,7,5]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,4,3,6,5,2,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,4,3,6,5,7,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,4,3,6,7,2,5]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,4,3,6,7,5,2]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,4,3,7,2,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,4,3,7,2,6,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,4,3,7,5,2,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,4,3,7,5,6,2]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,4,3,7,6,2,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,4,3,7,6,5,2]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,4,5,2,3,6,7]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,4,5,2,3,7,6]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,4,5,2,6,3,7]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,4,5,2,6,7,3]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,4,5,2,7,3,6]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,4,5,2,7,6,3]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,4,5,3,2,6,7]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,4,5,3,2,7,6]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,4,5,3,6,2,7]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,4,5,3,6,7,2]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,4,5,3,7,2,6]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,4,5,3,7,6,2]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,4,5,6,2,3,7]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,4,5,6,2,7,3]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,4,5,6,3,2,7]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,4,5,6,3,7,2]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,4,5,6,7,2,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,4,5,6,7,3,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,4,5,7,2,3,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,4,5,7,2,6,3]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,4,5,7,3,2,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,4,5,7,3,6,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,4,5,7,6,2,3]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,4,5,7,6,3,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,4,6,2,3,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,4,6,2,3,7,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,4,6,2,5,3,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,4,6,2,5,7,3]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,4,6,2,7,3,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,4,6,2,7,5,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,4,6,3,2,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,4,6,3,2,7,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,4,6,3,5,2,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,4,6,3,5,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,4,6,3,7,2,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,4,6,3,7,5,2]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,4,6,5,2,3,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,4,6,5,2,7,3]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,4,6,5,3,2,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,4,6,5,3,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,4,6,5,7,2,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,4,6,5,7,3,2]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,4,6,7,2,3,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,4,6,7,2,5,3]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,4,6,7,3,2,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,4,6,7,3,5,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,4,6,7,5,2,3]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,4,6,7,5,3,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,4,7,2,3,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,2,3,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,2,5,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,2,5,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,2,6,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,2,6,5,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,3,2,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,3,2,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,3,5,2,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,3,5,6,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,3,6,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,3,6,5,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,5,2,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,5,2,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,5,3,2,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,5,3,6,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,5,6,2,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,5,6,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,6,2,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,6,2,5,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,6,3,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,6,3,5,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,6,5,2,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,7,6,5,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,5,2,3,4,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,5,2,3,4,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,5,2,3,6,4,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,5,2,3,6,7,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,5,2,3,7,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,2,3,7,6,4]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,2,4,3,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,5,2,4,3,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,5,2,4,6,3,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,5,2,4,6,7,3]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,5,2,4,7,3,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,2,4,7,6,3]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,2,6,3,4,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,5,2,6,3,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,5,2,6,4,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,5,2,6,4,7,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,5,2,6,7,3,4]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,5,2,6,7,4,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,5,2,7,3,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,2,7,3,6,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,2,7,4,3,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,2,7,4,6,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,2,7,6,3,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,2,7,6,4,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,3,2,4,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,5,3,2,4,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,5,3,2,6,4,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,5,3,2,6,7,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,5,3,2,7,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,3,2,7,6,4]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,3,4,2,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,5,3,4,2,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,5,3,4,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,5,3,4,6,7,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,5,3,4,7,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,3,4,7,6,2]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,3,6,2,4,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,5,3,6,2,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,5,3,6,4,2,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,5,3,6,4,7,2]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,5,3,6,7,2,4]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,5,3,6,7,4,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,5,3,7,2,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,3,7,2,6,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,3,7,4,2,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,3,7,4,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,3,7,6,2,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,3,7,6,4,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,4,2,3,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,5,4,2,3,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,5,4,2,6,3,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,5,4,2,6,7,3]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,5,4,2,7,3,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,4,2,7,6,3]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,4,3,2,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,5,4,3,2,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,5,4,3,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,5,4,3,6,7,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,5,4,3,7,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,4,3,7,6,2]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,4,6,2,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,5,4,6,2,7,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,5,4,6,3,2,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,5,4,6,3,7,2]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,5,4,6,7,2,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,5,4,6,7,3,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,5,4,7,2,3,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,4,7,2,6,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,4,7,3,2,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,4,7,3,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,4,7,6,2,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,4,7,6,3,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,6,2,3,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,5,6,2,3,7,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,5,6,2,4,3,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,5,6,2,4,7,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,5,6,2,7,3,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,5,6,2,7,4,3]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,5,6,3,2,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,5,6,3,2,7,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,5,6,3,4,2,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,5,6,3,4,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,5,6,3,7,2,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,5,6,3,7,4,2]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,5,6,4,2,3,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,5,6,4,2,7,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,5,6,4,3,2,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,5,6,4,3,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,5,6,4,7,2,3]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,5,6,4,7,3,2]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,5,6,7,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,5,6,7,2,4,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,5,6,7,3,2,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,5,6,7,3,4,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,5,6,7,4,2,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,5,6,7,4,3,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,5,7,2,3,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,2,3,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,2,4,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,2,4,6,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,2,6,3,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,2,6,4,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,3,2,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,3,2,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,3,4,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,3,4,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,3,6,2,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,3,6,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,4,2,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,4,2,6,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,4,3,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,4,3,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,4,6,2,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,4,6,3,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,6,2,3,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,6,2,4,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,6,3,2,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,6,3,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,6,4,2,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,6,4,3,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,6,2,3,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,2,3,4,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,2,3,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,2,3,5,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,2,3,7,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,2,3,7,5,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,2,4,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,2,4,3,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,2,4,5,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,2,4,5,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,2,4,7,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,2,4,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,2,5,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,2,5,3,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,2,5,4,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,2,5,4,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,2,5,7,3,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,2,5,7,4,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,2,7,3,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,2,7,3,5,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,2,7,4,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,2,7,4,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,2,7,5,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,2,7,5,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,3,2,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,3,2,4,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,3,2,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,3,2,5,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,3,2,7,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,3,2,7,5,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,3,4,2,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,3,4,2,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,3,4,5,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,3,4,5,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,3,4,7,2,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,3,4,7,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,3,5,2,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,3,5,2,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,3,5,4,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,3,5,4,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,3,5,7,2,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,3,5,7,4,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,3,7,2,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,3,7,2,5,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,3,7,4,2,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,3,7,4,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,3,7,5,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,3,7,5,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,4,2,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,4,2,3,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,4,2,5,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,4,2,5,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,4,2,7,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,4,2,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,4,3,2,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,4,3,2,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,4,3,5,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,4,3,5,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,4,3,7,2,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,4,3,7,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,4,5,2,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,4,5,2,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,4,5,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,4,5,3,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,4,5,7,2,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,4,5,7,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,4,7,2,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,4,7,2,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,4,7,3,2,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,4,7,3,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,4,7,5,2,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,4,7,5,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,5,2,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,5,2,3,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,5,2,4,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,5,2,4,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,5,2,7,3,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,5,2,7,4,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,5,3,2,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,5,3,2,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,5,3,4,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,5,3,4,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,5,3,7,2,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,5,3,7,4,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,5,4,2,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,5,4,2,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,5,4,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6,5,4,3,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,5,4,7,2,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,5,4,7,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,5,7,2,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,5,7,2,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,5,7,3,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,5,7,3,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,5,7,4,2,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,5,7,4,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,7,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,2,3,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,2,4,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,2,4,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,2,5,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,2,5,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,3,2,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,3,2,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,3,4,2,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,3,4,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,3,5,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,3,5,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,4,2,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,4,2,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,4,3,2,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,4,3,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,4,5,2,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,4,5,3,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,5,2,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,5,2,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,5,3,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,5,3,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,5,4,2,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,5,4,3,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,7,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,3,4,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,3,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,3,5,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,3,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,3,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,4,3,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,4,3,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,4,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,4,5,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,4,6,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,4,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,5,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,5,3,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,5,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,5,4,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,5,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,5,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,6,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,6,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,6,4,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,6,4,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,6,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,6,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,2,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,2,4,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,2,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,2,5,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,2,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,2,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,4,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,4,2,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,4,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,4,5,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,4,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,4,6,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,5,2,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,5,2,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,5,4,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,5,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,5,6,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,5,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,6,2,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,6,2,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,6,4,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,6,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,6,5,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,6,5,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,2,3,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,2,3,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,2,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,2,5,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,2,6,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,2,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,3,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,3,2,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,3,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,3,5,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,3,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,3,6,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,5,2,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,5,2,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,5,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,5,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,5,6,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,5,6,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,6,2,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,6,2,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,6,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,6,3,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,6,5,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,6,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,2,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,2,3,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,2,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,2,4,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,2,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,2,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,3,2,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,3,2,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,3,4,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,3,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,3,6,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,3,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,4,2,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,4,2,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,4,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,4,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,4,6,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,4,6,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,6,2,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,6,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,6,3,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,6,3,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,6,4,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,6,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,2,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,2,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,2,4,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,2,4,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,2,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,3,2,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,3,2,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,3,4,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,3,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,3,5,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,3,5,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,4,2,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,4,2,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,4,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,4,3,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,4,5,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,4,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,5,2,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,5,3,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,5,3,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,5,4,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,4,5,6,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,4,5,7,6]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[2,1,3,4,6,5,7]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[2,1,3,4,6,7,5]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[2,1,3,4,7,5,6]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[2,1,3,4,7,6,5]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[2,1,3,5,4,6,7]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[2,1,3,5,4,7,6]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[2,1,3,5,6,4,7]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[2,1,3,5,6,7,4]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,5,7,4,6]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[2,1,3,5,7,6,4]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[2,1,3,6,4,5,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[2,1,3,6,4,7,5]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[2,1,3,6,5,4,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[2,1,3,6,5,7,4]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[2,1,3,6,7,4,5]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[2,1,3,6,7,5,4]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[2,1,3,7,4,5,6]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,1,3,7,4,6,5]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,1,3,7,5,4,6]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,1,3,7,5,6,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,1,3,7,6,4,5]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,1,3,7,6,5,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,1,4,3,5,6,7]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[2,1,4,3,5,7,6]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[2,1,4,3,6,5,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[2,1,4,3,6,7,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[2,1,4,3,7,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[2,1,4,3,7,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[2,1,4,5,3,6,7]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[2,1,4,5,3,7,6]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[2,1,4,5,6,3,7]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[2,1,4,5,6,7,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[2,1,4,5,7,3,6]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[2,1,4,5,7,6,3]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[2,1,4,6,3,5,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[2,1,4,6,3,7,5]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[2,1,4,6,5,3,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[2,1,4,6,5,7,3]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[2,1,4,6,7,3,5]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[2,1,4,6,7,5,3]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[2,1,4,7,3,5,6]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[2,1,4,7,3,6,5]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[2,1,4,7,5,3,6]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[2,1,4,7,5,6,3]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[2,1,4,7,6,3,5]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[2,1,4,7,6,5,3]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[2,1,5,3,4,6,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[2,1,5,3,4,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[2,1,5,3,6,4,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[2,1,5,3,6,7,4]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[2,1,5,3,7,4,6]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[2,1,5,3,7,6,4]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[2,1,5,4,3,6,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[2,1,5,4,3,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[2,1,5,4,6,3,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[2,1,5,4,6,7,3]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[2,1,5,4,7,3,6]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[2,1,5,4,7,6,3]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[2,1,5,6,3,4,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[2,1,5,6,3,7,4]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[2,1,5,6,4,3,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[2,1,5,6,4,7,3]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[2,1,5,6,7,3,4]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[2,1,5,6,7,4,3]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[2,1,5,7,3,4,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[2,1,5,7,3,6,4]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[2,1,5,7,4,3,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[2,1,5,7,4,6,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[2,1,5,7,6,3,4]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[2,1,5,7,6,4,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[2,1,6,3,4,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,1,6,3,4,7,5]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[2,1,6,3,5,4,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,1,6,3,5,7,4]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[2,1,6,3,7,4,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[2,1,6,3,7,5,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[2,1,6,4,3,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,1,6,4,3,7,5]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[2,1,6,4,5,3,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,1,6,4,5,7,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[2,1,6,4,7,3,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[2,1,6,4,7,5,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[2,1,6,5,3,4,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,1,6,5,3,7,4]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[2,1,6,5,4,3,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,1,6,5,4,7,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[2,1,6,5,7,3,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[2,1,6,5,7,4,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[2,1,6,7,3,4,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[2,1,6,7,3,5,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[2,1,6,7,4,3,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[2,1,6,7,4,5,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[2,1,6,7,5,3,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[2,1,6,7,5,4,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[2,1,7,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,3,4,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,3,5,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,3,5,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,3,6,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,3,6,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,4,3,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,4,3,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,4,5,3,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,4,5,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,4,6,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,4,6,5,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,5,3,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,5,3,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,5,4,3,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,5,4,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,5,6,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,5,6,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,6,3,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,6,3,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,6,4,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,6,4,5,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,6,5,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,3,1,4,5,6,7]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[2,3,1,4,5,7,6]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[2,3,1,4,6,5,7]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[2,3,1,4,6,7,5]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[2,3,1,4,7,5,6]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[2,3,1,4,7,6,5]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[2,3,1,5,4,6,7]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[2,3,1,5,4,7,6]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[2,3,1,5,6,4,7]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[2,3,1,5,6,7,4]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[2,3,1,5,7,4,6]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[2,3,1,5,7,6,4]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[2,3,1,6,4,5,7]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[2,3,1,6,4,7,5]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[2,3,1,6,5,4,7]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[2,3,1,6,5,7,4]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[2,3,1,6,7,4,5]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[2,3,1,6,7,5,4]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[2,3,1,7,4,5,6]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[2,3,1,7,4,6,5]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[2,3,1,7,5,4,6]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[2,3,1,7,5,6,4]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[2,3,1,7,6,4,5]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[2,3,1,7,6,5,4]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[2,3,4,1,5,6,7]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[2,3,4,1,5,7,6]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[2,3,4,1,6,5,7]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[2,3,4,1,6,7,5]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[2,3,4,1,7,5,6]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[2,3,4,1,7,6,5]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[2,3,4,5,1,6,7]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[2,3,4,5,1,7,6]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[2,3,4,5,6,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[2,3,4,5,6,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,5,7,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[2,3,4,5,7,6,1]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[2,3,4,6,1,5,7]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[2,3,4,6,1,7,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[2,3,4,6,5,1,7]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[2,3,4,6,5,7,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[2,3,4,6,7,1,5]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[2,3,4,6,7,5,1]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[2,3,4,7,1,5,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,7,1,6,5]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,7,5,1,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,7,5,6,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,7,6,1,5]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,7,6,5,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,5,1,4,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[2,3,5,1,4,7,6]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[2,3,5,1,6,4,7]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[2,3,5,1,6,7,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[2,3,5,1,7,4,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[2,3,5,1,7,6,4]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[2,3,5,4,1,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[2,3,5,4,1,7,6]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[2,3,5,4,6,1,7]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[2,3,5,4,6,7,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[2,3,5,4,7,1,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[2,3,5,4,7,6,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[2,3,5,6,1,4,7]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[2,3,5,6,1,7,4]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[2,3,5,6,4,1,7]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[2,3,5,6,4,7,1]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[2,3,5,6,7,1,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[2,3,5,6,7,4,1]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[2,3,5,7,1,4,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[2,3,5,7,1,6,4]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[2,3,5,7,4,1,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[2,3,5,7,4,6,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[2,3,5,7,6,1,4]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[2,3,5,7,6,4,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[2,3,6,1,4,5,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[2,3,6,1,4,7,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,6,1,5,4,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[2,3,6,1,5,7,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,6,1,7,4,5]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[2,3,6,1,7,5,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[2,3,6,4,1,5,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[2,3,6,4,1,7,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,6,4,5,1,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[2,3,6,4,5,7,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,6,4,7,1,5]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[2,3,6,4,7,5,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[2,3,6,5,1,4,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[2,3,6,5,1,7,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,6,5,4,1,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[2,3,6,5,4,7,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,6,5,7,1,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[2,3,6,5,7,4,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[2,3,6,7,1,4,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[2,3,6,7,1,5,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[2,3,6,7,4,1,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[2,3,6,7,4,5,1]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[2,3,6,7,5,1,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[2,3,6,7,5,4,1]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[2,3,7,1,4,5,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,1,4,6,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,1,5,4,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,1,5,6,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,1,6,4,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,1,6,5,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,4,1,5,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,4,1,6,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,4,5,1,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,4,5,6,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,4,6,1,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,4,6,5,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,5,1,4,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,5,1,6,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,5,4,1,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,5,4,6,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,5,6,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,5,6,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,6,1,4,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,6,1,5,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,6,4,1,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,6,4,5,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,6,5,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,6,5,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,4,1,3,5,6,7]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[2,4,1,3,5,7,6]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[2,4,1,3,6,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[2,4,1,3,6,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[2,4,1,3,7,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[2,4,1,3,7,6,5]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[2,4,1,5,3,6,7]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[2,4,1,5,3,7,6]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[2,4,1,5,6,3,7]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[2,4,1,5,6,7,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[2,4,1,5,7,3,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[2,4,1,5,7,6,3]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[2,4,1,6,3,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[2,4,1,6,3,7,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[2,4,1,6,5,3,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[2,4,1,6,5,7,3]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[2,4,1,6,7,3,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[2,4,1,6,7,5,3]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[2,4,1,7,3,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,1,7,3,6,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,1,7,5,3,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,1,7,5,6,3]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,1,7,6,3,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,1,7,6,5,3]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,3,1,5,6,7]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[2,4,3,1,5,7,6]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[2,4,3,1,6,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[2,4,3,1,6,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[2,4,3,1,7,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[2,4,3,1,7,6,5]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[2,4,3,5,1,6,7]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[2,4,3,5,1,7,6]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[2,4,3,5,6,1,7]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[2,4,3,5,6,7,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[2,4,3,5,7,1,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[2,4,3,5,7,6,1]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[2,4,3,6,1,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[2,4,3,6,1,7,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[2,4,3,6,5,1,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[2,4,3,6,5,7,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[2,4,3,6,7,1,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[2,4,3,6,7,5,1]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[2,4,3,7,1,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,3,7,1,6,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,3,7,5,1,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,3,7,5,6,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,3,7,6,1,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,3,7,6,5,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,5,1,3,6,7]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[2,4,5,1,3,7,6]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[2,4,5,1,6,3,7]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[2,4,5,1,6,7,3]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[2,4,5,1,7,3,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[2,4,5,1,7,6,3]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[2,4,5,3,1,6,7]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[2,4,5,3,1,7,6]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[2,4,5,3,6,1,7]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[2,4,5,3,6,7,1]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[2,4,5,3,7,1,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[2,4,5,3,7,6,1]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[2,4,5,6,1,3,7]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[2,4,5,6,1,7,3]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[2,4,5,6,3,1,7]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[2,4,5,6,3,7,1]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[2,4,5,6,7,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[2,4,5,6,7,3,1]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[2,4,5,7,1,3,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[2,4,5,7,1,6,3]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[2,4,5,7,3,1,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[2,4,5,7,3,6,1]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[2,4,5,7,6,1,3]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[2,4,5,7,6,3,1]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[2,4,6,1,3,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[2,4,6,1,3,7,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[2,4,6,1,5,3,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[2,4,6,1,5,7,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[2,4,6,1,7,3,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[2,4,6,1,7,5,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[2,4,6,3,1,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[2,4,6,3,1,7,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[2,4,6,3,5,1,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[2,4,6,3,5,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[2,4,6,3,7,1,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[2,4,6,3,7,5,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[2,4,6,5,1,3,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[2,4,6,5,1,7,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[2,4,6,5,3,1,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[2,4,6,5,3,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[2,4,6,5,7,1,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[2,4,6,5,7,3,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[2,4,6,7,1,3,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[2,4,6,7,1,5,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[2,4,6,7,3,1,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[2,4,6,7,3,5,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[2,4,6,7,5,1,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[2,4,6,7,5,3,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[2,4,7,1,3,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,1,3,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,1,5,3,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,1,5,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,1,6,3,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,1,6,5,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,3,1,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,3,1,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,3,5,1,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,3,5,6,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,3,6,1,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,3,6,5,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,5,1,3,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,5,1,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,5,3,1,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,5,3,6,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,5,6,1,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,5,6,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,6,1,3,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,6,1,5,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,6,3,1,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,6,3,5,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,6,5,1,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,6,5,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,5,1,3,4,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[2,5,1,3,4,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,5,1,3,6,4,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[2,5,1,3,6,7,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[2,5,1,3,7,4,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,5,1,3,7,6,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,5,1,4,3,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[2,5,1,4,3,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,5,1,4,6,3,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[2,5,1,4,6,7,3]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[2,5,1,4,7,3,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,5,1,4,7,6,3]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,5,1,6,3,4,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[2,5,1,6,3,7,4]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[2,5,1,6,4,3,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[2,5,1,6,4,7,3]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[2,5,1,6,7,3,4]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[2,5,1,6,7,4,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[2,5,1,7,3,4,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,1,7,3,6,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,1,7,4,3,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,1,7,4,6,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,1,7,6,3,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,1,7,6,4,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,3,1,4,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[2,5,3,1,4,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,5,3,1,6,4,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[2,5,3,1,6,7,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[2,5,3,1,7,4,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,5,3,1,7,6,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,5,3,4,1,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[2,5,3,4,1,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,5,3,4,6,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[2,5,3,4,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[2,5,3,4,7,1,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,5,3,4,7,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,5,3,6,1,4,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[2,5,3,6,1,7,4]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[2,5,3,6,4,1,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[2,5,3,6,4,7,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[2,5,3,6,7,1,4]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[2,5,3,6,7,4,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[2,5,3,7,1,4,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,3,7,1,6,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,3,7,4,1,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,3,7,4,6,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,3,7,6,1,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,3,7,6,4,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,4,1,3,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[2,5,4,1,3,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,5,4,1,6,3,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[2,5,4,1,6,7,3]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[2,5,4,1,7,3,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,5,4,1,7,6,3]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,5,4,3,1,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[2,5,4,3,1,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,5,4,3,6,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[2,5,4,3,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[2,5,4,3,7,1,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,5,4,3,7,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,5,4,6,1,3,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[2,5,4,6,1,7,3]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[2,5,4,6,3,1,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[2,5,4,6,3,7,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[2,5,4,6,7,1,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[2,5,4,6,7,3,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[2,5,4,7,1,3,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,4,7,1,6,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,4,7,3,1,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,4,7,3,6,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,4,7,6,1,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,4,7,6,3,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,5,6,1,3,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[2,5,6,1,3,7,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[2,5,6,1,4,3,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[2,5,6,1,4,7,3]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[2,5,6,1,7,3,4]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[2,5,6,1,7,4,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[2,5,6,3,1,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[2,5,6,3,1,7,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[2,5,6,3,4,1,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[2,5,6,3,4,7,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[2,5,6,3,7,1,4]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[2,5,6,3,7,4,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[2,5,6,4,1,3,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[2,5,6,4,1,7,3]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[2,5,6,4,3,1,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[2,5,6,4,3,7,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[2,5,6,4,7,1,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[2,5,6,4,7,3,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[2,5,6,7,1,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[2,5,6,7,1,4,3]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[2,5,6,7,3,1,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[2,5,6,7,3,4,1]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[2,5,6,7,4,1,3]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[2,5,6,7,4,3,1]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[2,5,7,1,3,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,1,3,6,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,1,4,3,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,1,4,6,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,1,6,3,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,1,6,4,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,3,1,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,3,1,6,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,3,4,1,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,3,4,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,3,6,1,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,3,6,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,4,1,3,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,4,1,6,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,4,3,1,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,4,3,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,4,6,1,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,4,6,3,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,6,1,3,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,6,1,4,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,6,3,1,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,6,3,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,6,4,1,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,7,6,4,3,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,6,1,3,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,1,3,4,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,1,3,5,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,1,3,5,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,1,3,7,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,1,3,7,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,1,4,3,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,1,4,3,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,1,4,5,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,1,4,5,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,1,4,7,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,1,4,7,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,1,5,3,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,1,5,3,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,1,5,4,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,1,5,4,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,1,5,7,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,1,5,7,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,1,7,3,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,1,7,3,5,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,1,7,4,3,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,1,7,4,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,1,7,5,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,1,7,5,4,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,3,1,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,3,1,4,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,3,1,5,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,3,1,5,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,3,1,7,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,3,1,7,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,3,4,1,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,3,4,1,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,3,4,5,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,3,4,5,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,3,4,7,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,3,4,7,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,3,5,1,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,3,5,1,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,3,5,4,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,3,5,4,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,3,5,7,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,3,5,7,4,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,3,7,1,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,3,7,1,5,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,3,7,4,1,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,3,7,4,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,3,7,5,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,3,7,5,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,4,1,3,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,4,1,3,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,4,1,5,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,4,1,5,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,4,1,7,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,4,1,7,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,4,3,1,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,4,3,1,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,4,3,5,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,4,3,5,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,4,3,7,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,4,3,7,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,4,5,1,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,4,5,1,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,4,5,3,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,4,5,3,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,4,5,7,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,4,5,7,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,4,7,1,3,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,4,7,1,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,4,7,3,1,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,4,7,3,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,4,7,5,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,4,7,5,3,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,5,1,3,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,5,1,3,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,5,1,4,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,5,1,4,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,5,1,7,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,5,1,7,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,5,3,1,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,5,3,1,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,5,3,4,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,5,3,4,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,5,3,7,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,5,3,7,4,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,5,4,1,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,5,4,1,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,5,4,3,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,5,4,3,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,5,4,7,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,5,4,7,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,5,7,1,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,5,7,1,4,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,5,7,3,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,5,7,3,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,5,7,4,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,5,7,4,3,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,7,1,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,1,3,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,1,4,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,1,4,5,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,1,5,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,1,5,4,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,3,1,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,3,1,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,3,4,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,3,4,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,3,5,1,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,3,5,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,4,1,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,4,1,5,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,4,3,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,4,3,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,4,5,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,4,5,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,5,1,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,5,1,4,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,5,3,1,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,5,3,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,5,4,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,5,4,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,7,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,3,4,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,3,5,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,3,5,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,3,6,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,3,6,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,4,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,4,3,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,4,5,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,4,5,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,4,6,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,4,6,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,5,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,5,3,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,5,4,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,5,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,5,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,5,6,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,6,3,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,6,3,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,6,4,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,6,4,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,6,5,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,1,6,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,1,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,1,4,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,1,5,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,1,5,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,1,6,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,1,6,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,4,1,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,4,1,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,4,5,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,4,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,4,6,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,4,6,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,5,1,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,5,1,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,5,4,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,5,4,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,5,6,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,5,6,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,6,1,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,6,1,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,6,4,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,6,4,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,6,5,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,6,5,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,1,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,1,3,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,1,5,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,1,5,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,1,6,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,1,6,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,3,1,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,3,1,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,3,5,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,3,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,3,6,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,3,6,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,5,1,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,5,1,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,5,3,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,5,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,5,6,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,5,6,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,6,1,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,6,1,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,6,3,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,6,3,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,6,5,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,6,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,1,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,1,3,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,1,4,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,1,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,1,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,1,6,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,3,1,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,3,1,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,3,4,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,3,4,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,3,6,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,3,6,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,4,1,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,4,1,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,4,3,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,4,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,4,6,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,4,6,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,6,1,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,6,1,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,6,3,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,6,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,6,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,6,4,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,1,3,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,1,3,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,1,4,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,1,4,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,1,5,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,1,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,3,1,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,3,1,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,3,4,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,3,4,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,3,5,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,3,5,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,4,1,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,4,1,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,4,3,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,4,3,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,4,5,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,4,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,5,1,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,5,1,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,5,3,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,5,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[3,1,2,4,5,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[3,1,2,4,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[3,1,2,4,6,7,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[3,1,2,4,7,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[3,1,2,4,7,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[3,1,2,5,4,6,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[3,1,2,5,4,7,6]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,1,2,5,6,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[3,1,2,5,6,7,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[3,1,2,5,7,4,6]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[3,1,2,5,7,6,4]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[3,1,2,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[3,1,2,6,4,7,5]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[3,1,2,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[3,1,2,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[3,1,2,6,7,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[3,1,2,6,7,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[3,1,2,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,1,2,7,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,1,2,7,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,1,2,7,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,1,2,7,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,1,2,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,1,4,2,5,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[3,1,4,2,5,7,6]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[3,1,4,2,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[3,1,4,2,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[3,1,4,2,7,5,6]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[3,1,4,2,7,6,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[3,1,4,5,2,6,7]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[3,1,4,5,2,7,6]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[3,1,4,5,6,2,7]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[3,1,4,5,6,7,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[3,1,4,5,7,2,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[3,1,4,5,7,6,2]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[3,1,4,6,2,5,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[3,1,4,6,2,7,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[3,1,4,6,5,2,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[3,1,4,6,5,7,2]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[3,1,4,6,7,2,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[3,1,4,6,7,5,2]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[3,1,4,7,2,5,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,1,4,7,2,6,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,1,4,7,5,2,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,1,4,7,5,6,2]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,1,4,7,6,2,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,1,4,7,6,5,2]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,1,5,2,4,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[3,1,5,2,4,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[3,1,5,2,6,4,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[3,1,5,2,6,7,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[3,1,5,2,7,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,1,5,2,7,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,1,5,4,2,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[3,1,5,4,2,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[3,1,5,4,6,2,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[3,1,5,4,6,7,2]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[3,1,5,4,7,2,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,1,5,4,7,6,2]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,1,5,6,2,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[3,1,5,6,2,7,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[3,1,5,6,4,2,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[3,1,5,6,4,7,2]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[3,1,5,6,7,2,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[3,1,5,6,7,4,2]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[3,1,5,7,2,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,1,5,7,2,6,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,1,5,7,4,2,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,1,5,7,4,6,2]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,1,5,7,6,2,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,1,5,7,6,4,2]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,1,6,2,4,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[3,1,6,2,4,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,1,6,2,5,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[3,1,6,2,5,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,1,6,2,7,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,1,6,2,7,5,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,1,6,4,2,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[3,1,6,4,2,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,1,6,4,5,2,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[3,1,6,4,5,7,2]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,1,6,4,7,2,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,1,6,4,7,5,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,1,6,5,2,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[3,1,6,5,2,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,1,6,5,4,2,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[3,1,6,5,4,7,2]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,1,6,5,7,2,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,1,6,5,7,4,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,1,6,7,2,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,1,6,7,2,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,1,6,7,4,2,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,1,6,7,4,5,2]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,1,6,7,5,2,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,1,6,7,5,4,2]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,1,7,2,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,2,4,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,2,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,2,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,2,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,2,6,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,4,2,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,4,2,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,4,5,2,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,4,5,6,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,4,6,2,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,4,6,5,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,5,2,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,5,2,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,5,4,2,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,5,4,6,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,5,6,2,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,5,6,4,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,6,2,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,6,2,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,6,4,2,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,6,4,5,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,6,5,2,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,6,5,4,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,1,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[3,2,1,4,5,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[3,2,1,4,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[3,2,1,4,6,7,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[3,2,1,4,7,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[3,2,1,4,7,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[3,2,1,5,4,6,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[3,2,1,5,4,7,6]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,2,1,5,6,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[3,2,1,5,6,7,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[3,2,1,5,7,4,6]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[3,2,1,5,7,6,4]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[3,2,1,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[3,2,1,6,4,7,5]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[3,2,1,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[3,2,1,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[3,2,1,6,7,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[3,2,1,6,7,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[3,2,1,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,2,1,7,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,2,1,7,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,2,1,7,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,2,1,7,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,2,1,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,2,4,1,5,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[3,2,4,1,5,7,6]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[3,2,4,1,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[3,2,4,1,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[3,2,4,1,7,5,6]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[3,2,4,1,7,6,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[3,2,4,5,1,6,7]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[3,2,4,5,1,7,6]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[3,2,4,5,6,1,7]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[3,2,4,5,6,7,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[3,2,4,5,7,1,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[3,2,4,5,7,6,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[3,2,4,6,1,5,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[3,2,4,6,1,7,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[3,2,4,6,5,1,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[3,2,4,6,5,7,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[3,2,4,6,7,1,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[3,2,4,6,7,5,1]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[3,2,4,7,1,5,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,2,4,7,1,6,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,2,4,7,5,1,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,2,4,7,5,6,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,2,4,7,6,1,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,2,4,7,6,5,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,2,5,1,4,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[3,2,5,1,4,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[3,2,5,1,6,4,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[3,2,5,1,6,7,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[3,2,5,1,7,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,2,5,1,7,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,2,5,4,1,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[3,2,5,4,1,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[3,2,5,4,6,1,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[3,2,5,4,6,7,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[3,2,5,4,7,1,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,2,5,4,7,6,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,2,5,6,1,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[3,2,5,6,1,7,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[3,2,5,6,4,1,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[3,2,5,6,4,7,1]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[3,2,5,6,7,1,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[3,2,5,6,7,4,1]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[3,2,5,7,1,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,2,5,7,1,6,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,2,5,7,4,1,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,2,5,7,4,6,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,2,5,7,6,1,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,2,5,7,6,4,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,2,6,1,4,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[3,2,6,1,4,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,2,6,1,5,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[3,2,6,1,5,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,2,6,1,7,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,2,6,1,7,5,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,2,6,4,1,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[3,2,6,4,1,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,2,6,4,5,1,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[3,2,6,4,5,7,1]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,2,6,4,7,1,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,2,6,4,7,5,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,2,6,5,1,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[3,2,6,5,1,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,2,6,5,4,1,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[3,2,6,5,4,7,1]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,2,6,5,7,1,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,2,6,5,7,4,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,2,6,7,1,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,2,6,7,1,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,2,6,7,4,1,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,2,6,7,4,5,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,2,6,7,5,1,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,2,6,7,5,4,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,2,7,1,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,1,4,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,1,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,1,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,1,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,1,6,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,4,1,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,4,1,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,4,5,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,4,5,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,4,6,1,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,4,6,5,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,5,1,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,5,1,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,5,4,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,5,4,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,5,6,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,5,6,4,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,6,1,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,6,1,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,6,4,1,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,6,4,5,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,6,5,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,6,5,4,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,4,1,2,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[3,4,1,2,5,7,6]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[3,4,1,2,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[3,4,1,2,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[3,4,1,2,7,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[3,4,1,2,7,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[3,4,1,5,2,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[3,4,1,5,2,7,6]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[3,4,1,5,6,2,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[3,4,1,5,6,7,2]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[3,4,1,5,7,2,6]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[3,4,1,5,7,6,2]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[3,4,1,6,2,5,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[3,4,1,6,2,7,5]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[3,4,1,6,5,2,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[3,4,1,6,5,7,2]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[3,4,1,6,7,2,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[3,4,1,6,7,5,2]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[3,4,1,7,2,5,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,1,7,2,6,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,1,7,5,2,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,1,7,5,6,2]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,1,7,6,2,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,1,7,6,5,2]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,2,1,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[3,4,2,1,5,7,6]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[3,4,2,1,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[3,4,2,1,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[3,4,2,1,7,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[3,4,2,1,7,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[3,4,2,5,1,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[3,4,2,5,1,7,6]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[3,4,2,5,6,1,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[3,4,2,5,6,7,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[3,4,2,5,7,1,6]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[3,4,2,5,7,6,1]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[3,4,2,6,1,5,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[3,4,2,6,1,7,5]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[3,4,2,6,5,1,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[3,4,2,6,5,7,1]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[3,4,2,6,7,1,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[3,4,2,6,7,5,1]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[3,4,2,7,1,5,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,2,7,1,6,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,2,7,5,1,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,2,7,5,6,1]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,2,7,6,1,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,2,7,6,5,1]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,5,1,2,6,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[3,4,5,1,2,7,6]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[3,4,5,1,6,2,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[3,4,5,1,6,7,2]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[3,4,5,1,7,2,6]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[3,4,5,1,7,6,2]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[3,4,5,2,1,6,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[3,4,5,2,1,7,6]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[3,4,5,2,6,1,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[3,4,5,2,6,7,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[3,4,5,2,7,1,6]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[3,4,5,2,7,6,1]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[3,4,5,6,1,2,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[3,4,5,6,1,7,2]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[3,4,5,6,2,1,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[3,4,5,6,2,7,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[3,4,5,6,7,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[3,4,5,6,7,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[3,4,5,7,1,2,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[3,4,5,7,1,6,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[3,4,5,7,2,1,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[3,4,5,7,2,6,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[3,4,5,7,6,1,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[3,4,5,7,6,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[3,4,6,1,2,5,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[3,4,6,1,2,7,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[3,4,6,1,5,2,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[3,4,6,1,5,7,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[3,4,6,1,7,2,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[3,4,6,1,7,5,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[3,4,6,2,1,5,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[3,4,6,2,1,7,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[3,4,6,2,5,1,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[3,4,6,2,5,7,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[3,4,6,2,7,1,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[3,4,6,2,7,5,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[3,4,6,5,1,2,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[3,4,6,5,1,7,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[3,4,6,5,2,1,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[3,4,6,5,2,7,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[3,4,6,5,7,1,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[3,4,6,5,7,2,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[3,4,6,7,1,2,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,6,7,1,5,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,6,7,2,1,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,6,7,2,5,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,6,7,5,1,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,6,7,5,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,7,1,2,5,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,1,2,6,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,1,5,2,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,1,5,6,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,1,6,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,1,6,5,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,2,1,5,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,2,1,6,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,2,5,1,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,2,5,6,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,2,6,1,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,2,6,5,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,5,1,2,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,5,1,6,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,5,2,1,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,5,2,6,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,5,6,1,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,5,6,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,6,1,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,6,1,5,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,6,2,1,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,6,2,5,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,6,5,1,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,7,6,5,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,5,1,2,4,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[3,5,1,2,4,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[3,5,1,2,6,4,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[3,5,1,2,6,7,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[3,5,1,2,7,4,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,1,2,7,6,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,1,4,2,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[3,5,1,4,2,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[3,5,1,4,6,2,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[3,5,1,4,6,7,2]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[3,5,1,4,7,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,1,4,7,6,2]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,1,6,2,4,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[3,5,1,6,2,7,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[3,5,1,6,4,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[3,5,1,6,4,7,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[3,5,1,6,7,2,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[3,5,1,6,7,4,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[3,5,1,7,2,4,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,1,7,2,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,1,7,4,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,1,7,4,6,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,1,7,6,2,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,1,7,6,4,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,2,1,4,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[3,5,2,1,4,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[3,5,2,1,6,4,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[3,5,2,1,6,7,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[3,5,2,1,7,4,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,2,1,7,6,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,2,4,1,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[3,5,2,4,1,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[3,5,2,4,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[3,5,2,4,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[3,5,2,4,7,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,2,4,7,6,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,2,6,1,4,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[3,5,2,6,1,7,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[3,5,2,6,4,1,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[3,5,2,6,4,7,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[3,5,2,6,7,1,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[3,5,2,6,7,4,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[3,5,2,7,1,4,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,2,7,1,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,2,7,4,1,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,2,7,4,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,2,7,6,1,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,2,7,6,4,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,4,1,2,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[3,5,4,1,2,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[3,5,4,1,6,2,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[3,5,4,1,6,7,2]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[3,5,4,1,7,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,4,1,7,6,2]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,4,2,1,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[3,5,4,2,1,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[3,5,4,2,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[3,5,4,2,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[3,5,4,2,7,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,4,2,7,6,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,4,6,1,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[3,5,4,6,1,7,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[3,5,4,6,2,1,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[3,5,4,6,2,7,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[3,5,4,6,7,1,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[3,5,4,6,7,2,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[3,5,4,7,1,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,4,7,1,6,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,4,7,2,1,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,4,7,2,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,4,7,6,1,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,4,7,6,2,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,6,1,2,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[3,5,6,1,2,7,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[3,5,6,1,4,2,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[3,5,6,1,4,7,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[3,5,6,1,7,2,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[3,5,6,1,7,4,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[3,5,6,2,1,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[3,5,6,2,1,7,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[3,5,6,2,4,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[3,5,6,2,4,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[3,5,6,2,7,1,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[3,5,6,2,7,4,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[3,5,6,4,1,2,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[3,5,6,4,1,7,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[3,5,6,4,2,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[3,5,6,4,2,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[3,5,6,4,7,1,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[3,5,6,4,7,2,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[3,5,6,7,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[3,5,6,7,1,4,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[3,5,6,7,2,1,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[3,5,6,7,2,4,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[3,5,6,7,4,1,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[3,5,6,7,4,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[3,5,7,1,2,4,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,1,2,6,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,1,4,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,1,4,6,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,1,6,2,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,1,6,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,2,1,4,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,2,1,6,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,2,4,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,2,4,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,2,6,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,2,6,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,4,1,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,4,1,6,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,4,2,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,4,2,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,4,6,1,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,4,6,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,6,1,2,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,6,1,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,6,2,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,6,2,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,6,4,1,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,6,4,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,6,1,2,4,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,1,2,4,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,1,2,5,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,1,2,5,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,1,2,7,4,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,1,2,7,5,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,1,4,2,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,1,4,2,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,1,4,5,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,1,4,5,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,1,4,7,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,1,4,7,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,1,5,2,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,1,5,2,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,1,5,4,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,1,5,4,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,1,5,7,2,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,1,5,7,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,1,7,2,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,1,7,2,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,1,7,4,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,1,7,4,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,1,7,5,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,1,7,5,4,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,2,1,4,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,2,1,4,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,2,1,5,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,2,1,5,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,2,1,7,4,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,2,1,7,5,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,2,4,1,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,2,4,1,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,2,4,5,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,2,4,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,2,4,7,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,2,4,7,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,2,5,1,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,2,5,1,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,2,5,4,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,2,5,4,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,2,5,7,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,2,5,7,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,2,7,1,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,2,7,1,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,2,7,4,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,2,7,4,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,2,7,5,1,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,2,7,5,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,4,1,2,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,4,1,2,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,4,1,5,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,4,1,5,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,4,1,7,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,4,1,7,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,4,2,1,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,4,2,1,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,4,2,5,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,4,2,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,4,2,7,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,4,2,7,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,4,5,1,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,4,5,1,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,4,5,2,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,4,5,2,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,4,5,7,1,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,4,5,7,2,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,4,7,1,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,4,7,1,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,4,7,2,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,4,7,2,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,4,7,5,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,4,7,5,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,5,1,2,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,5,1,2,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,5,1,4,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,5,1,4,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,5,1,7,2,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,5,1,7,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,5,2,1,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,5,2,1,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,5,2,4,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,5,2,4,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,5,2,7,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,5,2,7,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,5,4,1,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,5,4,1,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,5,4,2,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[3,6,5,4,2,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,5,4,7,1,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,5,4,7,2,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,5,7,1,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,5,7,1,4,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,5,7,2,1,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,5,7,2,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,5,7,4,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,5,7,4,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,7,1,2,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,1,2,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,1,4,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,1,4,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,1,5,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,1,5,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,2,1,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,2,1,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,2,4,1,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,2,4,5,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,2,5,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,2,5,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,4,1,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,4,1,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,4,2,1,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,4,2,5,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,4,5,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,4,5,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,5,1,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,5,1,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,5,2,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,5,2,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,5,4,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,5,4,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,7,1,2,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,2,4,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,2,5,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,2,5,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,2,6,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,2,6,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,4,2,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,4,2,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,4,5,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,4,5,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,4,6,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,4,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,5,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,5,2,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,5,4,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,5,4,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,5,6,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,5,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,6,2,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,6,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,6,4,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,6,4,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,6,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,6,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,1,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,1,4,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,1,5,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,1,5,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,1,6,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,1,6,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,4,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,4,1,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,4,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,4,5,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,4,6,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,4,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,5,1,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,5,1,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,5,4,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,5,4,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,5,6,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,5,6,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,6,1,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,6,1,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,6,4,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,6,4,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,6,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,6,5,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,1,2,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,1,2,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,1,5,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,1,5,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,1,6,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,1,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,2,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,2,1,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,2,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,2,5,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,2,6,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,2,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,5,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,5,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,5,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,5,2,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,5,6,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,5,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,6,1,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,6,1,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,6,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,6,2,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,6,5,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,6,5,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,1,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,1,2,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,1,4,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,1,4,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,1,6,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,1,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,2,1,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,2,1,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,2,4,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,2,4,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,2,6,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,2,6,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,4,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,4,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,4,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,4,2,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,4,6,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,4,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,6,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,6,1,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,6,2,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,6,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,6,4,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,6,4,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,1,2,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,1,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,1,4,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,1,4,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,1,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,1,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,2,1,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,2,1,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,2,4,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,2,4,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,2,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,2,5,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,4,1,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,4,1,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,4,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,4,2,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,4,5,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,4,5,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,5,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,5,1,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,5,2,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,5,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,5,4,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,5,4,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,1,2,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[4,1,2,3,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[4,1,2,3,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[4,1,2,3,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[4,1,2,3,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,1,2,3,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,1,2,5,3,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[4,1,2,5,3,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[4,1,2,5,6,3,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[4,1,2,5,6,7,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[4,1,2,5,7,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,1,2,5,7,6,3]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,1,2,6,3,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[4,1,2,6,3,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,1,2,6,5,3,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[4,1,2,6,5,7,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,1,2,6,7,3,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,1,2,6,7,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,1,2,7,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,1,2,7,3,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,1,2,7,5,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,1,2,7,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,1,2,7,6,3,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,1,2,7,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,1,3,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[4,1,3,2,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[4,1,3,2,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[4,1,3,2,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[4,1,3,2,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,1,3,2,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,1,3,5,2,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[4,1,3,5,2,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[4,1,3,5,6,2,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[4,1,3,5,6,7,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[4,1,3,5,7,2,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,1,3,5,7,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,1,3,6,2,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[4,1,3,6,2,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,1,3,6,5,2,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[4,1,3,6,5,7,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,1,3,6,7,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,1,3,6,7,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,1,3,7,2,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,1,3,7,2,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,1,3,7,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,1,3,7,5,6,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,1,3,7,6,2,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,1,3,7,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,1,5,2,3,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[4,1,5,2,3,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[4,1,5,2,6,3,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[4,1,5,2,6,7,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[4,1,5,2,7,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[4,1,5,2,7,6,3]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[4,1,5,3,2,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[4,1,5,3,2,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[4,1,5,3,6,2,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[4,1,5,3,6,7,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[4,1,5,3,7,2,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[4,1,5,3,7,6,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[4,1,5,6,2,3,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[4,1,5,6,2,7,3]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[4,1,5,6,3,2,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[4,1,5,6,3,7,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[4,1,5,6,7,2,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[4,1,5,6,7,3,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[4,1,5,7,2,3,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,1,5,7,2,6,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,1,5,7,3,2,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,1,5,7,3,6,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,1,5,7,6,2,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,1,5,7,6,3,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,1,6,2,3,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,1,6,2,3,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,1,6,2,5,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,1,6,2,5,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,1,6,2,7,3,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,1,6,2,7,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,1,6,3,2,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,1,6,3,2,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,1,6,3,5,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,1,6,3,5,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,1,6,3,7,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,1,6,3,7,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,1,6,5,2,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,1,6,5,2,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,1,6,5,3,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,1,6,5,3,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,1,6,5,7,2,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,1,6,5,7,3,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,1,6,7,2,3,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,1,6,7,2,5,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,1,6,7,3,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,1,6,7,3,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,1,6,7,5,2,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,1,6,7,5,3,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,1,7,2,3,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,2,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,2,5,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,2,5,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,2,6,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,2,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,3,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,3,2,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,3,5,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,3,5,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,3,6,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,3,6,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,5,2,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,5,2,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,5,3,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,5,3,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,5,6,2,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,5,6,3,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,6,2,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,6,2,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,6,3,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,6,3,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,6,5,2,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,7,6,5,3,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,1,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[4,2,1,3,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[4,2,1,3,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[4,2,1,3,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[4,2,1,3,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,2,1,3,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,2,1,5,3,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[4,2,1,5,3,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[4,2,1,5,6,3,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[4,2,1,5,6,7,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[4,2,1,5,7,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,2,1,5,7,6,3]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,2,1,6,3,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[4,2,1,6,3,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,2,1,6,5,3,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[4,2,1,6,5,7,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,2,1,6,7,3,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,2,1,6,7,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,2,1,7,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,1,7,3,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,1,7,5,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,1,7,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,1,7,6,3,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,1,7,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,3,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[4,2,3,1,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[4,2,3,1,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[4,2,3,1,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[4,2,3,1,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,2,3,1,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,2,3,5,1,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[4,2,3,5,1,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[4,2,3,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[4,2,3,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[4,2,3,5,7,1,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,2,3,5,7,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,2,3,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[4,2,3,6,1,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,2,3,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[4,2,3,6,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,2,3,6,7,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,2,3,6,7,5,1]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,2,3,7,1,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,3,7,1,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,3,7,5,1,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,3,7,5,6,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,3,7,6,1,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,3,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,5,1,3,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[4,2,5,1,3,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[4,2,5,1,6,3,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[4,2,5,1,6,7,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[4,2,5,1,7,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[4,2,5,1,7,6,3]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[4,2,5,3,1,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[4,2,5,3,1,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[4,2,5,3,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[4,2,5,3,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[4,2,5,3,7,1,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[4,2,5,3,7,6,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[4,2,5,6,1,3,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[4,2,5,6,1,7,3]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[4,2,5,6,3,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[4,2,5,6,3,7,1]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[4,2,5,6,7,1,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[4,2,5,6,7,3,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[4,2,5,7,1,3,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,2,5,7,1,6,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,2,5,7,3,1,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,2,5,7,3,6,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,2,5,7,6,1,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,2,5,7,6,3,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,2,6,1,3,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,2,6,1,3,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,2,6,1,5,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,2,6,1,5,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,2,6,1,7,3,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,2,6,1,7,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,2,6,3,1,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,2,6,3,1,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,2,6,3,5,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,2,6,3,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,2,6,3,7,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,2,6,3,7,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,2,6,5,1,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,2,6,5,1,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,2,6,5,3,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,2,6,5,3,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,2,6,5,7,1,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,2,6,5,7,3,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,2,6,7,1,3,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,2,6,7,1,5,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,2,6,7,3,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,2,6,7,3,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,2,6,7,5,1,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,2,6,7,5,3,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,2,7,1,3,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,1,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,1,5,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,1,5,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,1,6,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,1,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,3,1,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,3,1,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,3,5,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,3,5,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,3,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,3,6,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,5,1,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,5,1,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,5,3,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,5,3,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,5,6,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,5,6,3,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,6,1,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,6,1,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,6,3,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,6,3,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,6,5,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,7,6,5,3,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,1,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[4,3,1,2,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[4,3,1,2,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[4,3,1,2,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[4,3,1,2,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,3,1,2,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,3,1,5,2,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[4,3,1,5,2,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[4,3,1,5,6,2,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[4,3,1,5,6,7,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[4,3,1,5,7,2,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,3,1,5,7,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,3,1,6,2,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[4,3,1,6,2,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,3,1,6,5,2,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[4,3,1,6,5,7,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,3,1,6,7,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,3,1,6,7,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,3,1,7,2,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,3,1,7,2,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,3,1,7,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,3,1,7,5,6,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,3,1,7,6,2,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,3,1,7,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,3,2,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[4,3,2,1,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[4,3,2,1,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[4,3,2,1,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[4,3,2,1,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,3,2,1,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,3,2,5,1,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[4,3,2,5,1,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[4,3,2,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[4,3,2,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[4,3,2,5,7,1,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,3,2,5,7,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,3,2,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[4,3,2,6,1,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,3,2,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[4,3,2,6,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,3,2,6,7,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,3,2,6,7,5,1]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,3,2,7,1,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,3,2,7,1,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,3,2,7,5,1,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,3,2,7,5,6,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,3,2,7,6,1,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,3,2,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,3,5,1,2,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[4,3,5,1,2,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[4,3,5,1,6,2,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[4,3,5,1,6,7,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[4,3,5,1,7,2,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[4,3,5,1,7,6,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[4,3,5,2,1,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[4,3,5,2,1,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[4,3,5,2,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[4,3,5,2,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[4,3,5,2,7,1,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[4,3,5,2,7,6,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[4,3,5,6,1,2,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[4,3,5,6,1,7,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[4,3,5,6,2,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[4,3,5,6,2,7,1]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[4,3,5,6,7,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[4,3,5,6,7,2,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[4,3,5,7,1,2,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,3,5,7,1,6,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,3,5,7,2,1,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,3,5,7,2,6,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,3,5,7,6,1,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,3,5,7,6,2,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,3,6,1,2,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,3,6,1,2,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,3,6,1,5,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,3,6,1,5,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,3,6,1,7,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,3,6,1,7,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,3,6,2,1,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,3,6,2,1,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,3,6,2,5,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,3,6,2,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,3,6,2,7,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,3,6,2,7,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,3,6,5,1,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,3,6,5,1,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,3,6,5,2,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,3,6,5,2,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,3,6,5,7,1,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,3,6,5,7,2,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,3,6,7,1,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,3,6,7,1,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,3,6,7,2,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,3,6,7,2,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,3,6,7,5,1,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,3,6,7,5,2,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,3,7,1,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,1,2,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,1,5,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,1,5,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,1,6,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,1,6,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,2,1,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,2,1,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,2,5,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,2,5,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,2,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,2,6,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,5,1,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,5,1,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,5,2,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,5,2,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,5,6,1,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,5,6,2,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,6,1,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,6,1,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,6,2,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,6,2,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,6,5,1,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,6,5,2,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,5,1,2,3,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[4,5,1,2,3,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[4,5,1,2,6,3,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[4,5,1,2,6,7,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[4,5,1,2,7,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,5,1,2,7,6,3]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,5,1,3,2,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[4,5,1,3,2,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[4,5,1,3,6,2,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[4,5,1,3,6,7,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[4,5,1,3,7,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,5,1,3,7,6,2]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,5,1,6,2,3,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[4,5,1,6,2,7,3]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[4,5,1,6,3,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[4,5,1,6,3,7,2]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[4,5,1,6,7,2,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[4,5,1,6,7,3,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[4,5,1,7,2,3,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,1,7,2,6,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,1,7,3,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,1,7,3,6,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,1,7,6,2,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,1,7,6,3,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,2,1,3,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[4,5,2,1,3,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[4,5,2,1,6,3,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[4,5,2,1,6,7,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[4,5,2,1,7,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,5,2,1,7,6,3]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,5,2,3,1,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[4,5,2,3,1,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[4,5,2,3,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[4,5,2,3,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[4,5,2,3,7,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,5,2,3,7,6,1]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,5,2,6,1,3,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[4,5,2,6,1,7,3]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[4,5,2,6,3,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[4,5,2,6,3,7,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[4,5,2,6,7,1,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[4,5,2,6,7,3,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[4,5,2,7,1,3,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,2,7,1,6,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,2,7,3,1,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,2,7,3,6,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,2,7,6,1,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,2,7,6,3,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,3,1,2,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[4,5,3,1,2,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[4,5,3,1,6,2,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[4,5,3,1,6,7,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[4,5,3,1,7,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,5,3,1,7,6,2]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,5,3,2,1,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[4,5,3,2,1,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[4,5,3,2,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[4,5,3,2,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[4,5,3,2,7,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,5,3,2,7,6,1]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,5,3,6,1,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[4,5,3,6,1,7,2]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[4,5,3,6,2,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[4,5,3,6,2,7,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[4,5,3,6,7,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[4,5,3,6,7,2,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[4,5,3,7,1,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,3,7,1,6,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,3,7,2,1,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,3,7,2,6,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,3,7,6,1,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,3,7,6,2,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,5,6,1,2,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[4,5,6,1,2,7,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[4,5,6,1,3,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[4,5,6,1,3,7,2]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[4,5,6,1,7,2,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[4,5,6,1,7,3,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[4,5,6,2,1,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[4,5,6,2,1,7,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[4,5,6,2,3,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[4,5,6,2,3,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[4,5,6,2,7,1,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[4,5,6,2,7,3,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[4,5,6,3,1,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[4,5,6,3,1,7,2]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[4,5,6,3,2,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[4,5,6,3,2,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[4,5,6,3,7,1,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[4,5,6,3,7,2,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[4,5,6,7,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,1,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,2,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[4,5,7,1,2,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,1,2,6,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,1,3,2,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,1,3,6,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,1,6,2,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,1,6,3,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,2,1,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,2,1,6,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,2,3,1,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,2,3,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,2,6,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,2,6,3,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,3,1,2,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,3,1,6,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,3,2,1,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,3,2,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,3,6,1,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,3,6,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,6,1,2,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,6,1,3,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,6,2,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,6,2,3,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,6,3,1,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,6,3,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,6,1,2,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,1,2,3,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,1,2,5,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,1,2,5,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,1,2,7,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,1,2,7,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,1,3,2,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,1,3,2,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,1,3,5,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,1,3,5,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,1,3,7,2,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,1,3,7,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,1,5,2,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,1,5,2,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,1,5,3,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,1,5,3,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,1,5,7,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,1,5,7,3,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,1,7,2,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,1,7,2,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,1,7,3,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,1,7,3,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,1,7,5,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,1,7,5,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,2,1,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,2,1,3,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,2,1,5,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,2,1,5,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,2,1,7,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,2,1,7,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,2,3,1,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,2,3,1,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,2,3,5,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,2,3,5,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,2,3,7,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,2,3,7,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,2,5,1,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,2,5,1,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,2,5,3,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,2,5,3,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,2,5,7,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,2,5,7,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,2,7,1,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,2,7,1,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,2,7,3,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,2,7,3,5,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,2,7,5,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,2,7,5,3,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,3,1,2,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,3,1,2,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,3,1,5,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,3,1,5,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,3,1,7,2,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,3,1,7,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,3,2,1,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,3,2,1,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,3,2,5,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,3,2,5,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,3,2,7,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,3,2,7,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,3,5,1,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,3,5,1,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,3,5,2,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,3,5,2,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,3,5,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,3,5,7,2,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,3,7,1,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,3,7,1,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,3,7,2,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,3,7,2,5,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,3,7,5,1,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,3,7,5,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,5,1,2,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,5,1,2,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,5,1,3,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,5,1,3,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,5,1,7,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,5,1,7,3,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,5,2,1,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,5,2,1,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,5,2,3,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,5,2,3,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,5,2,7,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,5,2,7,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,5,3,1,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,5,3,1,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,5,3,2,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,5,3,2,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,6,5,3,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,5,3,7,2,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,5,7,1,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,5,7,1,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,5,7,2,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,5,7,2,3,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,5,7,3,1,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,5,7,3,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,7,1,2,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,1,2,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,1,3,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,1,3,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,1,5,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,1,5,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,2,1,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,2,1,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,2,3,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,2,3,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,2,5,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,2,5,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,3,1,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,3,1,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,3,2,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,3,2,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,3,5,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,3,5,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,5,1,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,5,1,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,5,2,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,5,2,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,5,3,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,5,3,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,7,1,2,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,2,3,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,2,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,2,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,2,6,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,2,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,3,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,3,2,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,3,5,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,3,5,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,3,6,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,3,6,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,5,2,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,5,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,5,3,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,5,3,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,5,6,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,5,6,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,6,2,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,6,2,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,6,3,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,6,3,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,6,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,6,5,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,1,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,1,3,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,1,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,1,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,1,6,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,1,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,3,1,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,3,1,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,3,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,3,5,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,3,6,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,3,6,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,5,1,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,5,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,5,3,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,5,3,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,5,6,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,5,6,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,6,1,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,6,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,6,3,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,6,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,6,5,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,2,6,5,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,1,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,1,2,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,1,5,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,1,5,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,1,6,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,1,6,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,2,1,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,2,1,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,2,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,2,5,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,2,6,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,2,6,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,5,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,5,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,5,2,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,5,2,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,5,6,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,5,6,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,6,1,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,6,1,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,6,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,6,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,6,5,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,6,5,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,1,2,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,1,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,1,3,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,1,3,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,1,6,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,1,6,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,2,1,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,2,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,2,3,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,2,3,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,2,6,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,2,6,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,3,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,3,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,3,2,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,3,2,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,3,6,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,3,6,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,6,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,6,1,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,6,2,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,6,2,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,6,3,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,6,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,1,2,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,1,2,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,1,3,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,1,3,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,1,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,1,5,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,2,1,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,2,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,2,3,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,2,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,2,5,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,2,5,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,3,1,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,3,1,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,3,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,3,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,3,5,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,3,5,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,5,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,5,1,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,5,2,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,5,2,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,5,3,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,5,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,1,2,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,1,2,3,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,1,2,3,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,1,2,3,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,1,2,3,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,2,3,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,2,4,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,1,2,4,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,1,2,4,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,1,2,4,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,1,2,4,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,2,4,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,2,6,3,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,1,2,6,3,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,1,2,6,4,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,1,2,6,4,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,1,2,6,7,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,1,2,6,7,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,1,2,7,3,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,2,7,3,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,2,7,4,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,2,7,4,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,2,7,6,3,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,2,7,6,4,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,3,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,1,3,2,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,1,3,2,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,1,3,2,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,1,3,2,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,3,2,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,3,4,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,1,3,4,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,1,3,4,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,1,3,4,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,1,3,4,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,3,4,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,3,6,2,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,1,3,6,2,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,1,3,6,4,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,1,3,6,4,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,1,3,6,7,2,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,1,3,6,7,4,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,1,3,7,2,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,3,7,2,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,3,7,4,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,3,7,4,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,3,7,6,2,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,3,7,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,4,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,1,4,2,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,1,4,2,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,1,4,2,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,1,4,2,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,4,2,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,4,3,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,1,4,3,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,1,4,3,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,1,4,3,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,1,4,3,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,4,3,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,4,6,2,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,1,4,6,2,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,1,4,6,3,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,1,4,6,3,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,1,4,6,7,2,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,1,4,6,7,3,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,1,4,7,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,4,7,2,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,4,7,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,4,7,3,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,4,7,6,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,4,7,6,3,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,6,2,3,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,1,6,2,3,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,1,6,2,4,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,1,6,2,4,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,1,6,2,7,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,1,6,2,7,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,1,6,3,2,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,1,6,3,2,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,1,6,3,4,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,1,6,3,4,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,1,6,3,7,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,1,6,3,7,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,1,6,4,2,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,1,6,4,2,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,1,6,4,3,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,1,6,4,3,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,1,6,4,7,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,1,6,4,7,3,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,1,6,7,2,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,1,6,7,2,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,1,6,7,3,2,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,1,6,7,3,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,1,6,7,4,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,1,6,7,4,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,1,7,2,3,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,2,3,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,2,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,2,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,2,6,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,2,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,3,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,3,2,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,3,4,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,3,4,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,3,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,3,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,4,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,4,2,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,4,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,4,3,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,4,6,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,4,6,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,6,2,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,6,2,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,6,3,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,6,3,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,6,4,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,7,6,4,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,1,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,2,1,3,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,2,1,3,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,2,1,3,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,2,1,3,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,1,3,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,1,4,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,2,1,4,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,2,1,4,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,2,1,4,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,2,1,4,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,1,4,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,1,6,3,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,2,1,6,3,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,2,1,6,4,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,2,1,6,4,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,2,1,6,7,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,2,1,6,7,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,2,1,7,3,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,1,7,3,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,1,7,4,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,1,7,4,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,1,7,6,3,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,1,7,6,4,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,3,1,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,2,3,1,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,2,3,1,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,2,3,1,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,2,3,1,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,3,1,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,3,4,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,2,3,4,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,2,3,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,2,3,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,2,3,4,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,3,4,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,3,6,1,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,2,3,6,1,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,2,3,6,4,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,2,3,6,4,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,2,3,6,7,1,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,2,3,6,7,4,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,2,3,7,1,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,3,7,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,3,7,4,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,3,7,4,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,3,7,6,1,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,3,7,6,4,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,4,1,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,2,4,1,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,2,4,1,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,2,4,1,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,2,4,1,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,4,1,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,4,3,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,2,4,3,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,2,4,3,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,2,4,3,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,2,4,3,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,4,3,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,4,6,1,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,2,4,6,1,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,2,4,6,3,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,2,4,6,3,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,2,4,6,7,1,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,2,4,6,7,3,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,2,4,7,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,4,7,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,4,7,3,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,4,7,3,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,4,7,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,4,7,6,3,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,6,1,3,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,2,6,1,3,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,2,6,1,4,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,2,6,1,4,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,2,6,1,7,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,2,6,1,7,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,2,6,3,1,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,2,6,3,1,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,2,6,3,4,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,2,6,3,4,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,2,6,3,7,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,2,6,3,7,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,2,6,4,1,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,2,6,4,1,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,2,6,4,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,2,6,4,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,2,6,4,7,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,2,6,4,7,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,2,6,7,1,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,2,6,7,1,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,2,6,7,3,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,2,6,7,3,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,2,6,7,4,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,2,6,7,4,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,2,7,1,3,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,1,3,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,1,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,1,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,1,6,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,1,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,3,1,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,3,1,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,3,4,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,3,4,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,3,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,3,6,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,4,1,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,4,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,4,3,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,4,3,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,4,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,4,6,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,6,1,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,6,1,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,6,3,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,6,3,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,6,4,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,6,4,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,1,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,3,1,2,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,3,1,2,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,3,1,2,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,3,1,2,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,1,2,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,1,4,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,3,1,4,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,3,1,4,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,3,1,4,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,3,1,4,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,1,4,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,1,6,2,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,3,1,6,2,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,3,1,6,4,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,3,1,6,4,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,3,1,6,7,2,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,3,1,6,7,4,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,3,1,7,2,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,1,7,2,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,1,7,4,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,1,7,4,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,1,7,6,2,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,1,7,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,2,1,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,3,2,1,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,3,2,1,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,3,2,1,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,3,2,1,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,2,1,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,2,4,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,3,2,4,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,3,2,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,3,2,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,3,2,4,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,2,4,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,2,6,1,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,3,2,6,1,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,3,2,6,4,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,3,2,6,4,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,3,2,6,7,1,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,3,2,6,7,4,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,3,2,7,1,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,2,7,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,2,7,4,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,2,7,4,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,2,7,6,1,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,2,7,6,4,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,4,1,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,3,4,1,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,3,4,1,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,3,4,1,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,3,4,1,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,4,1,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,4,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,3,4,2,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,3,4,2,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,3,4,2,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,3,4,2,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,4,2,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,4,6,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,3,4,6,1,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,3,4,6,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,3,4,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,3,4,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,3,4,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,3,4,7,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,4,7,1,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,4,7,2,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,4,7,2,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,4,7,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,4,7,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,3,6,1,2,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,3,6,1,2,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,3,6,1,4,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,3,6,1,4,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,3,6,1,7,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,3,6,1,7,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,3,6,2,1,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,3,6,2,1,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,3,6,2,4,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,3,6,2,4,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,3,6,2,7,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,3,6,2,7,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,3,6,4,1,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,3,6,4,1,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,3,6,4,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,3,6,4,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,3,6,4,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,3,6,4,7,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,3,6,7,1,2,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,3,6,7,1,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,3,6,7,2,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,3,6,7,2,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,3,6,7,4,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,3,6,7,4,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,3,7,1,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,1,2,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,1,4,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,1,4,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,1,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,1,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,2,1,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,2,1,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,2,4,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,2,4,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,2,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,2,6,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,4,1,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,4,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,4,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,4,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,4,6,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,4,6,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,6,1,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,6,1,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,6,2,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,6,2,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,6,4,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,7,6,4,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,1,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,4,1,2,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,4,1,2,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,4,1,2,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,4,1,2,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,1,2,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,1,3,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,4,1,3,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,4,1,3,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,4,1,3,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,4,1,3,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,1,3,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,1,6,2,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,4,1,6,2,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,4,1,6,3,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,4,1,6,3,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,4,1,6,7,2,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,4,1,6,7,3,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,4,1,7,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,1,7,2,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,1,7,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,1,7,3,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,1,7,6,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,1,7,6,3,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,2,1,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,4,2,1,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,4,2,1,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,4,2,1,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,4,2,1,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,2,1,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,2,3,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,4,2,3,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,4,2,3,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,4,2,3,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,4,2,3,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,2,3,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,2,6,1,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,4,2,6,1,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,4,2,6,3,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,4,2,6,3,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,4,2,6,7,1,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,4,2,6,7,3,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,4,2,7,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,2,7,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,2,7,3,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,2,7,3,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,2,7,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,2,7,6,3,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,3,1,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,4,3,1,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,4,3,1,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,4,3,1,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,4,3,1,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,3,1,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,3,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,4,3,2,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,4,3,2,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[5,4,3,2,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,4,3,2,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,3,2,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,3,6,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,4,3,6,1,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,4,3,6,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,4,3,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,4,3,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,4,3,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,4,3,7,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,3,7,1,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,3,7,2,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,3,7,2,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,3,7,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,3,7,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,6,1,2,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,4,6,1,2,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,4,6,1,3,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,4,6,1,3,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,4,6,1,7,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,4,6,1,7,3,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,4,6,2,1,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,4,6,2,1,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,4,6,2,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,4,6,2,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,4,6,2,7,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,4,6,2,7,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,4,6,3,1,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,4,6,3,1,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,4,6,3,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,4,6,3,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,4,6,3,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,4,6,3,7,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,4,6,7,1,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,4,6,7,1,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,4,6,7,2,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,4,6,7,2,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,4,6,7,3,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,4,6,7,3,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,4,7,1,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,1,2,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,1,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,1,3,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,1,6,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,1,6,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,2,1,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,2,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,2,3,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,2,3,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,2,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,2,6,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,3,1,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,3,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,3,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,3,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,3,6,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,3,6,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,6,1,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,6,1,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,6,2,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,6,2,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,6,3,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,6,3,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,6,1,2,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,1,2,3,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,1,2,4,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,1,2,4,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,1,2,7,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,1,2,7,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,1,3,2,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,1,3,2,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,1,3,4,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,1,3,4,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,1,3,7,2,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,1,3,7,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,1,4,2,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,1,4,2,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,1,4,3,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,1,4,3,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,1,4,7,2,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,1,4,7,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,1,7,2,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,1,7,2,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,1,7,3,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,1,7,3,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,1,7,4,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,1,7,4,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,2,1,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,2,1,3,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,2,1,4,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,2,1,4,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,2,1,7,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,2,1,7,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,2,3,1,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,2,3,1,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,2,3,4,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,2,3,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,2,3,7,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,2,3,7,4,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,2,4,1,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,2,4,1,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,2,4,3,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,2,4,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,2,4,7,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,2,4,7,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,2,7,1,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,2,7,1,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,2,7,3,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,2,7,3,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,2,7,4,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,2,7,4,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,3,1,2,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,3,1,2,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,3,1,4,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,3,1,4,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,3,1,7,2,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,3,1,7,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,3,2,1,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,3,2,1,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,3,2,4,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,3,2,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,3,2,7,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,3,2,7,4,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,3,4,1,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,3,4,1,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,3,4,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,3,4,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,3,4,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,3,4,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,3,7,1,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,3,7,1,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,3,7,2,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,3,7,2,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,3,7,4,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,3,7,4,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,4,1,2,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,4,1,2,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,4,1,3,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,4,1,3,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,4,1,7,2,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,4,1,7,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,4,2,1,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,4,2,1,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,4,2,3,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,4,2,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,4,2,7,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,4,2,7,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,4,3,1,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,4,3,1,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,4,3,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,6,4,3,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,6,4,3,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,4,3,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,4,7,1,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,4,7,1,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,4,7,2,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,4,7,2,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,4,7,3,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,4,7,3,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,6,7,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,1,2,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,1,3,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,1,3,4,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,1,4,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,2,1,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,2,3,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,2,4,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,2,4,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,3,1,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,3,1,4,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,3,2,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,3,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,4,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,4,1,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,4,2,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,4,2,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,4,3,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,6,7,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,7,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,2,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,2,4,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,2,4,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,2,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,2,6,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,3,2,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,3,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,3,4,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,3,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,3,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,3,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,4,2,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,4,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,4,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,4,3,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,4,6,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,4,6,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,6,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,6,2,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,6,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,6,3,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,6,4,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,6,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,1,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,1,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,1,4,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,1,4,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,1,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,1,6,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,3,1,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,3,1,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,3,4,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,3,4,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,3,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,3,6,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,4,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,4,1,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,4,3,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,4,3,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,4,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,4,6,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,6,1,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,6,1,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,6,3,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,6,3,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,6,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,6,4,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,1,2,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,1,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,1,4,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,1,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,1,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,1,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,2,1,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,2,1,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,2,4,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,2,4,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,2,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,2,6,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,4,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,4,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,4,2,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,4,2,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,4,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,4,6,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,6,1,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,6,1,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,6,2,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,6,2,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,6,4,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,6,4,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,1,2,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,1,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,1,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,1,3,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,1,6,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,1,6,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,2,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,2,1,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,2,3,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,2,3,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,2,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,2,6,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,3,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,3,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,3,2,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,3,2,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,3,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,3,6,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,6,1,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,6,1,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,6,2,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,6,2,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,6,3,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,6,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,1,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,1,2,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,1,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,1,3,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,1,4,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,1,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,2,1,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,2,1,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,2,3,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,2,3,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,2,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,2,4,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,3,1,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,3,1,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,3,2,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,3,2,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,3,4,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,3,4,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,4,1,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,4,1,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,4,2,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,4,2,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,4,3,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,6,4,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,2,3,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,2,3,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,2,3,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,2,3,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,2,3,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,2,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,2,4,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,2,4,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,2,4,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,2,4,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,2,4,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,2,5,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,2,5,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,2,5,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,2,5,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,2,5,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,2,5,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,2,7,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,2,7,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,2,7,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,2,7,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,2,7,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,2,7,5,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,3,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,3,2,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,3,2,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,3,2,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,3,2,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,3,2,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,3,4,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,3,4,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,3,4,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,3,4,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,3,4,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,3,4,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,3,5,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,3,5,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,3,5,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,3,5,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,3,5,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,3,5,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,3,7,2,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,3,7,2,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,3,7,4,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,3,7,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,3,7,5,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,3,7,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,4,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,4,2,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,4,2,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,4,2,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,4,2,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,4,2,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,4,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,4,3,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,4,3,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,4,3,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,4,3,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,4,3,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,4,5,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,4,5,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,4,5,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,4,5,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,4,5,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,4,5,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,4,7,2,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,4,7,2,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,4,7,3,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,4,7,3,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,4,7,5,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,4,7,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,5,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,5,2,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,5,2,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,5,2,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,5,2,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,5,2,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,5,3,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,5,3,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,5,3,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,5,3,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,5,3,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,5,3,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,5,4,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,5,4,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,5,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,5,4,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,5,4,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,5,4,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,5,7,2,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,5,7,2,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,5,7,3,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,5,7,3,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,5,7,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,5,7,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,7,2,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,2,3,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,2,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,2,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,2,5,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,2,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,3,2,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,3,2,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,3,4,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,3,4,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,3,5,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,3,5,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,4,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,4,2,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,4,3,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,4,3,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,4,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,4,5,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,5,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,5,2,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,5,3,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,5,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,5,4,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,7,5,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,1,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,1,3,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,1,3,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,1,3,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,1,3,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,1,3,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,1,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,1,4,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,1,4,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,1,4,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,1,4,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,1,4,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,1,5,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,1,5,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,1,5,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,1,5,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,1,5,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,1,5,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,1,7,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,1,7,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,1,7,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,1,7,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,1,7,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,1,7,5,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,3,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,3,1,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,3,1,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,3,1,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,3,1,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,3,1,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,3,4,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,3,4,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,3,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,3,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,3,4,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,3,4,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,3,5,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,3,5,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,3,5,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,3,5,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,3,5,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,3,5,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,3,7,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,3,7,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,3,7,4,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,3,7,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,3,7,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,3,7,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,4,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,4,1,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,4,1,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,4,1,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,4,1,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,4,1,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,4,3,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,4,3,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,4,3,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,4,3,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,4,3,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,4,3,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,4,5,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,4,5,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,4,5,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,4,5,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,4,5,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,4,5,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,4,7,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,4,7,1,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,4,7,3,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,4,7,3,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,4,7,5,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,4,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,5,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,5,1,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,5,1,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,5,1,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,5,1,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,5,1,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,5,3,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,5,3,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,5,3,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,5,3,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,5,3,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,5,3,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,5,4,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,5,4,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,5,4,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,5,4,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,5,4,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,5,4,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,5,7,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,5,7,1,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,5,7,3,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,5,7,3,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,5,7,4,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,5,7,4,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,7,1,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,1,3,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,1,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,1,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,1,5,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,1,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,3,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,3,1,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,3,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,3,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,3,5,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,3,5,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,4,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,4,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,4,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,4,3,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,4,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,4,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,5,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,5,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,5,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,5,3,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,5,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,7,5,4,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,1,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,1,2,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,1,2,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,1,2,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,1,2,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,1,2,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,1,4,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,1,4,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,1,4,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,1,4,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,1,4,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,1,4,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,1,5,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,1,5,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,1,5,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,1,5,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,1,5,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,1,5,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,1,7,2,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,1,7,2,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,1,7,4,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,1,7,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,1,7,5,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,1,7,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,2,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,2,1,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,2,1,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,2,1,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,2,1,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,2,1,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,2,4,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,2,4,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,2,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,2,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,2,4,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,2,4,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,2,5,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,2,5,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,2,5,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,2,5,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,2,5,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,2,5,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,2,7,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,2,7,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,2,7,4,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,2,7,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,2,7,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,2,7,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,4,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,4,1,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,4,1,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,4,1,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,4,1,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,4,1,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,4,2,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,4,2,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,4,2,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,4,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,4,2,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,4,2,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,4,5,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,4,5,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,4,5,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,4,5,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,4,5,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,4,5,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,4,7,1,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,4,7,1,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,4,7,2,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,4,7,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,4,7,5,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,4,7,5,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,5,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,5,1,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,5,1,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,5,1,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,5,1,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,5,1,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,5,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,5,2,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,5,2,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,5,2,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,5,2,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,5,2,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,5,4,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,5,4,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,5,4,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,5,4,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,5,4,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,5,4,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,5,7,1,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,5,7,1,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,5,7,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,5,7,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,5,7,4,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,5,7,4,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,7,1,2,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,1,2,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,1,4,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,1,4,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,1,5,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,1,5,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,2,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,2,1,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,2,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,2,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,2,5,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,2,5,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,4,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,4,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,4,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,4,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,4,5,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,4,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,5,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,5,1,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,5,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,5,2,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,5,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,5,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,1,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,1,2,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,1,2,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,1,2,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,1,2,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,1,2,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,1,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,1,3,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,1,3,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,1,3,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,1,3,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,1,3,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,1,5,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,1,5,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,1,5,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,1,5,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,1,5,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,1,5,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,1,7,2,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,1,7,2,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,1,7,3,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,1,7,3,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,1,7,5,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,1,7,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,2,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,2,1,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,2,1,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,2,1,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,2,1,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,2,1,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,2,3,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,2,3,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,2,3,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,2,3,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,2,3,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,2,3,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,2,5,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,2,5,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,2,5,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,2,5,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,2,5,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,2,5,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,2,7,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,2,7,1,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,2,7,3,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,2,7,3,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,2,7,5,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,2,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,3,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,3,1,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,3,1,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,3,1,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,3,1,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,3,1,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,3,2,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,3,2,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,3,2,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,3,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,3,2,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,3,2,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,3,5,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,3,5,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,3,5,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,3,5,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,3,5,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,3,5,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,3,7,1,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,3,7,1,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,3,7,2,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,3,7,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,3,7,5,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,3,7,5,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,5,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,5,1,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,5,1,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,5,1,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,5,1,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,5,1,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,5,2,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,5,2,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,5,2,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,5,2,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,5,2,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,5,2,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,5,3,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,5,3,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,5,3,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,4,5,3,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,5,3,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,5,3,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,5,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,5,7,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,5,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,5,7,2,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,5,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,5,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,7,1,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,1,2,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,1,3,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,1,3,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,1,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,1,5,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,2,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,2,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,2,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,2,3,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,2,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,2,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,3,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,3,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,3,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,3,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,3,5,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,3,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,5,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,5,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,5,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,5,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,5,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,5,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,1,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,1,2,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,1,2,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,1,2,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,1,2,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,1,2,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,1,3,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,1,3,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,1,3,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,1,3,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,1,3,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,1,3,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,1,4,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,1,4,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,1,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,1,4,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,1,4,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,1,4,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,1,7,2,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,1,7,2,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,1,7,3,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,1,7,3,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,1,7,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,1,7,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,2,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,2,1,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,2,1,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,2,1,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,2,1,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,2,1,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,2,3,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,2,3,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,2,3,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,2,3,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,2,3,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,2,3,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,2,4,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,2,4,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,2,4,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,2,4,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,2,4,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,2,4,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,2,7,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,2,7,1,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,2,7,3,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,2,7,3,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,2,7,4,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,2,7,4,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,3,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,3,1,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,3,1,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,3,1,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,3,1,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,3,1,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,3,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,3,2,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,3,2,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,3,2,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,3,2,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,3,2,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,3,4,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,3,4,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,3,4,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,3,4,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,3,4,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,3,4,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,3,7,1,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,3,7,1,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,3,7,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,3,7,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,3,7,4,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,3,7,4,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,4,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,4,1,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,4,1,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,4,1,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,4,1,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,4,1,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,4,2,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,4,2,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,4,2,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,4,2,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,4,2,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,4,2,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,4,3,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,4,3,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,4,3,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,4,3,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,4,3,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,4,3,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,4,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,4,7,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,4,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,4,7,2,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,4,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,4,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,7,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,1,2,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,1,3,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,1,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,1,4,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,1,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,2,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,2,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,2,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,2,3,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,2,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,2,4,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,3,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,3,1,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,3,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,3,2,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,3,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,3,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,4,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,4,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,4,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,4,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,4,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,7,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,2,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,2,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,2,4,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,2,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,2,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,3,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,3,2,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,3,4,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,3,4,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,3,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,3,5,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,4,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,4,2,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,4,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,4,3,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,4,5,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,4,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,5,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,5,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,5,3,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,5,3,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,5,4,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,1,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,1,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,1,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,1,4,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,1,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,1,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,3,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,3,1,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,3,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,3,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,3,5,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,3,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,4,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,4,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,4,3,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,4,3,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,4,5,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,4,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,5,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,5,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,5,3,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,5,3,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,5,4,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,5,4,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,1,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,1,2,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,1,4,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,1,4,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,1,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,1,5,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,2,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,2,1,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,2,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,2,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,2,5,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,2,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,4,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,4,1,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,4,2,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,4,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,4,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,4,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,5,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,5,1,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,5,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,5,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,5,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,5,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,1,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,1,2,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,1,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,1,3,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,1,5,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,1,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,2,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,2,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,2,3,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,2,3,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,2,5,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,2,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,3,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,3,1,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,3,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,3,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,3,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,5,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,5,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,5,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,5,2,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,5,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,4,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,1,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,1,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,1,3,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,1,3,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,1,4,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,1,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,2,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,2,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,2,3,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,2,3,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,2,4,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,2,4,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,3,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,3,1,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,3,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,3,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,3,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,3,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,4,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,4,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,4,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,4,2,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,4,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,4,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,5,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,3,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,3,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,5,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,6,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,4,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,6,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,4,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,4,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,5,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,5,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,3,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,3,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,5,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,2,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,2,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,3,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,4,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,3,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,3,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,5,6,8,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,7,8,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,4,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,7,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,5,4,8,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,5,6,4,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,7,4,8,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,6,7,4,8,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[7,6,4,5,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,4,5,8,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,5,4,6,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,5,6,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,4,7,8,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,6,4,7,8,3,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[6,4,5,7,8,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,4,6,7,8,3,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,8,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[8,7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,5,6,7,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,3,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,5,7,8,3,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,3,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,4,3,5,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,3,4,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,3,4,5,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,5,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,6,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,6,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,6,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,7,5,4,3,8,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[7,5,6,4,3,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,6,7,4,3,8,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[7,6,4,5,3,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,7,4,5,3,8,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[7,5,4,6,3,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,4,5,6,3,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,5,4,7,3,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,4,5,7,3,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,4,6,7,3,8,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[4,5,6,7,3,8,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[7,6,5,3,4,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,4,3,5,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,3,4,5,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,4,3,6,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,3,4,6,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,4,5,6,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,5,4,3,7,8,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,5,3,4,7,8,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,3,4,5,7,8,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,4,3,6,7,8,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[5,3,4,6,7,8,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[4,3,5,6,7,8,2,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[3,4,5,6,7,8,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,4,2,3,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,5,6,8,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,6,7,8,4,2,3,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,4,5,2,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,6,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,6,2,3,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,8,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,6,4,8,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,7,4,8,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,6,4,5,8,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,4,5,8,2,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[4,5,6,7,8,2,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,5,3,2,4,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,3,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,6,7,8,3,2,4,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,5,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,2,3,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,5,2,3,4,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,6,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,2,3,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,2,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,2,3,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,5,7,8,2,3,4,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,2,3,4,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,4,3,2,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,3,4,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,4,2,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,3,4,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,4,2,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,3,4,2,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[7,6,8,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,4,2,3,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,3,2,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,2,4,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,3,2,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,2,4,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,2,3,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,3,4,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,2,3,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,3,4,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,2,3,4,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,3,5,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,5,2,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,4,2,5,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,2,3,5,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,2,3,4,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,3,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,6,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,6,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,6,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,2,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,2,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,3,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,4,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,4,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,2,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,5,4,3,2,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,5,6,4,3,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,5,7,4,3,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[7,6,4,5,3,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,4,5,3,2,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,4,5,6,3,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,4,5,7,3,2,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[4,5,6,7,3,2,8,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[7,6,5,3,4,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,6,3,4,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,5,7,3,4,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[7,6,4,3,5,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,3,4,5,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,4,3,6,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,5,3,6,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,3,4,6,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,3,4,5,6,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,5,4,3,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,4,5,3,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[5,4,6,3,7,2,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,5,6,3,7,2,8,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[6,5,3,4,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[5,6,3,4,7,2,8,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[6,4,3,5,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,3,4,5,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[5,4,3,6,7,2,8,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[4,5,3,6,7,2,8,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[3,4,5,6,7,2,8,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[7,6,5,4,2,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,5,4,2,3,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,5,6,4,2,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,5,7,4,2,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,6,7,4,2,3,8,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[7,6,4,5,2,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,4,5,2,3,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,5,4,6,2,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,5,6,2,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,5,4,7,2,3,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,6,4,7,2,3,8,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[6,4,5,7,2,3,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,4,6,7,2,3,8,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[4,5,6,7,2,3,8,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[7,6,5,3,2,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,5,3,2,4,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,5,7,3,2,4,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[7,6,5,2,3,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,6,2,3,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,6,7,2,3,4,8,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[6,7,4,3,2,5,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,6,4,2,3,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,3,2,4,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,3,2,4,5,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,6,2,3,4,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,2,3,4,5,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,5,4,3,2,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,3,5,2,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,4,2,3,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,5,2,3,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,3,2,4,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,2,3,4,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,3,2,5,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,2,3,5,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,3,2,4,5,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,2,3,4,5,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,5,4,3,2,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,4,6,3,2,7,8,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[4,5,6,3,2,7,8,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[6,5,3,4,2,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,3,4,5,2,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,4,3,6,2,7,8,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[4,3,5,6,2,7,8,1]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[3,4,5,6,2,7,8,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[6,5,4,2,3,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,6,4,2,3,7,8,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[6,4,5,2,3,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,4,6,2,3,7,8,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[4,5,6,2,3,7,8,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[6,5,3,2,4,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,5,2,3,4,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,2,3,4,5,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,4,3,2,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[4,5,3,2,6,7,8,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[5,3,4,2,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[4,3,5,2,6,7,8,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[3,4,5,2,6,7,8,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[5,4,2,3,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[4,5,2,3,6,7,8,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[5,3,2,4,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[5,2,3,4,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[4,3,2,5,6,7,8,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,4,2,5,6,7,8,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[4,2,3,5,6,7,8,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,2,4,5,6,7,8,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,5,6,7,8,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,5,4,3,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,7,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,4,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,5,6,8,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,7,8,4,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,4,3,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,4,5,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,5,3,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,6,3,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,5,6,4,7,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,7,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,7,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,8,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,6,4,8,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,7,4,8,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,6,4,5,8,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,4,5,8,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,5,4,7,8,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,6,4,7,8,3,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[5,4,6,7,8,3,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,8,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[8,7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,6,8,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,5,3,4,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,3,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,5,6,8,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,7,8,3,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[6,7,8,4,3,5,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,3,4,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,4,5,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,3,4,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,4,5,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[7,8,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,5,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,3,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,4,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,6,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,6,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,6,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,6,4,3,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,5,7,4,3,8,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[5,6,7,4,3,8,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[6,7,4,5,3,8,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[7,5,4,6,3,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,5,4,7,3,8,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,6,4,7,3,8,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[6,4,5,7,3,8,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,4,6,7,3,8,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[4,5,6,7,3,8,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[7,6,5,3,4,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,6,3,4,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,4,3,5,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,3,4,5,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,4,3,6,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,4,5,3,6,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,3,4,6,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,4,5,6,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,5,4,3,7,8,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,6,4,3,7,8,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[5,4,6,3,7,8,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[4,5,6,3,7,8,1,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[5,6,3,4,7,8,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[6,4,3,5,7,8,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,3,4,5,7,8,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,4,3,6,7,8,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[4,5,3,6,7,8,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[5,3,4,6,7,8,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[4,3,5,6,7,8,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[3,4,5,6,7,8,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,5,4,2,1,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,6,5,8,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,4,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,5,6,8,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,7,8,4,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,4,2,1,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,4,5,6,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,7,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,8,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,5,4,8,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,5,6,4,8,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,7,4,8,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,6,7,4,8,2,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[7,6,4,5,8,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,4,6,8,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,5,6,8,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,4,6,7,8,2,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,8,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[8,7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,6,8,5,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,5,4,1,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[7,8,5,6,4,1,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,7,4,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,4,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,4,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,5,6,8,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,7,8,4,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,4,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,4,5,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,4,5,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,5,1,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,4,6,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,6,1,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,4,7,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,7,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,7,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,7,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,7,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,5,4,8,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,5,6,4,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,7,4,8,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,6,7,4,8,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[7,6,4,5,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,4,5,8,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,5,4,6,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,5,6,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,4,7,8,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,6,4,7,8,1,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[6,4,5,7,8,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,4,6,7,8,1,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,8,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,5,3,2,1,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,3,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,5,6,8,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,7,8,3,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,5,2,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,2,3,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,5,2,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,2,3,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,5,2,3,1,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,6,2,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,2,3,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,7,2,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,2,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,2,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,2,3,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,5,6,8,2,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,7,8,2,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,7,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,3,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,5,6,8,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,7,8,3,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,3,1,2,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,6,8,5,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,5,2,1,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,7,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,2,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,5,6,8,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,7,8,2,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,5,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,5,1,2,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,7,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,5,8,1,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,5,6,8,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,7,8,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,3,4,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,4,2,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,7,8,3,4,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,4,2,3,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,3,2,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,2,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,2,4,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,2,3,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,3,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,3,4,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,2,3,4,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,3,1,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,3,4,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,4,1,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,3,4,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,4,1,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,4,2,1,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,4,1,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,1,2,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,6,8,4,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,4,1,2,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,3,2,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,2,1,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,3,2,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,2,1,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,3,2,1,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,2,3,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,3,1,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,2,3,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,3,1,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,2,3,1,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,3,1,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,3,1,2,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,3,1,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,1,2,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,3,1,2,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,2,1,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,1,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,2,1,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,1,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,7,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,5,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,5,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,5,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,5,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,5,2,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,2,3,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,2,3,4,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,3,2,5,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,2,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,3,4,2,5,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,2,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,2,3,4,5,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,3,4,5,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,5,1,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,4,1,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,1,2,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,5,1,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,5,1,2,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,2,3,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,2,1,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,2,1,3,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,3,4,2,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,2,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,2,3,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,3,2,4,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,2,3,4,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,3,1,2,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,3,4,1,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,1,2,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,2,1,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,2,1,3,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,1,2,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,2,3,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,2,3,1,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,1,2,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,6,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,6,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,3,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,3,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,4,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,2,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,2,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,3,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,3,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,4,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,4,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,2,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,4,5,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,6,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,6,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,6,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,6,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,1,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,1,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,1,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,1,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,3,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,3,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,1,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,1,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,2,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,2,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,4,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,4,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,4,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,4,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,2,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,1,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,3,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,2,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,2,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,2,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,2,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,3,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,4,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,1,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,1,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,2,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,2,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,1,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,1,2,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,3,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,3,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,2,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,2,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,3,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,3,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,5,4,3,2,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,5,6,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,7,4,3,2,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[5,6,7,4,3,2,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[7,6,4,5,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,4,5,3,2,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,5,4,6,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,6,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,4,7,3,2,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[5,6,4,7,3,2,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[5,4,6,7,3,2,1,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[4,5,6,7,3,2,1,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[7,6,5,3,4,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,5,3,4,2,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,5,6,3,4,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,7,3,4,2,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[5,6,7,3,4,2,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[7,6,4,3,5,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,4,3,5,2,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,3,4,5,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,4,3,6,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,3,6,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,4,5,6,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,4,3,7,2,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[5,6,4,3,7,2,1,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[5,4,6,3,7,2,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[5,4,3,6,7,2,1,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[3,4,5,6,7,2,1,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[7,6,5,4,2,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,5,4,2,3,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,5,6,4,2,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,6,7,4,2,3,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[7,6,4,5,2,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,4,5,2,3,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,5,4,6,2,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,6,2,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,4,7,2,3,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[5,6,4,7,2,3,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[5,4,6,7,2,3,1,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[4,5,6,7,2,3,1,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[7,6,5,3,2,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,7,3,2,4,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[5,6,7,3,2,4,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[7,6,5,2,3,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,5,2,3,4,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,5,6,2,3,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,7,2,3,4,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[5,6,7,2,3,4,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[7,6,4,3,2,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,4,3,2,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,7,3,4,2,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,4,2,3,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,4,2,3,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,3,2,4,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,3,2,4,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,2,3,4,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,2,3,4,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,5,4,3,2,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,3,2,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,3,4,2,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,3,5,2,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,2,3,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,3,2,4,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,2,3,5,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,3,4,5,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,4,3,2,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[5,6,4,3,2,7,1,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[5,4,6,3,2,7,1,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[5,6,3,4,2,7,1,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[6,3,4,5,2,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[5,4,3,6,2,7,1,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[4,5,3,6,2,7,1,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[5,3,4,6,2,7,1,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[4,3,5,6,2,7,1,8]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[3,4,5,6,2,7,1,8]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[5,4,6,2,3,7,1,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[6,5,3,2,4,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,4,2,3,5,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,3,2,4,5,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,2,3,4,5,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[5,4,3,2,6,7,1,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[5,4,2,3,6,7,1,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[4,5,2,3,6,7,1,8]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[5,2,3,4,6,7,1,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[4,3,2,5,6,7,1,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[3,4,2,5,6,7,1,8]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[4,2,3,5,6,7,1,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[3,2,4,5,6,7,1,8]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[2,3,4,5,6,7,1,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[7,6,5,4,3,1,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,5,4,3,1,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,5,6,4,3,1,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,4,5,3,1,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,6,3,1,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,4,6,7,3,1,2,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[4,5,6,7,3,1,2,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[7,6,5,3,4,1,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,6,3,4,1,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,7,3,4,1,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,7,3,4,5,1,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,5,3,4,6,1,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,4,3,7,1,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,4,5,3,7,1,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[5,6,3,4,7,1,2,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[6,4,3,5,7,1,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,3,4,5,7,1,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[4,3,5,6,7,1,2,8]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[3,4,5,6,7,1,2,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[7,6,5,4,2,1,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,7,4,2,1,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,6,4,5,2,1,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,4,6,2,1,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,6,2,1,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,4,6,7,2,1,3,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[4,5,6,7,2,1,3,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[7,6,5,4,1,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,6,4,1,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,6,7,4,1,2,3,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[7,6,4,5,1,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,4,6,1,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,6,1,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,6,4,7,1,2,3,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[5,4,6,7,1,2,3,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[4,5,6,7,1,2,3,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[7,6,5,3,2,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,5,2,3,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,5,2,3,1,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,5,6,2,3,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,7,2,3,1,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[5,6,7,2,3,1,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[7,5,6,3,1,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,6,7,3,1,2,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[7,6,5,2,1,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,5,2,1,3,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,5,6,2,1,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,6,7,2,1,3,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[7,6,5,1,2,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,5,1,2,3,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,5,6,1,2,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,7,1,2,3,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[5,6,7,1,2,3,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[7,6,4,3,2,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,4,3,2,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,3,4,2,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,3,4,2,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,4,2,3,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,4,2,3,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,3,2,4,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,3,2,4,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,2,3,4,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,2,3,4,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,4,3,1,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,3,4,1,2,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,4,2,1,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,3,2,1,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,3,2,1,4,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,2,3,1,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,2,3,1,4,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,7,3,1,2,4,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,1,2,3,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,1,2,3,4,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,5,4,3,2,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,3,2,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,3,5,2,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,4,5,2,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,4,2,3,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,3,2,4,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,2,3,4,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,2,3,5,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,3,4,5,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,4,3,1,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,3,4,1,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,2,1,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,1,2,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,3,2,1,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,2,3,1,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,3,1,2,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,1,2,3,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,3,2,1,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,3,4,1,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,3,1,2,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,4,1,2,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,1,2,3,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,2,1,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,3,1,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,1,2,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,1,3,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,2,3,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,4,3,2,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,6,4,3,2,1,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[5,4,6,3,2,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[4,5,6,3,2,1,7,8]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[6,5,3,4,2,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,6,3,4,2,1,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[6,3,4,5,2,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,4,3,6,2,1,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[3,4,5,6,2,1,7,8]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[5,4,6,2,3,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[5,6,3,2,4,1,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[6,5,2,3,4,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,6,2,3,4,1,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[6,4,3,2,5,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,2,3,4,5,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,4,3,2,6,1,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[4,5,3,2,6,1,7,8]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[4,3,5,2,6,1,7,8]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[3,4,5,2,6,1,7,8]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[5,3,2,4,6,1,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[5,2,3,4,6,1,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[4,3,2,5,6,1,7,8]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[3,4,2,5,6,1,7,8]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[4,2,3,5,6,1,7,8]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[3,2,4,5,6,1,7,8]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[2,3,4,5,6,1,7,8]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[6,5,4,3,1,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,6,4,3,1,2,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[6,4,5,3,1,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,4,6,3,1,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[5,6,3,4,1,2,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[6,4,3,5,1,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,4,3,6,1,2,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[4,3,5,6,1,2,7,8]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[3,4,5,6,1,2,7,8]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[6,5,4,2,1,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,6,4,2,1,3,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[6,4,5,2,1,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,4,6,2,1,3,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[4,5,6,2,1,3,7,8]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[6,5,4,1,2,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[4,5,6,1,2,3,7,8]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[6,5,3,2,1,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,6,3,2,1,4,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[5,6,2,1,3,4,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[6,5,1,2,3,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,4,3,2,1,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,3,4,2,1,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,4,3,1,2,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,4,2,1,3,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,4,1,2,3,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,3,2,1,4,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,2,3,1,4,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,3,1,2,4,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,2,1,3,4,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,1,2,3,4,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,4,3,2,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[4,5,3,2,1,6,7,8]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[5,3,4,2,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[4,3,5,2,1,6,7,8]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[3,4,5,2,1,6,7,8]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[5,4,2,3,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[4,5,2,3,1,6,7,8]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[5,3,2,4,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[5,2,3,4,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[4,3,2,5,1,6,7,8]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[3,4,2,5,1,6,7,8]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[4,2,3,5,1,6,7,8]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[3,2,4,5,1,6,7,8]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[2,3,4,5,1,6,7,8]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[5,4,3,1,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[5,3,4,1,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[4,3,5,1,2,6,7,8]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[3,4,5,1,2,6,7,8]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[5,4,2,1,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[4,5,2,1,3,6,7,8]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[5,4,1,2,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[4,5,1,2,3,6,7,8]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[5,3,2,1,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[5,2,3,1,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[5,3,1,2,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[5,2,1,3,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[5,1,2,3,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[4,3,2,1,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[3,4,2,1,5,6,7,8]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[4,2,3,1,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[3,2,4,1,5,6,7,8]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[2,3,4,1,5,6,7,8]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[4,3,1,2,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[3,4,1,2,5,6,7,8]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[4,2,1,3,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[4,1,2,3,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[3,2,1,4,5,6,7,8]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[2,3,1,4,5,6,7,8]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[3,1,2,4,5,6,7,8]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,4,5,6,7,8]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,3,4,5,6,7,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[6,8,7,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,7,6,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,7,8,6,4,3,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[6,5,8,7,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,6,8,7,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,7,6,8,4,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,8,7,6,5,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,8,6,5,3,2,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,6,8,7,5,3,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,7,6,8,5,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,6,7,8,5,3,2,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[4,5,8,7,6,3,2,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,7,8,6,3,2,1]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[6,5,4,8,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,6,5,8,7,3,2,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,5,6,8,7,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[5,7,6,4,8,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[4,7,6,5,8,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,6,7,5,8,3,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[5,4,7,6,8,3,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[4,5,7,6,8,3,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[4,6,5,7,8,3,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[3,8,7,6,5,4,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,8,6,5,4,2,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,6,8,7,5,4,2,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,7,6,8,5,4,2,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,5,8,7,6,4,2,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,7,8,6,4,2,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[3,5,6,8,7,4,2,1]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[3,7,6,5,8,4,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,6,7,5,8,4,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[3,5,7,6,8,4,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[3,5,6,7,8,4,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[4,3,8,7,6,5,2,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,6,7,8,5,2,1]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[3,4,8,7,6,5,2,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,6,7,8,5,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[5,4,3,8,7,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,4,3,7,8,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[4,5,3,7,8,6,2,1]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[3,5,4,7,8,6,2,1]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[4,3,5,7,8,6,2,1]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[3,4,5,8,7,6,2,1]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,5,7,8,6,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[6,5,4,3,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,6,4,3,8,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[4,5,6,3,8,7,2,1]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[4,3,6,5,8,7,2,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[5,4,3,6,8,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[4,5,3,6,8,7,2,1]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[4,3,5,6,8,7,2,1]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[3,4,5,6,8,7,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[5,7,6,4,3,8,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[4,7,6,5,3,8,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[5,4,7,6,3,8,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[3,7,6,5,4,8,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,5,7,6,4,8,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[3,5,6,7,4,8,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[4,3,7,6,5,8,2,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[3,4,7,6,5,8,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[3,4,6,7,5,8,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[4,5,3,7,6,8,2,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[3,5,4,7,6,8,2,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[4,3,5,7,6,8,2,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[3,4,5,7,6,8,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[3,6,5,4,7,8,2,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[3,5,6,4,7,8,2,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[4,3,6,5,7,8,2,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[3,4,6,5,7,8,2,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[3,5,4,6,7,8,2,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[2,8,7,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,8,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,6,8,7,5,4,3,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,7,6,8,5,4,3,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,6,7,8,5,4,3,1]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[2,5,8,7,6,4,3,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,6,7,5,8,4,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[2,6,5,7,8,4,3,1]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[2,5,6,7,8,4,3,1]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[2,4,8,7,6,5,3,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,7,8,6,5,3,1]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[2,4,6,8,7,5,3,1]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,7,8,5,3,1]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[2,5,4,8,7,6,3,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,5,4,7,8,6,3,1]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[2,4,5,7,8,6,3,1]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[2,6,5,4,8,7,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,5,6,4,8,7,3,1]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[2,4,6,5,8,7,3,1]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,5,6,8,7,3,1]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[2,7,6,5,4,8,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,6,7,5,4,8,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[2,5,6,7,4,8,3,1]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[2,4,7,6,5,8,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[2,4,6,7,5,8,3,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[2,5,4,7,6,8,3,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[2,6,5,4,7,8,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[2,5,6,4,7,8,3,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[2,4,6,5,7,8,3,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[2,5,4,6,7,8,3,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[2,4,5,6,7,8,3,1]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[3,2,8,7,6,5,4,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,8,7,5,4,1]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[3,2,5,7,8,6,4,1]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[3,2,6,7,5,8,4,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[3,2,5,7,6,8,4,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[3,2,5,6,7,8,4,1]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[2,3,8,7,6,5,4,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,7,8,5,4,1]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[2,3,5,8,7,6,4,1]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,3,5,7,8,6,4,1]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[2,3,6,5,8,7,4,1]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,3,5,6,8,7,4,1]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[2,3,7,6,5,8,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,3,5,7,6,8,4,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[2,3,5,6,7,8,4,1]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[4,3,2,8,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,2,7,8,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[4,3,2,6,8,7,5,1]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[3,4,2,8,7,6,5,1]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,4,2,7,8,6,5,1]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[2,4,3,8,7,6,5,1]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,4,3,6,8,7,5,1]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[2,4,3,6,7,8,5,1]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[3,2,4,8,7,6,5,1]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,2,4,7,8,6,5,1]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[2,3,4,8,7,6,5,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,6,8,7,5,1]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[2,3,4,7,6,8,5,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[2,3,4,6,7,8,5,1]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[5,4,3,2,8,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,4,3,2,7,8,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[4,5,3,2,8,7,6,1]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[3,5,4,2,7,8,6,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[4,3,5,2,8,7,6,1]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[3,4,5,2,7,8,6,1]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[2,5,4,3,8,7,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,5,4,3,7,8,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[2,4,5,3,8,7,6,1]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[2,4,5,3,7,8,6,1]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[3,2,5,4,7,8,6,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[2,3,5,4,8,7,6,1]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,3,5,4,7,8,6,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[4,3,2,5,8,7,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[4,3,2,5,7,8,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[3,4,2,5,8,7,6,1]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[3,4,2,5,7,8,6,1]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[2,4,3,5,8,7,6,1]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,2,4,5,7,8,6,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[2,3,4,5,8,7,6,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,5,7,8,6,1]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[6,5,4,3,2,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,6,5,3,2,8,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[5,4,6,3,2,8,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[4,5,6,3,2,8,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[3,6,5,4,2,8,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[3,5,6,4,2,8,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[4,3,6,5,2,8,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[5,4,3,6,2,8,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[4,5,3,6,2,8,7,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[2,6,5,4,3,8,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,4,6,5,3,8,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[2,4,5,6,3,8,7,1]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[3,2,6,5,4,8,7,1]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[2,3,5,6,4,8,7,1]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[4,3,2,6,5,8,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[3,4,2,6,5,8,7,1]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[2,4,3,6,5,8,7,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,2,4,6,5,8,7,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[2,3,4,6,5,8,7,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[5,4,3,2,6,8,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[4,5,3,2,6,8,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[2,5,4,3,6,8,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[2,4,5,3,6,8,7,1]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[3,2,5,4,6,8,7,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[4,3,2,5,6,8,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[3,4,2,5,6,8,7,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[2,4,3,5,6,8,7,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[3,2,4,5,6,8,7,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[2,3,4,5,6,8,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[5,7,6,4,3,2,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[4,7,6,5,3,2,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[4,6,7,5,3,2,8,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[4,6,5,7,3,2,8,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[3,5,7,6,4,2,8,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,5,6,7,4,2,8,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[4,3,7,6,5,2,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,3,6,7,5,2,8,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[3,4,7,6,5,2,8,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[3,4,6,7,5,2,8,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[5,4,3,7,6,2,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[4,5,3,7,6,2,8,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[3,5,4,7,6,2,8,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[3,4,5,7,6,2,8,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[4,6,5,3,7,2,8,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[3,6,5,4,7,2,8,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[3,5,6,4,7,2,8,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[4,3,6,5,7,2,8,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,4,6,5,7,2,8,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[3,5,4,6,7,2,8,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[2,7,6,5,4,3,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,6,5,7,4,3,8,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[2,5,6,7,4,3,8,1]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[2,4,6,7,5,3,8,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[2,5,4,7,6,3,8,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[2,4,6,5,7,3,8,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[2,5,4,6,7,3,8,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[2,4,5,6,7,3,8,1]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[3,2,7,6,5,4,8,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[3,2,6,7,5,4,8,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[3,2,5,7,6,4,8,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[3,2,6,5,7,4,8,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,2,5,6,7,4,8,1]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[2,3,7,6,5,4,8,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,3,5,7,6,4,8,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[2,3,5,6,7,4,8,1]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[4,3,2,7,6,5,8,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[4,3,2,6,7,5,8,1]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[3,4,2,7,6,5,8,1]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[3,4,2,6,7,5,8,1]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[2,4,3,7,6,5,8,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[2,4,3,6,7,5,8,1]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[3,2,4,7,6,5,8,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,4,7,6,5,8,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,4,6,7,5,8,1]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[5,4,3,2,7,6,8,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[3,5,4,2,7,6,8,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[4,3,5,2,7,6,8,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[3,4,5,2,7,6,8,1]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[2,5,4,3,7,6,8,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[3,2,5,4,7,6,8,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,3,5,4,7,6,8,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[4,3,2,5,7,6,8,1]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[3,4,2,5,7,6,8,1]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[2,4,3,5,7,6,8,1]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[3,2,4,5,7,6,8,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[2,3,4,5,7,6,8,1]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[3,6,5,4,2,7,8,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[3,5,6,4,2,7,8,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[3,4,6,5,2,7,8,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[3,5,4,6,2,7,8,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[2,6,5,4,3,7,8,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[2,5,6,4,3,7,8,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[2,4,6,5,3,7,8,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[2,5,4,6,3,7,8,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[2,4,5,6,3,7,8,1]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[3,2,5,6,4,7,8,1]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[2,3,6,5,4,7,8,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[2,3,5,6,4,7,8,1]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[4,3,2,6,5,7,8,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[3,4,2,6,5,7,8,1]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[2,4,3,6,5,7,8,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[2,3,4,6,5,7,8,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[3,5,4,2,6,7,8,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[2,5,4,3,6,7,8,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[2,4,5,3,6,7,8,1]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[3,2,5,4,6,7,8,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[2,3,5,4,6,7,8,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[2,4,3,5,6,7,8,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,8,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,6,8,7,5,4,3,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,7,6,8,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,6,7,8,5,4,3,2]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,5,8,7,6,4,3,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,6,5,8,7,4,3,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,7,6,5,8,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,6,7,5,8,4,3,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,5,7,6,8,4,3,2]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,6,5,7,8,4,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,5,6,7,8,4,3,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,4,8,7,6,5,3,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,4,7,8,6,5,3,2]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,4,6,8,7,5,3,2]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,4,6,7,8,5,3,2]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,5,4,7,8,6,3,2]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,4,5,8,7,6,3,2]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,4,5,7,8,6,3,2]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,6,5,4,8,7,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,4,6,5,8,7,3,2]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,5,4,6,8,7,3,2]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,7,6,5,4,8,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,4,7,6,5,8,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,4,6,7,5,8,3,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,6,5,4,7,8,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,5,4,6,7,8,3,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,4,5,6,7,8,3,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,3,8,7,6,5,4,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,7,8,6,5,4,2]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,3,6,8,7,5,4,2]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,3,6,7,8,5,4,2]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,3,5,8,7,6,4,2]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,3,5,7,8,6,4,2]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,3,5,6,8,7,4,2]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,3,6,7,5,8,4,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,3,5,7,6,8,4,2]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,3,6,5,7,8,4,2]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,3,5,6,7,8,4,2]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,4,3,8,7,6,5,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,4,3,7,8,6,5,2]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,4,3,6,8,7,5,2]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,4,3,7,6,8,5,2]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,4,3,6,7,8,5,2]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,3,4,8,7,6,5,2]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,3,4,7,6,8,5,2]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,3,4,6,7,8,5,2]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,5,4,3,8,7,6,2]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,4,5,3,8,7,6,2]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,4,5,3,7,8,6,2]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,3,5,4,8,7,6,2]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,3,5,4,7,8,6,2]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,4,3,5,8,7,6,2]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,4,3,5,7,8,6,2]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,3,4,5,8,7,6,2]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,3,4,5,7,8,6,2]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,6,5,4,3,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,5,6,4,3,8,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,4,6,5,3,8,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,4,5,6,3,8,7,2]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,3,6,5,4,8,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,4,3,6,5,8,7,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,5,4,3,6,8,7,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,4,5,3,6,8,7,2]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,3,4,5,6,8,7,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,7,6,5,4,3,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,6,7,5,4,3,8,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,6,5,7,4,3,8,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,4,6,7,5,3,8,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,5,6,4,7,3,8,2]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,4,6,5,7,3,8,2]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,5,4,6,7,3,8,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,4,5,6,7,3,8,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,3,5,7,6,4,8,2]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,3,6,5,7,4,8,2]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,3,5,6,7,4,8,2]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,4,3,6,7,5,8,2]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,3,4,7,6,5,8,2]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,3,4,6,7,5,8,2]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,3,5,4,7,6,8,2]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,3,4,5,7,6,8,2]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,6,5,4,3,7,8,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,5,4,6,3,7,8,2]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,3,5,6,4,7,8,2]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,4,3,6,5,7,8,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,3,4,6,5,7,8,2]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,5,4,3,6,7,8,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,4,5,3,6,7,8,2]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,3,5,4,6,7,8,2]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,4,3,5,6,7,8,2]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,3,4,5,6,7,8,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,8,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,7,8,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[2,1,6,8,7,5,4,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,7,6,8,5,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[2,1,6,7,8,5,4,3]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,5,8,7,6,4,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,1,5,7,8,6,4,3]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,6,5,8,7,4,3]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[2,1,5,6,8,7,4,3]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[2,1,7,6,5,8,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,1,6,7,5,8,4,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[2,1,5,7,6,8,4,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[2,1,6,5,7,8,4,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[2,1,5,6,7,8,4,3]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,4,8,7,6,5,3]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,4,7,8,6,5,3]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[2,1,4,6,8,7,5,3]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,4,6,7,8,5,3]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,5,4,8,7,6,3]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[2,1,5,4,7,8,6,3]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[2,1,4,5,8,7,6,3]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[2,1,4,5,7,8,6,3]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[2,1,6,5,4,8,7,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[2,1,5,6,4,8,7,3]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[2,1,4,6,5,8,7,3]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[2,1,5,4,6,8,7,3]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[2,1,4,5,6,8,7,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[2,1,7,6,5,4,8,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[2,1,6,7,5,4,8,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[2,1,5,7,6,4,8,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[2,1,6,5,7,4,8,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[2,1,5,6,7,4,8,3]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,4,7,6,5,8,3]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[2,1,4,6,7,5,8,3]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[2,1,5,4,7,6,8,3]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[2,1,5,6,4,7,8,3]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[2,1,5,4,6,7,8,3]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[2,1,4,5,6,7,8,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,8,7,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,7,8,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,2,6,7,8,5,4,3]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,5,8,7,6,4,3]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,6,5,8,7,4,3]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,2,5,6,8,7,4,3]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,2,7,6,5,8,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,2,5,7,6,8,4,3]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,6,5,7,8,4,3]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,2,5,6,7,8,4,3]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,4,8,7,6,5,3]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,4,7,8,6,5,3]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,4,6,8,7,5,3]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,4,6,7,8,5,3]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,5,4,8,7,6,3]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,2,5,4,7,8,6,3]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,2,4,5,8,7,6,3]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,2,4,5,7,8,6,3]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,6,5,4,8,7,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,2,4,6,5,8,7,3]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,2,5,4,6,8,7,3]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,2,4,5,6,8,7,3]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,2,7,6,5,4,8,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,2,5,7,6,4,8,3]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,2,5,6,7,4,8,3]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,2,4,7,6,5,8,3]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,2,5,4,7,6,8,3]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,2,6,5,4,7,8,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,2,5,4,6,7,8,3]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,2,4,5,6,7,8,3]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[3,2,1,8,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,7,8,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[3,2,1,6,8,7,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[3,2,1,7,6,8,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[3,2,1,6,7,8,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[3,2,1,5,8,7,6,4]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[3,2,1,5,7,8,6,4]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[3,2,1,6,5,8,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[3,2,1,5,6,8,7,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[3,2,1,7,6,5,8,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[3,2,1,6,7,5,8,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[3,2,1,5,7,6,8,4]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[3,2,1,6,5,7,8,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[3,2,1,5,6,7,8,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[2,3,1,8,7,6,5,4]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,3,1,6,8,7,5,4]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[2,3,1,7,6,8,5,4]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[2,3,1,6,7,8,5,4]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[2,3,1,5,7,8,6,4]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[2,3,1,6,5,8,7,4]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[2,3,1,7,6,5,8,4]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[2,3,1,6,7,5,8,4]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[2,3,1,5,7,6,8,4]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[2,3,1,5,6,7,8,4]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,8,7,6,5,4]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,3,2,6,8,7,5,4]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,3,2,7,6,8,5,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,3,2,6,7,8,5,4]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,3,2,5,8,7,6,4]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,3,2,5,7,8,6,4]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,3,2,6,5,8,7,4]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,3,2,5,6,8,7,4]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,3,2,7,6,5,8,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,3,2,6,7,5,8,4]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,3,2,5,7,6,8,4]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,3,2,6,5,7,8,4]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,3,2,5,6,7,8,4]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[2,1,3,8,7,6,5,4]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,7,8,6,5,4]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,3,6,8,7,5,4]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[2,1,3,6,5,8,7,4]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[2,1,3,5,6,7,8,4]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,8,7,6,5,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,7,8,6,5,4]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,3,6,8,7,5,4]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,3,7,6,8,5,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,2,3,6,7,8,5,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,3,5,8,7,6,4]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,3,5,7,8,6,4]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,3,6,5,8,7,4]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,2,3,5,6,8,7,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,3,7,6,5,8,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,2,3,6,7,5,8,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,3,5,7,6,8,4]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,3,6,5,7,8,4]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,2,3,5,6,7,8,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[4,3,2,1,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,3,2,1,7,8,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[4,3,2,1,6,8,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[4,3,2,1,7,6,8,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[4,3,2,1,6,7,8,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[3,4,2,1,8,7,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[3,4,2,1,7,8,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[3,4,2,1,6,8,7,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[3,4,2,1,7,6,8,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[3,4,2,1,6,7,8,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[2,4,3,1,8,7,6,5]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,4,3,1,7,8,6,5]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[2,4,3,1,6,8,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[2,4,3,1,7,6,8,5]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[2,4,3,1,6,7,8,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[3,2,4,1,8,7,6,5]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[3,2,4,1,7,8,6,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[3,2,4,1,6,8,7,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[3,2,4,1,7,6,8,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[3,2,4,1,6,7,8,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[2,3,4,1,8,7,6,5]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[2,3,4,1,7,8,6,5]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[2,3,4,1,6,8,7,5]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[2,3,4,1,7,6,8,5]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[2,3,4,1,6,7,8,5]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,4,3,2,8,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,4,3,2,6,8,7,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,4,3,2,7,6,8,5]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,4,3,2,6,7,8,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,3,4,2,8,7,6,5]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,3,4,2,7,8,6,5]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,3,4,2,6,8,7,5]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,3,4,2,7,6,8,5]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,3,4,2,6,7,8,5]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[2,1,4,3,8,7,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,4,3,7,8,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,4,3,6,8,7,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,4,3,7,6,8,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[2,1,4,3,6,7,8,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,2,4,3,8,7,6,5]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,4,3,7,8,6,5]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,2,4,3,6,8,7,5]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,2,4,3,7,6,8,5]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,2,4,3,6,7,8,5]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[3,2,1,4,8,7,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[3,2,1,4,7,8,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[3,2,1,4,6,8,7,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[3,2,1,4,7,6,8,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[3,2,1,4,6,7,8,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[2,3,1,4,8,7,6,5]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,3,1,4,7,8,6,5]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[2,3,1,4,7,6,8,5]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[2,3,1,4,6,7,8,5]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,3,2,4,8,7,6,5]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,3,2,4,6,8,7,5]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,3,2,4,7,6,8,5]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,3,2,4,6,7,8,5]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,4,8,7,6,5]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,1,3,4,7,8,6,5]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,3,4,7,6,8,5]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[2,1,3,4,6,7,8,5]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,3,4,8,7,6,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,4,7,8,6,5]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,3,4,6,8,7,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,3,4,7,6,8,5]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,2,3,4,6,7,8,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[5,4,3,2,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,4,3,2,1,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[4,5,3,2,1,8,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[3,5,4,2,1,8,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[3,5,4,2,1,7,8,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[4,3,5,2,1,8,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[3,4,5,2,1,8,7,6]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[3,4,5,2,1,7,8,6]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[2,5,4,3,1,8,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[2,5,4,3,1,7,8,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[2,4,5,3,1,8,7,6]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[2,4,5,3,1,7,8,6]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[3,2,5,4,1,8,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[3,2,5,4,1,7,8,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[2,3,5,4,1,8,7,6]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[4,3,2,5,1,8,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[4,3,2,5,1,7,8,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[3,4,2,5,1,8,7,6]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[3,4,2,5,1,7,8,6]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[2,4,3,5,1,8,7,6]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[2,4,3,5,1,7,8,6]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[3,2,4,5,1,8,7,6]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[2,3,4,5,1,8,7,6]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[2,3,4,5,1,7,8,6]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,5,4,3,2,8,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,5,4,3,2,7,8,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,4,5,3,2,8,7,6]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,4,5,3,2,7,8,6]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,3,5,4,2,7,8,6]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,4,3,5,2,8,7,6]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,4,3,5,2,7,8,6]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,3,4,5,2,8,7,6]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,3,4,5,2,7,8,6]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[2,1,5,4,3,8,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,1,4,5,3,8,7,6]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,2,5,4,3,8,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,5,4,3,7,8,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,2,4,5,3,8,7,6]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,2,4,5,3,7,8,6]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,3,2,5,4,8,7,6]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,3,2,5,4,7,8,6]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[2,1,3,5,4,8,7,6]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[2,1,3,5,4,7,8,6]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,2,3,5,4,8,7,6]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,3,5,4,7,8,6]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[4,3,2,1,5,8,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[4,3,2,1,5,7,8,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[2,4,3,1,5,8,7,6]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[3,2,4,1,5,8,7,6]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[3,2,4,1,5,7,8,6]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[2,3,4,1,5,8,7,6]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[2,3,4,1,5,7,8,6]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,4,3,2,5,8,7,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,4,3,2,5,7,8,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,3,4,2,5,8,7,6]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,3,4,2,5,7,8,6]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[2,1,4,3,5,8,7,6]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[2,1,4,3,5,7,8,6]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,2,4,3,5,8,7,6]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,4,3,5,7,8,6]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[3,2,1,4,5,8,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[3,2,1,4,5,7,8,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[2,3,1,4,5,7,8,6]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,3,2,4,5,8,7,6]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,3,2,4,5,7,8,6]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[2,1,3,4,5,8,7,6]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,3,4,5,7,8,6]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,3,4,5,8,7,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,3,4,5,7,8,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[6,5,4,3,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,6,4,3,2,1,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[4,6,5,3,2,1,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[5,4,6,3,2,1,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[4,5,6,3,2,1,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[3,6,5,4,2,1,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[3,5,6,4,2,1,8,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[4,3,6,5,2,1,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[3,4,6,5,2,1,8,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[5,4,3,6,2,1,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[4,5,3,6,2,1,8,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[4,3,5,6,2,1,8,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[3,4,5,6,2,1,8,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[2,6,5,4,3,1,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,5,6,4,3,1,8,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[2,4,6,5,3,1,8,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[3,2,6,5,4,1,8,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[3,2,5,6,4,1,8,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[2,3,6,5,4,1,8,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,3,5,6,4,1,8,7]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[4,3,2,6,5,1,8,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[3,4,2,6,5,1,8,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[2,4,3,6,5,1,8,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[5,4,3,2,6,1,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[4,5,3,2,6,1,8,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[3,5,4,2,6,1,8,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[4,3,5,2,6,1,8,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[3,4,5,2,6,1,8,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[2,5,4,3,6,1,8,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[2,4,5,3,6,1,8,7]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[3,2,5,4,6,1,8,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[4,3,2,5,6,1,8,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[3,4,2,5,6,1,8,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[2,4,3,5,6,1,8,7]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[2,3,4,5,6,1,8,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,6,5,4,3,2,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,5,6,4,3,2,8,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,5,4,6,3,2,8,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,3,6,5,4,2,8,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,3,4,5,6,2,8,7]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[2,1,6,5,4,3,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,5,6,4,3,8,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[2,1,4,6,5,3,8,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[2,1,5,4,6,3,8,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[2,1,4,5,6,3,8,7]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,4,5,6,3,8,7]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[3,2,1,6,5,4,8,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[2,3,1,6,5,4,8,7]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,3,2,6,5,4,8,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,3,2,5,6,4,8,7]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[2,1,3,6,5,4,8,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[2,1,3,5,6,4,8,7]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,3,6,5,4,8,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,3,5,6,4,8,7]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[4,3,2,1,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[3,4,2,1,6,5,8,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[2,4,3,1,6,5,8,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,2,4,1,6,5,8,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[2,3,4,1,6,5,8,7]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,3,4,2,6,5,8,7]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,4,3,6,5,8,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,4,3,6,5,8,7]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,3,1,4,6,5,8,7]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,3,2,4,6,5,8,7]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[2,1,3,4,6,5,8,7]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,2,3,4,6,5,8,7]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[5,4,3,2,1,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[4,5,3,2,1,6,8,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[3,5,4,2,1,6,8,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[4,3,5,2,1,6,8,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[3,4,5,2,1,6,8,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[2,5,4,3,1,6,8,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[2,4,5,3,1,6,8,7]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[3,2,5,4,1,6,8,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[2,3,5,4,1,6,8,7]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[2,4,3,5,1,6,8,7]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[2,3,4,5,1,6,8,7]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,4,5,3,2,6,8,7]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,3,5,4,2,6,8,7]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,3,4,5,2,6,8,7]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[2,1,5,4,3,6,8,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[2,1,4,5,3,6,8,7]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,2,5,4,3,6,8,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[2,1,3,5,4,6,8,7]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,3,5,4,6,8,7]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[4,3,2,1,5,6,8,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[3,2,4,1,5,6,8,7]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[2,3,4,1,5,6,8,7]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,4,3,2,5,6,8,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,3,4,2,5,6,8,7]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[2,1,4,3,5,6,8,7]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,4,3,5,6,8,7]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[3,2,1,4,5,6,8,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[2,3,1,4,5,6,8,7]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,3,2,4,5,6,8,7]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[2,1,3,4,5,6,8,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,3,4,5,6,8,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[5,7,6,4,3,2,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[4,7,6,5,3,2,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,6,7,5,3,2,1,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[5,4,7,6,3,2,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[4,5,7,6,3,2,1,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[4,6,5,7,3,2,1,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[3,5,7,6,4,2,1,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,5,6,7,4,2,1,8]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[4,3,7,6,5,2,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[3,4,7,6,5,2,1,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[5,4,3,7,6,2,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,5,3,7,6,2,1,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[3,5,4,7,6,2,1,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[4,3,5,7,6,2,1,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[3,6,5,4,7,2,1,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[3,5,6,4,7,2,1,8]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[4,3,6,5,7,2,1,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[2,7,6,5,4,3,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,6,7,5,4,3,1,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[2,5,7,6,4,3,1,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[2,5,6,7,4,3,1,8]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[2,4,6,7,5,3,1,8]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[2,5,4,7,6,3,1,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[2,5,6,4,7,3,1,8]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[2,5,4,6,7,3,1,8]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[2,4,5,6,7,3,1,8]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[3,2,7,6,5,4,1,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,2,6,7,5,4,1,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[3,2,5,7,6,4,1,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[3,2,6,5,7,4,1,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[3,2,5,6,7,4,1,8]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[2,3,7,6,5,4,1,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,3,6,7,5,4,1,8]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[2,3,5,7,6,4,1,8]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[2,3,6,5,7,4,1,8]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[2,3,5,6,7,4,1,8]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[4,3,2,6,7,5,1,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[3,4,2,7,6,5,1,8]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[3,4,2,6,7,5,1,8]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[3,2,4,6,7,5,1,8]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[2,3,4,7,6,5,1,8]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[2,3,4,6,7,5,1,8]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[5,4,3,2,7,6,1,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[4,5,3,2,7,6,1,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[3,5,4,2,7,6,1,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[4,3,5,2,7,6,1,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[3,4,5,2,7,6,1,8]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[3,2,5,4,7,6,1,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[4,3,2,5,7,6,1,8]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[3,4,2,5,7,6,1,8]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[2,3,4,5,7,6,1,8]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[3,6,5,4,2,7,1,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[3,5,6,4,2,7,1,8]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[3,4,6,5,2,7,1,8]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[3,5,4,6,2,7,1,8]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[2,5,4,6,3,7,1,8]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[2,4,5,6,3,7,1,8]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[3,2,6,5,4,7,1,8]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[2,3,5,6,4,7,1,8]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[4,3,2,6,5,7,1,8]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[3,4,2,6,5,7,1,8]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[2,4,3,6,5,7,1,8]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[2,3,4,6,5,7,1,8]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[3,5,4,2,6,7,1,8]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[2,5,4,3,6,7,1,8]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[2,3,5,4,6,7,1,8]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[2,4,3,5,6,7,1,8]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,7,6,5,4,3,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,6,7,5,4,3,2,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,6,5,7,4,3,2,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,5,6,7,4,3,2,8]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,4,7,6,5,3,2,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,4,6,7,5,3,2,8]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,5,4,7,6,3,2,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,5,6,4,7,3,2,8]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,4,6,5,7,3,2,8]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,5,4,6,7,3,2,8]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,3,7,6,5,4,2,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,3,6,7,5,4,2,8]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,3,5,7,6,4,2,8]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,3,6,5,7,4,2,8]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,3,5,6,7,4,2,8]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,3,4,6,7,5,2,8]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,3,5,4,7,6,2,8]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,4,3,5,7,6,2,8]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,3,4,5,7,6,2,8]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,5,4,6,3,7,2,8]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,4,5,6,3,7,2,8]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,3,6,5,4,7,2,8]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,3,5,6,4,7,2,8]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,4,3,6,5,7,2,8]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,3,4,6,5,7,2,8]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,5,4,3,6,7,2,8]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,4,5,3,6,7,2,8]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,3,5,4,6,7,2,8]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,4,3,5,6,7,2,8]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,3,4,5,6,7,2,8]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[2,1,7,6,5,4,3,8]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,1,6,7,5,4,3,8]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[2,1,5,6,7,4,3,8]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[2,1,4,6,7,5,3,8]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[2,1,5,4,6,7,3,8]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[2,1,4,5,6,7,3,8]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,7,6,5,4,3,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,2,6,7,5,4,3,8]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,2,5,7,6,4,3,8]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,2,5,6,7,4,3,8]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,2,4,6,7,5,3,8]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,5,6,4,7,3,8]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,2,4,6,5,7,3,8]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,5,4,6,7,3,8]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,2,4,5,6,7,3,8]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[3,2,1,7,6,5,4,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[3,2,1,6,7,5,4,8]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[3,2,1,5,7,6,4,8]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[3,2,1,6,5,7,4,8]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[3,2,1,5,6,7,4,8]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[2,3,1,6,7,5,4,8]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[2,3,1,6,5,7,4,8]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[2,3,1,5,6,7,4,8]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,3,2,7,6,5,4,8]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,3,2,6,7,5,4,8]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,3,2,5,7,6,4,8]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,3,2,6,5,7,4,8]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,3,2,5,6,7,4,8]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[2,1,3,6,7,5,4,8]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,3,7,6,5,4,8]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,3,6,7,5,4,8]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,3,5,7,6,4,8]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,3,6,5,7,4,8]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,2,3,5,6,7,4,8]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[4,3,2,1,7,6,5,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[4,3,2,1,6,7,5,8]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[3,2,4,1,7,6,5,8]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[3,2,4,1,6,7,5,8]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[2,3,4,1,7,6,5,8]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[2,3,4,1,6,7,5,8]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,4,3,2,7,6,5,8]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,4,3,2,6,7,5,8]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,3,4,2,6,7,5,8]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[2,1,4,3,6,7,5,8]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,2,4,3,6,7,5,8]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[3,2,1,4,7,6,5,8]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[2,3,1,4,6,7,5,8]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,3,2,4,7,6,5,8]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,3,2,4,6,7,5,8]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[2,1,3,4,6,7,5,8]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,3,4,7,6,5,8]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,3,4,6,7,5,8]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[5,4,3,2,1,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[4,5,3,2,1,7,6,8]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[3,5,4,2,1,7,6,8]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[3,4,5,2,1,7,6,8]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[2,5,4,3,1,7,6,8]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[2,4,5,3,1,7,6,8]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[3,2,5,4,1,7,6,8]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[2,3,5,4,1,7,6,8]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[3,4,2,5,1,7,6,8]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[2,4,3,5,1,7,6,8]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[2,3,4,5,1,7,6,8]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,5,4,3,2,7,6,8]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,4,5,3,2,7,6,8]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,3,5,4,2,7,6,8]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,4,3,5,2,7,6,8]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,3,4,5,2,7,6,8]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[2,1,5,4,3,7,6,8]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,2,4,5,3,7,6,8]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[3,2,1,5,4,7,6,8]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[2,3,1,5,4,7,6,8]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,3,2,5,4,7,6,8]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,2,3,5,4,7,6,8]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[4,3,2,1,5,7,6,8]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[3,2,4,1,5,7,6,8]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[2,3,4,1,5,7,6,8]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,4,3,2,5,7,6,8]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,3,4,2,5,7,6,8]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,2,4,3,5,7,6,8]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[3,2,1,4,5,7,6,8]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[2,3,1,4,5,7,6,8]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,3,2,4,5,7,6,8]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[2,1,3,4,5,7,6,8]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,3,4,5,7,6,8]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[3,6,5,4,2,1,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[4,3,6,5,2,1,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[2,4,6,5,3,1,7,8]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[2,4,5,6,3,1,7,8]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[2,3,6,5,4,1,7,8]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[2,3,5,6,4,1,7,8]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[4,3,2,6,5,1,7,8]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[2,4,3,6,5,1,7,8]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[2,3,4,6,5,1,7,8]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[3,5,4,2,6,1,7,8]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[2,3,5,4,6,1,7,8]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,6,5,4,3,2,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,5,6,4,3,2,7,8]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,4,6,5,3,2,7,8]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,5,4,6,3,2,7,8]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,4,5,6,3,2,7,8]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,3,5,6,4,2,7,8]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,4,3,6,5,2,7,8]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,5,4,3,6,2,7,8]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,4,5,3,6,2,7,8]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,3,5,4,6,2,7,8]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,4,3,5,6,2,7,8]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,3,4,5,6,2,7,8]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[2,1,5,6,4,3,7,8]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[2,1,4,6,5,3,7,8]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,6,5,4,3,7,8]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,2,5,6,4,3,7,8]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,2,4,6,5,3,7,8]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,4,5,6,3,7,8]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[3,2,1,6,5,4,7,8]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[3,2,1,5,6,4,7,8]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[2,3,1,6,5,4,7,8]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[2,3,1,5,6,4,7,8]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,3,2,6,5,4,7,8]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,3,2,5,6,4,7,8]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,2,3,6,5,4,7,8]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,3,5,6,4,7,8]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[4,3,2,1,6,5,7,8]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[2,4,3,1,6,5,7,8]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[3,2,4,1,6,5,7,8]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[2,3,4,1,6,5,7,8]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[2,1,4,3,6,5,7,8]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,2,4,3,6,5,7,8]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,2,4,6,5,7,8]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[2,1,3,4,6,5,7,8]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,3,4,6,5,7,8]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[3,5,4,2,1,6,7,8]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[2,5,4,3,1,6,7,8]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[2,4,5,3,1,6,7,8]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[3,2,5,4,1,6,7,8]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[2,3,5,4,1,6,7,8]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[2,4,3,5,1,6,7,8]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,5,4,3,2,6,7,8]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,4,5,3,2,6,7,8]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,3,5,4,2,6,7,8]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,4,3,5,2,6,7,8]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,3,4,5,2,6,7,8]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[2,1,5,4,3,6,7,8]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[2,1,4,5,3,6,7,8]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,5,4,3,6,7,8]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,2,4,5,3,6,7,8]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[3,2,1,5,4,6,7,8]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[2,3,1,5,4,6,7,8]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,3,2,5,4,6,7,8]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[2,1,3,5,4,6,7,8]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,3,5,4,6,7,8]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[2,4,3,1,5,6,7,8]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,4,3,2,5,6,7,8]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,3,4,2,5,6,7,8]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[2,1,4,3,5,6,7,8]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,4,3,5,6,7,8]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,2,4,5,6,7,8]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,2,3,4,8,6,7,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,5,8,6,7,4]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,3,7,5,6,4,8]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,3,7,5,6,8,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,2,3,8,5,6,7,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,8,5,7,6,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,8,6,5,7,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,8,6,7,5,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,4,3,8,6,7,5]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,4,5,8,6,7,3]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,2,4,7,5,6,8,3]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,2,4,8,5,6,7,3]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,4,8,6,5,7,3]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,5,4,8,6,7,3]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,2,6,4,5,3,7,8]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,2,6,4,5,7,8,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,2,6,4,5,8,7,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,2,7,4,5,6,8,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,2,8,4,5,6,7,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,4,6,7,5,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,4,7,6,5,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,7,5,4,6,3,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,2,7,5,4,6,8,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,2,8,5,4,6,7,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,5,4,7,6,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,5,6,4,7,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,5,6,7,4,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,6,5,4,7,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,6,5,7,4,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,7,5,6,4,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,4,8,6,7,5]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,3,2,7,5,6,8,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,3,2,8,5,7,6,4]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,3,2,8,6,5,7,4]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,3,2,8,6,7,5,4]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,3,4,2,8,6,7,5]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,3,4,5,8,6,7,2]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,3,4,8,5,6,7,2]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,3,4,8,6,5,7,2]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,3,4,8,6,7,5,2]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,3,6,4,5,2,8,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,3,6,4,5,7,2,8]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,3,6,4,5,7,8,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,3,6,4,5,8,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,3,7,4,5,6,2,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,3,7,4,5,6,8,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,3,8,4,5,6,7,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,4,6,5,7,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,4,6,7,5,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,5,4,6,7,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,5,4,7,6,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,5,6,7,4,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,5,7,6,4,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,6,5,7,4,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,7,5,6,4,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,2,8,6,7,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,4,3,5,8,6,7,2]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,4,3,8,5,6,7,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,4,3,8,5,7,6,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,4,3,8,6,5,7,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,4,3,8,6,7,5,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,5,3,4,2,6,7,8]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,5,3,4,2,7,8,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,5,3,4,2,8,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,5,3,4,6,2,7,8]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,5,3,4,6,2,8,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,5,3,4,6,7,2,8]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,5,3,4,6,7,8,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,5,3,4,7,6,2,8]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,5,3,4,8,6,7,2]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,6,3,4,5,2,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,6,3,4,5,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,7,3,4,5,6,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,3,4,5,6,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,3,4,5,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,4,6,7,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,4,7,6,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,4,2,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,6,3,5,4,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,7,3,5,4,6,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,3,5,4,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,5,4,7,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,5,6,4,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,5,6,7,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,5,7,6,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,5,4,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,3,6,5,4,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,3,6,5,4,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,7,5,6,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,7,6,5,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,5,2,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,6,4,3,5,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,8,4,3,5,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,3,5,7,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,6,5,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,4,3,6,5,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,3,6,7,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,5,3,2,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,6,4,5,3,2,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,6,4,5,3,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,7,4,5,3,6,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,4,5,3,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,5,6,3,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,4,5,6,3,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,4,5,6,7,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,5,3,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,4,6,5,3,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,6,5,7,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,7,6,5,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,3,6,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,5,4,3,6,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,5,4,3,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,4,3,7,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,4,6,3,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,4,6,7,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,4,7,6,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,4,5,3,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,6,4,5,3,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,4,5,7,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,4,5,6,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,4,6,5,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,5,4,3,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,5,4,7,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,5,4,6,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,5,6,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,8,6,7,5]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,1,3,5,8,6,7,4]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[2,1,3,8,5,6,7,4]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,8,5,7,6,4]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,8,6,5,7,4]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,8,6,7,5,4]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,4,3,8,6,7,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,4,5,8,6,7,3]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[2,1,4,8,5,6,7,3]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,4,8,5,7,6,3]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,4,8,6,5,7,3]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,4,8,6,7,5,3]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,5,4,8,6,7,3]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[2,1,6,4,5,3,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,6,4,5,7,8,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[2,1,6,4,5,8,7,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[2,1,8,4,5,6,7,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,4,5,7,6,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,7,4,6,5,8,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[2,1,8,4,6,5,7,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,4,6,7,5,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,4,7,6,5,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,5,4,6,7,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,5,4,7,6,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,7,5,6,4,8,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[2,1,8,5,6,4,7,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,5,6,7,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,5,7,6,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,6,5,4,7,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,6,5,7,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,7,5,6,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,5,8,6,7,4]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[2,3,1,7,5,6,4,8]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,3,1,8,5,6,7,4]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,3,1,8,6,7,5,4]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,3,4,1,8,6,7,5]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[2,3,4,5,8,6,7,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,7,5,6,1,8]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[2,3,4,7,5,6,8,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,4,8,5,6,7,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,8,5,7,6,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,8,6,5,7,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,8,6,7,5,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,5,4,8,6,7,1]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,3,6,4,5,1,7,8]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[2,3,6,4,5,1,8,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,3,6,4,5,7,8,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[2,3,6,4,5,8,7,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,3,7,4,5,6,8,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,3,8,4,5,6,7,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,7,4,6,5,8,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,3,8,4,6,7,5,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,7,5,4,6,1,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,3,7,5,4,6,8,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,3,8,5,4,6,7,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,7,5,6,4,1,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,3,7,5,6,4,8,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,3,8,5,6,4,7,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,5,6,7,4,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,5,7,6,4,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,6,5,4,7,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,1,8,6,7,5]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,4,3,5,8,6,7,1]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[2,4,3,7,5,6,8,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[2,4,3,8,5,6,7,1]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,4,3,8,5,7,6,1]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,4,3,8,6,5,7,1]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,4,3,8,6,7,5,1]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,5,3,4,1,6,7,8]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[2,5,3,4,1,8,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[2,5,3,4,6,7,1,8]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[2,5,3,4,6,7,8,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[2,5,3,4,6,8,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[2,5,3,4,7,6,8,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[2,5,3,4,8,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,5,3,4,8,7,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,6,3,4,5,1,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[2,6,3,4,5,7,8,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[2,6,3,4,5,8,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,7,3,4,5,6,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,8,3,4,5,6,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,4,5,7,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,5,4,1,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[2,6,3,5,4,1,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,6,3,5,4,7,8,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[2,6,3,5,4,8,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,7,3,5,4,6,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,3,5,4,7,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,5,6,4,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,3,5,6,7,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,5,7,6,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,5,4,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,8,3,7,5,6,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,7,6,5,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,8,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,6,4,3,5,1,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,6,4,3,5,7,8,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[2,6,4,3,5,8,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,7,4,3,5,6,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,4,3,5,6,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,3,5,7,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,6,5,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,4,3,6,5,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,3,6,7,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,3,7,6,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,3,1,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[2,6,4,5,3,1,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,6,4,5,3,7,8,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[2,6,4,5,3,8,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,8,4,5,3,6,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,6,3,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7,4,5,6,3,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,4,5,6,3,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,5,6,7,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,5,3,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7,4,6,5,3,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,4,6,5,3,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,7,6,5,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,3,6,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,5,4,3,6,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,4,3,7,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,6,3,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,5,4,6,7,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,4,7,6,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,4,5,3,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,7,4,5,6,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,4,6,5,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,5,4,6,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,5,6,4,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,4,8,6,7,5]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[3,2,1,5,8,6,7,4]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[3,2,1,7,5,6,4,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[3,2,1,7,5,6,8,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[3,2,1,8,5,6,7,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,8,5,7,6,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,8,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,8,6,7,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,4,1,8,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[3,2,4,5,8,6,7,1]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[3,2,4,7,5,6,8,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[3,2,4,8,5,6,7,1]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,2,4,8,6,7,5,1]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,2,5,4,8,6,7,1]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[3,2,6,4,5,1,7,8]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[3,2,6,4,5,1,8,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[3,2,6,4,5,7,1,8]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[3,2,7,4,5,6,1,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,2,8,4,5,6,7,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,7,4,6,5,1,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,2,7,4,6,5,8,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[3,2,8,4,6,5,7,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,7,5,4,6,1,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,2,8,5,4,6,7,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,8,5,4,7,6,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,7,5,6,4,1,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,2,7,5,6,4,8,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[3,2,8,5,6,4,7,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,8,5,7,6,4,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,8,6,5,7,4,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,8,7,5,6,4,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,1,5,7,6,8]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[4,2,3,1,5,7,8,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[4,2,3,1,5,8,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[4,2,3,1,6,5,7,8]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[4,2,3,1,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[4,2,3,1,6,7,8,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[4,2,3,1,6,8,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[4,2,3,1,7,6,5,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[4,2,3,1,7,6,8,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[4,2,3,1,8,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,2,3,1,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,2,3,5,1,6,8,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[4,2,3,5,1,7,8,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[4,2,3,5,1,8,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[4,2,3,5,6,1,8,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[4,2,3,5,6,8,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[4,2,3,5,8,7,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[4,2,3,6,5,1,7,8]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[4,2,3,6,5,1,8,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[4,2,3,6,5,8,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[4,2,3,7,5,6,1,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[4,2,3,7,5,6,8,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[4,2,3,8,5,6,7,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,2,3,8,5,7,6,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,2,3,7,6,5,8,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[4,2,3,8,6,7,5,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,2,3,8,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[5,2,3,4,1,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[5,2,3,4,1,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[5,2,3,4,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,2,3,4,6,1,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[5,2,3,4,7,6,1,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[5,2,3,4,8,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,2,3,4,8,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,2,3,4,5,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,2,3,4,5,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,2,3,4,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,6,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,3,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,5,4,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,2,3,5,4,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,2,3,5,4,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,2,3,5,4,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[7,2,3,5,4,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,3,5,4,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,5,6,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,3,5,6,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,7,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,6,5,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,3,6,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[5,2,4,3,1,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[5,2,4,3,1,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[5,2,4,3,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,2,4,3,6,1,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[5,2,4,3,6,1,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[5,2,4,3,6,7,1,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[5,2,4,3,7,6,1,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[5,2,4,3,7,6,8,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[5,2,4,3,8,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,2,4,3,5,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,2,4,3,6,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,4,3,6,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,4,3,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,6,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,5,3,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,2,4,5,3,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,2,4,5,3,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,2,4,5,3,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,4,5,3,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,4,5,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,6,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,6,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,7,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,6,5,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,4,6,5,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,4,7,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,4,3,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,2,5,4,3,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,2,5,4,3,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,2,5,4,3,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[7,2,5,4,3,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,5,4,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,4,6,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,2,6,4,5,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,6,4,5,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,6,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,5,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,5,4,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,6,5,4,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,6,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,4,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,6,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,8,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,3,2,7,5,6,8,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[4,3,2,8,5,6,7,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,2,8,5,7,6,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,2,8,6,7,5,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[5,3,2,4,1,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[5,3,2,4,1,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[5,3,2,4,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,3,2,4,6,1,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[5,3,2,4,7,6,1,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[8,3,2,4,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,6,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,4,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,3,2,5,4,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,3,2,5,4,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,3,2,5,4,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,3,2,5,4,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,3,2,5,4,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,3,2,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,5,6,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,3,2,5,6,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,6,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,7,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,5,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,2,1,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[5,3,4,2,1,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[5,3,4,2,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,3,4,2,6,1,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[5,3,4,2,7,6,1,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[5,3,4,2,7,6,8,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[5,3,4,2,8,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,3,4,2,5,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,3,4,2,6,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,4,2,6,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,3,4,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,3,4,5,2,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,3,4,5,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,6,5,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,3,4,7,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,4,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,3,5,4,2,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,3,5,4,2,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,3,5,4,2,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,3,5,4,2,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,3,5,4,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,4,6,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,5,4,6,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,3,5,4,6,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,4,5,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,6,4,5,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,3,6,4,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,4,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,6,5,4,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,3,6,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,5,4,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,8,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,4,3,2,5,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,4,3,2,5,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,4,3,2,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,6,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,3,2,6,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,3,2,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,6,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,7,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,5,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,4,3,5,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,6,5,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,3,6,5,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,3,7,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,4,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,5,3,4,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,5,4,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,3,5,4,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,6,3,5,4,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,4,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,3,6,5,8,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,4,6,3,5,8,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[2,4,1,6,3,5,8,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[2,4,6,1,3,5,8,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[2,1,4,3,6,8,5,7]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[2,4,1,3,6,8,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[2,1,4,6,3,8,5,7]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[2,4,1,6,3,8,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,4,6,1,3,8,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[2,1,4,6,8,3,5,7]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[2,4,1,6,8,3,5,7]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[2,4,6,1,8,3,5,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,8,1,3,5,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,1,3,6,5,7,8]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[2,1,4,6,3,5,7,8]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[2,4,1,6,3,5,7,8]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[2,4,6,1,3,5,7,8]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[2,1,4,6,3,7,5,8]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[2,4,1,6,3,7,5,8]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[2,4,6,1,3,7,5,8]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[2,1,4,6,7,3,5,8]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[2,4,1,6,7,3,5,8]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[2,4,6,7,1,3,5,8]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[2,4,1,3,6,7,8,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[2,1,4,6,3,7,8,5]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[2,4,1,6,3,7,8,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[2,4,6,1,3,7,8,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[2,1,4,6,7,3,8,5]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[2,4,1,6,7,3,8,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[2,4,6,1,7,3,8,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[2,4,6,7,1,3,8,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[2,1,4,6,7,8,3,5]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[2,4,1,6,7,8,3,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[2,4,6,1,7,8,3,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[2,4,6,7,1,8,3,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[2,4,6,7,8,1,3,5]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[2,1,4,3,7,5,8,6]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[2,4,1,3,7,5,8,6]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[2,1,4,7,3,5,8,6]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[2,4,1,7,3,5,8,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[2,4,7,1,3,5,8,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[2,1,4,3,7,8,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[2,4,1,3,7,8,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[2,4,1,7,3,8,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[2,4,7,1,3,8,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[2,1,4,7,8,3,5,6]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[2,4,1,7,8,3,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[2,4,7,1,8,3,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[2,4,7,8,1,3,5,6]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[2,4,1,5,3,7,6,8]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[2,4,5,1,3,7,6,8]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[2,4,5,1,7,3,6,8]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[2,4,1,3,5,7,8,6]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[2,4,1,5,3,7,8,6]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[2,4,5,1,3,7,8,6]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[2,1,4,5,7,3,8,6]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[2,4,1,5,7,3,8,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[2,4,5,1,7,3,8,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[2,4,5,7,1,3,8,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[2,1,4,5,7,8,3,6]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[2,4,5,1,7,8,3,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[2,4,5,7,1,8,3,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[2,4,5,7,8,1,3,6]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[2,1,4,3,8,5,6,7]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,4,1,3,8,5,6,7]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,1,4,8,3,5,6,7]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,4,1,8,3,5,6,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,4,8,1,3,5,6,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,5,8,6,7]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[2,4,1,5,3,8,6,7]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[2,1,4,5,8,3,6,7]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[2,4,1,5,8,3,6,7]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[2,4,5,1,8,3,6,7]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[2,4,1,5,3,6,8,7]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[2,4,1,5,6,3,8,7]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[2,4,5,1,6,3,8,7]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[2,4,5,6,1,3,8,7]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[2,1,4,5,6,8,3,7]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[2,4,1,5,6,8,3,7]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[2,4,5,1,6,8,3,7]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[2,4,5,6,1,8,3,7]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[2,4,5,6,8,1,3,7]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[2,4,1,3,5,6,7,8]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[2,4,1,5,3,6,7,8]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[2,4,5,1,3,6,7,8]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[2,4,1,5,6,3,7,8]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[2,4,5,1,6,3,7,8]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[2,4,5,6,1,3,7,8]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[2,4,1,5,6,7,3,8]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[2,4,5,1,6,7,3,8]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[2,4,5,6,1,7,3,8]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[2,4,5,6,7,1,3,8]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[2,4,1,5,6,7,8,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[2,4,5,6,1,7,8,3]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[2,4,5,6,7,1,8,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[2,4,5,6,7,8,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[2,1,5,3,6,4,8,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[2,5,1,3,6,4,8,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[2,1,5,6,3,4,8,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[2,5,1,6,3,4,8,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[2,5,6,1,3,4,8,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[2,1,5,3,6,8,4,7]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[2,5,1,3,6,8,4,7]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[2,5,1,6,3,8,4,7]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[2,5,6,1,3,8,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[2,1,5,6,8,3,4,7]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[2,5,1,6,8,3,4,7]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[2,5,6,8,1,3,4,7]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[2,5,1,3,6,4,7,8]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[2,1,5,6,3,4,7,8]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[2,5,1,6,3,4,7,8]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[2,1,5,3,6,7,4,8]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[2,1,5,6,3,7,4,8]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[2,5,1,6,3,7,4,8]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[2,5,6,1,3,7,4,8]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[2,1,5,6,7,3,4,8]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[2,5,1,6,7,3,4,8]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[2,5,6,1,7,3,4,8]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[2,1,5,3,6,7,8,4]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[2,5,1,3,6,7,8,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[2,1,5,6,3,7,8,4]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[2,5,1,6,3,7,8,4]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[2,5,6,1,3,7,8,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[2,1,5,6,7,3,8,4]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[2,5,1,6,7,3,8,4]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[2,5,6,7,1,3,8,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[2,1,5,6,7,8,3,4]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[2,5,1,6,7,8,3,4]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[2,5,6,1,7,8,3,4]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[2,5,6,7,1,8,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[2,5,6,7,8,1,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[2,1,5,3,7,4,8,6]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[2,5,1,3,7,4,8,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[2,1,5,7,3,4,8,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[2,5,1,7,3,4,8,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[2,5,7,1,3,4,8,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[2,1,5,3,7,8,4,6]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[2,5,1,3,7,8,4,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[2,1,5,7,3,8,4,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[2,5,1,7,3,8,4,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[2,5,7,1,3,8,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[2,1,5,7,8,3,4,6]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,5,1,7,8,3,4,6]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[2,5,7,1,8,3,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[2,5,7,8,1,3,4,6]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[2,5,1,3,7,4,6,8]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[2,1,5,7,3,4,6,8]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[2,3,5,1,4,7,6,8]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[2,3,5,7,1,4,6,8]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[2,3,5,1,7,4,8,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[2,3,5,7,1,4,8,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[2,3,1,5,7,8,4,6]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[2,3,5,7,1,8,4,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[2,1,5,3,8,4,6,7]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[2,5,1,3,8,4,6,7]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,1,5,8,3,4,6,7]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,5,1,8,3,4,6,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,5,8,1,3,4,6,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,3,5,1,4,8,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[2,1,3,5,8,4,6,7]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[2,3,5,1,8,4,6,7]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,3,5,8,1,4,6,7]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,1,5,3,4,6,8,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[2,3,5,1,6,4,8,7]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[2,3,5,6,1,4,8,7]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[2,1,3,5,6,8,4,7]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,1,5,6,8,4,7]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[2,3,5,1,6,8,4,7]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[2,3,5,6,1,8,4,7]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[2,3,5,6,8,1,4,7]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[2,1,5,3,4,6,7,8]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[2,5,1,3,4,6,7,8]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[2,3,5,1,4,6,7,8]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[2,3,5,1,6,4,7,8]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[2,3,5,6,1,4,7,8]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[2,3,5,6,1,7,4,8]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[2,3,5,6,7,1,4,8]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[2,3,5,1,6,7,8,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[2,3,5,6,1,7,8,4]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[2,3,5,6,7,1,8,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[2,3,5,6,7,8,1,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[2,1,6,3,7,4,8,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[2,6,1,3,7,4,8,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[2,1,6,7,3,4,8,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[2,6,1,7,3,4,8,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[2,6,7,1,3,4,8,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[2,1,6,3,7,8,4,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[2,6,1,3,7,8,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[2,1,6,7,3,8,4,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[2,6,1,7,3,8,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[2,6,7,1,3,8,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[2,1,6,7,8,3,4,5]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,6,1,7,8,3,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[2,6,7,1,8,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[2,6,7,8,1,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[2,1,6,3,7,4,5,8]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[2,6,1,7,3,4,5,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[2,6,7,1,3,4,5,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[2,6,1,3,4,7,5,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[2,3,1,6,4,7,5,8]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[2,3,6,1,4,7,5,8]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[2,3,6,7,1,4,5,8]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[2,1,6,3,4,7,8,5]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[2,6,1,3,4,7,8,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[2,3,6,1,4,7,8,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[2,1,3,6,7,4,8,5]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[2,3,6,7,1,4,8,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[2,1,3,6,7,8,4,5]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[2,3,1,6,7,8,4,5]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[2,3,6,1,7,8,4,5]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[2,3,6,7,1,8,4,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[2,3,6,7,8,1,4,5]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[2,1,6,3,8,4,5,7]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[2,6,1,3,8,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,1,6,8,3,4,5,7]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,6,1,8,3,4,5,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,8,1,3,4,5,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,1,6,3,4,8,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[2,6,1,3,4,8,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,1,3,6,4,8,5,7]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[2,3,1,6,4,8,5,7]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[2,3,6,1,4,8,5,7]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,3,1,6,8,4,5,7]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[2,3,6,1,8,4,5,7]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,3,6,8,1,4,5,7]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,1,6,3,4,5,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,6,1,3,4,5,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,1,3,6,4,5,8,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[2,3,6,1,4,5,8,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,3,4,1,6,8,5,7]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[2,3,4,6,1,8,5,7]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[2,3,4,6,8,1,5,7]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[2,6,1,3,4,5,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[2,1,3,6,4,5,7,8]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[2,3,1,6,4,5,7,8]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[2,3,6,1,4,5,7,8]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[2,3,4,6,1,5,7,8]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[2,3,4,6,1,7,5,8]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[2,3,4,6,7,1,5,8]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[2,3,4,6,1,7,8,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[2,3,4,6,7,8,1,5]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[2,1,7,3,8,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[2,7,1,3,8,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,1,7,8,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[2,7,1,8,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,8,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,1,7,3,4,8,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,1,3,7,4,8,5,6]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[2,3,1,7,4,8,5,6]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[2,3,7,1,4,8,5,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,1,3,7,8,4,5,6]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[2,3,1,7,8,4,5,6]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[2,3,7,8,1,4,5,6]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,1,7,3,4,5,8,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[2,7,1,3,4,5,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,3,1,7,4,5,8,6]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[2,3,7,1,4,5,8,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,1,3,4,7,5,8,6]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[2,3,4,1,7,5,8,6]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[2,3,4,7,1,5,8,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,1,3,4,7,8,5,6]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[2,3,1,4,7,8,5,6]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[2,3,4,1,7,8,5,6]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[2,3,4,7,1,8,5,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[2,3,4,7,8,1,5,6]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[2,1,7,3,4,5,6,8]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,7,1,3,4,5,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,3,7,1,4,5,6,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,1,3,4,7,5,6,8]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[2,3,1,4,7,5,6,8]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[2,3,4,1,7,5,6,8]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[2,3,4,7,1,5,6,8]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[2,3,4,5,7,1,6,8]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[2,3,4,5,7,1,8,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[2,3,4,5,7,8,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[2,1,8,3,4,5,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,8,1,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,8,4,5,6,7]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,3,1,8,4,5,6,7]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,3,8,1,4,5,6,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,1,3,4,8,5,6,7]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,3,1,4,8,5,6,7]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,3,4,1,8,5,6,7]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[2,3,4,8,1,5,6,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,1,3,4,5,8,6,7]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[2,3,1,4,5,8,6,7]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[2,3,4,1,5,8,6,7]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[2,3,4,5,1,8,6,7]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[2,3,4,5,8,1,6,7]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,5,6,8,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[3,1,4,2,6,5,8,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[3,4,1,2,6,5,8,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[3,1,4,6,2,5,8,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[3,4,1,6,2,5,8,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[3,4,6,1,2,5,8,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[3,1,4,2,6,8,5,7]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[3,4,1,2,6,8,5,7]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[3,1,4,6,2,8,5,7]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[3,4,1,6,2,8,5,7]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[3,1,4,6,8,2,5,7]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[3,4,1,6,8,2,5,7]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[3,4,6,8,1,2,5,7]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[3,1,4,2,6,5,7,8]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[3,4,1,2,6,5,7,8]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[3,1,4,2,6,7,5,8]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[3,4,1,2,6,7,5,8]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[3,4,1,6,2,7,5,8]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[3,4,6,1,2,7,5,8]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[3,4,1,6,7,2,5,8]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[3,4,6,7,1,2,5,8]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[3,1,4,2,6,7,8,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[3,4,1,2,6,7,8,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[3,1,4,6,2,7,8,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[3,4,1,6,2,7,8,5]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[3,4,6,1,2,7,8,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[3,1,4,6,7,2,8,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[3,4,1,6,7,2,8,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[3,4,6,1,7,2,8,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[3,4,6,7,1,2,8,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[3,1,4,6,7,8,2,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[3,4,1,6,7,8,2,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[3,4,6,1,7,8,2,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[3,4,6,7,1,8,2,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[3,4,6,7,8,1,2,5]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[3,1,4,2,7,5,8,6]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[3,4,1,2,7,5,8,6]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[3,1,4,7,2,5,8,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[3,4,1,7,2,5,8,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[3,4,7,1,2,5,8,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[3,1,4,2,7,8,5,6]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[3,4,1,2,7,8,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[3,1,4,7,2,8,5,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[3,4,7,1,8,2,5,6]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[3,4,7,8,1,2,5,6]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[3,1,4,2,7,5,6,8]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[3,4,1,2,7,5,6,8]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[3,4,1,2,5,7,6,8]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[3,1,4,5,2,7,6,8]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[3,4,1,5,2,7,6,8]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[3,4,1,5,7,2,6,8]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[3,4,5,1,7,2,6,8]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[3,4,5,7,1,2,6,8]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[3,1,4,2,5,7,8,6]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[3,4,1,2,5,7,8,6]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[3,1,4,5,2,7,8,6]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[3,4,5,1,2,7,8,6]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[3,1,4,5,7,2,8,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[3,4,1,5,7,2,8,6]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[3,4,5,7,1,2,8,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[3,1,4,5,7,8,2,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[3,4,1,5,7,8,2,6]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[3,4,5,1,7,8,2,6]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[3,4,5,7,1,8,2,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[3,4,5,7,8,1,2,6]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[3,1,4,2,8,5,6,7]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[3,4,1,2,8,5,6,7]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[3,1,4,8,2,5,6,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,4,1,8,2,5,6,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,4,8,1,2,5,6,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,1,4,2,5,8,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[3,4,1,2,5,8,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[3,4,1,5,2,8,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[3,1,4,5,8,2,6,7]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[3,4,1,5,8,2,6,7]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[3,4,5,8,1,2,6,7]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,1,2,5,6,8,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[3,4,5,1,2,6,8,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[3,1,4,5,6,2,8,7]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[3,4,1,5,6,2,8,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[3,4,5,1,6,2,8,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[3,4,5,6,1,2,8,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[3,1,4,5,6,8,2,7]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[3,4,1,5,6,8,2,7]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[3,4,5,6,1,8,2,7]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[3,4,5,6,8,1,2,7]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[3,1,4,2,5,6,7,8]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[3,1,4,5,2,6,7,8]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[3,4,1,5,2,6,7,8]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[3,4,1,5,6,2,7,8]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[3,4,5,1,6,2,7,8]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[3,1,4,5,6,7,2,8]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[3,4,1,5,6,7,2,8]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[3,4,5,6,1,7,2,8]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[3,1,4,5,6,7,8,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,4,1,5,6,7,8,2]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[3,4,5,1,6,7,8,2]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[3,4,5,6,1,7,8,2]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[3,4,5,6,7,1,8,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[3,1,5,2,6,4,8,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[3,5,1,2,6,4,8,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[3,1,5,6,2,4,8,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[3,5,1,6,2,4,8,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[3,5,6,1,2,4,8,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[3,1,5,2,6,8,4,7]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[3,5,1,2,6,8,4,7]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[3,1,5,6,2,8,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[3,5,6,1,2,8,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[3,1,5,6,8,2,4,7]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[3,5,1,6,8,2,4,7]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[3,5,6,1,8,2,4,7]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[3,5,6,8,1,2,4,7]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[3,1,5,6,2,4,7,8]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[3,5,1,6,2,4,7,8]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[3,5,6,1,2,4,7,8]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[3,5,1,2,6,7,4,8]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[3,5,1,6,2,7,4,8]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[3,5,6,1,2,7,4,8]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[3,5,1,6,7,2,4,8]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[3,5,6,1,7,2,4,8]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[3,5,6,7,1,2,4,8]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[3,1,5,2,6,7,8,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[3,5,1,2,6,7,8,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[3,1,5,6,2,7,8,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[3,5,1,6,2,7,8,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[3,5,6,1,2,7,8,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[3,1,5,6,7,2,8,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[3,5,1,6,7,2,8,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[3,5,6,1,7,2,8,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[3,5,6,7,1,2,8,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[3,1,5,6,7,8,2,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[3,5,1,6,7,8,2,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[3,5,6,1,7,8,2,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[3,5,6,7,1,8,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[3,5,6,7,8,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[3,1,5,2,7,4,8,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[3,5,1,2,7,4,8,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[3,1,5,7,2,4,8,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[3,5,1,7,2,4,8,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[3,5,7,1,2,4,8,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,1,5,2,7,8,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[3,5,1,2,7,8,4,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[3,1,5,7,2,8,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[3,5,1,7,2,8,4,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[3,5,7,1,2,8,4,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[3,1,5,7,8,2,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[3,5,1,7,8,2,4,6]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[3,5,7,8,1,2,4,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[3,1,5,2,7,4,6,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[3,5,1,2,7,4,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[3,1,5,7,2,4,6,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[3,5,1,7,2,4,6,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[3,5,7,1,2,4,6,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,1,5,2,4,7,6,8]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[3,5,1,2,4,7,6,8]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[3,1,2,5,4,7,6,8]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,3,5,2,4,7,6,8]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[3,1,2,5,7,4,6,8]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[1,3,2,5,7,4,6,8]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,3,5,2,7,4,6,8]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,3,5,7,2,4,6,8]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[3,1,5,2,4,7,8,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[3,5,1,2,4,7,8,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[1,3,5,2,4,7,8,6]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[3,1,2,5,7,4,8,6]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[1,3,2,5,7,4,8,6]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,3,5,2,7,4,8,6]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,3,5,7,2,4,8,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[3,1,2,5,7,8,4,6]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[1,3,2,5,7,8,4,6]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,3,5,2,7,8,4,6]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,3,5,7,2,8,4,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,3,5,7,8,2,4,6]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[3,1,5,2,8,4,6,7]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[3,5,1,2,8,4,6,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[3,1,5,8,2,4,6,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[3,5,1,8,2,4,6,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,1,5,2,4,8,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[3,5,1,2,4,8,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[1,3,2,5,4,8,6,7]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,3,5,2,4,8,6,7]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[3,1,2,5,8,4,6,7]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[1,3,2,5,8,4,6,7]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,3,5,2,8,4,6,7]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,3,5,8,2,4,6,7]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[3,1,5,2,4,6,8,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[3,5,1,2,4,6,8,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[3,1,2,5,4,6,8,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,3,5,2,4,6,8,7]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,3,5,2,6,4,8,7]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,3,5,6,2,4,8,7]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[3,1,2,5,6,8,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[1,3,5,2,6,8,4,7]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,3,5,6,2,8,4,7]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,3,5,6,8,2,4,7]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[3,1,5,2,4,6,7,8]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[3,5,1,2,4,6,7,8]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[1,3,5,2,4,6,7,8]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[3,1,2,5,6,4,7,8]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[1,3,5,2,6,4,7,8]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,3,5,6,2,4,7,8]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[3,1,2,5,6,7,4,8]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[1,3,5,2,6,7,4,8]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,3,5,6,2,7,4,8]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,3,5,6,7,2,4,8]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[3,1,2,5,6,7,8,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[1,3,5,2,6,7,8,4]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,3,5,6,2,7,8,4]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,3,5,6,7,2,8,4]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,3,5,6,7,8,2,4]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[3,1,6,2,7,4,8,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,6,1,2,7,4,8,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[3,6,1,7,2,4,8,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[3,6,7,1,2,4,8,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[3,6,1,2,7,8,4,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[3,1,6,7,2,8,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[3,6,1,7,2,8,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[3,6,7,1,2,8,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[3,6,1,7,8,2,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,6,7,8,1,2,4,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[3,1,6,2,7,4,5,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[3,1,6,7,2,4,5,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[3,6,7,1,2,4,5,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[3,1,6,2,4,7,5,8]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[3,6,1,2,4,7,5,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[3,1,2,6,4,7,5,8]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[1,3,2,6,4,7,5,8]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,3,6,2,4,7,5,8]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,3,2,6,7,4,5,8]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,3,6,2,7,4,5,8]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[3,1,6,2,4,7,8,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[3,6,1,2,4,7,8,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[3,1,2,6,4,7,8,5]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[1,3,2,6,4,7,8,5]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,3,6,2,4,7,8,5]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[3,1,2,6,7,4,8,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[1,3,2,6,7,4,8,5]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,3,6,2,7,4,8,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,3,6,7,2,4,8,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[3,1,2,6,7,8,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[1,3,2,6,7,8,4,5]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,3,6,2,7,8,4,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,3,6,7,8,2,4,5]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[3,1,6,2,8,4,5,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[3,1,6,8,2,4,5,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[3,6,1,8,2,4,5,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,1,6,2,4,8,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[3,6,1,2,4,8,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,3,2,6,4,8,5,7]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,3,6,2,4,8,5,7]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,3,2,6,8,4,5,7]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[3,1,6,2,4,5,8,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[3,6,1,2,4,5,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[3,1,2,6,4,5,8,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,3,6,2,4,5,8,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[3,1,2,4,6,5,8,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,3,4,6,2,5,8,7]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[3,1,2,4,6,8,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[1,3,2,4,6,8,5,7]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,3,4,6,8,2,5,7]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[3,1,6,2,4,5,7,8]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[3,6,1,2,4,5,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[1,3,2,6,4,5,7,8]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,3,6,2,4,5,7,8]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,3,4,6,2,5,7,8]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[3,1,2,4,6,7,5,8]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[1,3,4,6,2,7,5,8]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,3,4,6,7,2,5,8]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[3,1,2,4,6,7,8,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[1,3,4,6,7,2,8,5]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[3,1,7,2,8,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[3,7,1,2,8,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,1,7,8,2,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[3,7,8,1,2,4,5,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,1,2,4,8,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,1,2,7,4,8,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[1,3,2,7,4,8,5,6]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,3,7,2,4,8,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[3,1,2,7,8,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[1,3,7,2,8,4,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,3,7,8,2,4,5,6]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[3,1,7,2,4,5,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[3,7,1,2,4,5,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,3,7,2,4,5,8,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[3,1,2,4,7,5,8,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[1,3,2,4,7,5,8,6]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,3,4,2,7,5,8,6]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,3,4,7,2,5,8,6]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[3,1,2,4,7,8,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[1,3,2,4,7,8,5,6]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,3,4,2,7,8,5,6]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,3,4,7,8,2,5,6]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[3,1,7,2,4,5,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,7,1,2,4,5,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,1,2,7,4,5,6,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,3,2,7,4,5,6,8]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,3,7,2,4,5,6,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[3,1,2,4,7,5,6,8]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,3,4,7,2,5,6,8]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[3,1,2,4,5,7,6,8]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,3,4,5,7,2,6,8]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[3,1,2,4,5,7,8,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[1,3,4,5,7,2,8,6]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,3,4,5,7,8,2,6]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[3,1,8,2,4,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,8,1,2,4,5,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,8,4,5,6,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,3,2,8,4,5,6,7]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,3,8,2,4,5,6,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,4,8,5,6,7]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,3,2,4,8,5,6,7]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,3,4,2,8,5,6,7]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,3,4,8,2,5,6,7]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[3,1,2,4,5,8,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,3,2,4,5,8,6,7]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,3,4,2,5,8,6,7]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,3,4,5,2,8,6,7]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,3,4,5,8,2,6,7]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[3,1,2,4,5,6,8,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,3,4,5,6,8,2,7]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[4,1,5,2,6,3,8,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,5,1,2,6,3,8,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[4,1,5,6,2,3,8,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[4,5,1,6,2,3,8,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[4,5,6,1,2,3,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[4,1,5,2,6,8,3,7]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[4,5,1,2,6,8,3,7]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[4,1,5,6,2,8,3,7]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[4,5,1,6,2,8,3,7]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[4,5,6,1,2,8,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[4,1,5,6,8,2,3,7]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[4,5,1,6,8,2,3,7]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[4,5,6,1,8,2,3,7]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[4,5,6,8,1,2,3,7]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[4,1,5,2,6,3,7,8]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[4,1,5,6,2,3,7,8]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[4,5,1,6,2,3,7,8]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[4,5,1,2,6,7,3,8]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[4,5,1,6,2,7,3,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[4,5,6,1,2,7,3,8]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[4,1,5,6,7,2,3,8]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[4,5,1,6,7,2,3,8]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[4,5,6,1,7,2,3,8]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[4,1,5,2,6,7,8,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[4,5,1,2,6,7,8,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[4,5,1,6,2,7,8,3]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[4,5,6,1,2,7,8,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[4,1,5,6,7,2,8,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[4,5,1,6,7,2,8,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[4,5,6,1,7,2,8,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[4,5,6,7,1,2,8,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[4,1,5,6,7,8,2,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[4,5,1,6,7,8,2,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[4,5,6,1,7,8,2,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[4,5,6,7,1,8,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[4,1,5,2,7,3,8,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,5,1,2,7,3,8,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[4,5,1,7,2,3,8,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[4,5,7,1,2,3,8,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[4,1,5,2,7,8,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[4,5,1,2,7,8,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[4,1,5,7,2,8,3,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[4,5,1,7,2,8,3,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[4,5,7,1,2,8,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[4,5,1,7,8,2,3,6]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[4,5,7,8,1,2,3,6]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[4,1,5,2,7,3,6,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[4,5,1,2,7,3,6,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[4,1,5,7,2,3,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[4,5,1,7,2,3,6,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[4,1,5,2,3,7,6,8]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[4,5,1,2,3,7,6,8]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[4,1,2,5,3,7,6,8]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[1,4,2,5,3,7,6,8]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,4,5,2,3,7,6,8]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[4,1,2,5,7,3,6,8]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[1,4,2,5,7,3,6,8]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,4,5,2,7,3,6,8]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,4,5,7,2,3,6,8]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[4,1,5,2,3,7,8,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[4,1,2,5,3,7,8,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[1,4,2,5,3,7,8,6]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,4,5,2,3,7,8,6]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[4,1,2,5,7,3,8,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[1,4,2,5,7,3,8,6]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,4,5,2,7,3,8,6]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,4,5,7,2,3,8,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[4,1,2,5,7,8,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[1,4,2,5,7,8,3,6]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,4,5,2,7,8,3,6]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,4,5,7,8,2,3,6]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[4,1,5,2,8,3,6,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[4,5,1,2,8,3,6,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[4,5,1,8,2,3,6,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,5,8,1,2,3,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,1,5,2,3,8,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[4,5,1,2,3,8,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[4,1,2,5,3,8,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[1,4,2,5,3,8,6,7]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,4,5,2,3,8,6,7]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[4,1,2,5,8,3,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[1,4,2,5,8,3,6,7]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,4,5,2,8,3,6,7]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,4,2,5,3,6,8,7]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[4,1,2,5,6,3,8,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[1,4,5,2,6,3,8,7]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,4,5,6,2,3,8,7]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[4,1,2,5,6,8,3,7]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[1,4,2,5,6,8,3,7]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,4,5,2,6,8,3,7]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,4,5,6,2,8,3,7]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,4,5,6,8,2,3,7]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[4,1,2,5,3,6,7,8]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[1,4,2,5,3,6,7,8]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,4,5,2,3,6,7,8]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[4,1,2,5,6,3,7,8]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[1,4,5,2,6,3,7,8]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[4,1,2,5,6,7,3,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[1,4,2,5,6,7,3,8]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,4,5,2,6,7,3,8]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,4,5,6,2,7,3,8]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,4,5,6,7,2,3,8]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[4,1,2,5,6,7,8,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,4,2,5,6,7,8,3]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,4,5,2,6,7,8,3]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,4,5,6,2,7,8,3]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,4,5,6,7,2,8,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,4,5,6,7,8,2,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[4,1,6,2,7,3,8,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,1,6,7,2,3,8,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[4,6,1,7,2,3,8,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[4,6,7,1,2,3,8,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[4,6,1,2,7,8,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[4,6,1,7,2,8,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[4,6,7,1,2,8,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[4,6,1,7,8,2,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[4,6,7,1,8,2,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[4,6,7,8,1,2,3,5]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[4,1,6,2,7,3,5,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[4,6,1,2,7,3,5,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[4,1,6,7,2,3,5,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[4,6,1,7,2,3,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[4,6,7,1,2,3,5,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[4,1,6,2,3,7,5,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[4,6,1,2,3,7,5,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[4,1,2,6,3,7,5,8]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[1,4,2,6,3,7,5,8]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[4,1,2,6,7,3,5,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[1,4,2,6,7,3,5,8]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,4,6,2,7,3,5,8]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,4,6,7,2,3,5,8]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[4,1,6,2,3,7,8,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[4,1,2,6,3,7,8,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[1,4,6,2,3,7,8,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[4,1,2,6,7,3,8,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[1,4,6,2,7,3,8,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,4,2,6,7,8,3,5]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,4,6,2,7,8,3,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,4,6,7,2,8,3,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,4,6,7,8,2,3,5]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[4,1,6,2,8,3,5,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,6,1,2,8,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,1,6,8,2,3,5,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,6,1,8,2,3,5,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,6,8,1,2,3,5,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,1,6,2,3,8,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[4,6,1,2,3,8,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[4,1,2,6,3,8,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,4,2,6,3,8,5,7]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,4,6,2,3,8,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,4,2,6,8,3,5,7]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,4,6,2,8,3,5,7]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,4,6,8,2,3,5,7]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[4,1,6,2,3,5,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[4,6,1,2,3,5,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[4,1,2,6,3,5,8,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[1,4,2,6,3,5,8,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,4,6,2,3,5,8,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[4,1,2,3,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,4,2,3,6,5,8,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,2,4,6,3,5,8,7]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[4,1,2,3,6,8,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[1,2,4,3,6,8,5,7]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,2,4,6,3,8,5,7]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,2,4,6,8,3,5,7]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[4,1,6,2,3,5,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[4,6,1,2,3,5,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[1,4,2,6,3,5,7,8]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,4,6,2,3,5,7,8]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[4,1,2,3,6,5,7,8]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,4,2,3,6,5,7,8]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,2,4,6,3,5,7,8]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,2,3,6,7,5,8]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[1,4,2,3,6,7,5,8]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,2,4,6,3,7,5,8]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,4,6,7,3,5,8]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[4,1,2,3,6,7,8,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[1,4,2,3,6,7,8,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,2,4,6,3,7,8,5]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,2,4,6,7,3,8,5]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,4,6,7,8,3,5]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[4,1,7,2,8,3,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,7,1,2,8,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,1,7,8,2,3,5,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[4,7,1,8,2,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,8,1,2,3,5,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,1,7,2,3,8,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,7,1,2,3,8,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,4,2,7,3,8,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,4,7,2,3,8,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[4,1,2,7,8,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[1,4,2,7,8,3,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,4,7,2,8,3,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,4,7,8,2,3,5,6]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[4,1,7,2,3,5,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,1,2,7,3,5,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[1,4,2,7,3,5,8,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,4,7,2,3,5,8,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[4,1,2,3,7,5,8,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[1,4,2,3,7,5,8,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,2,4,3,7,5,8,6]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,2,4,7,3,5,8,6]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[4,1,2,3,7,8,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[1,4,2,3,7,8,5,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,2,4,3,7,8,5,6]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,2,4,7,3,8,5,6]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,2,4,7,8,3,5,6]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[4,1,7,2,3,5,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[4,1,2,7,3,5,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[1,4,2,7,3,5,6,8]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,4,7,2,3,5,6,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[4,1,2,3,7,5,6,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,4,2,3,7,5,6,8]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,2,4,3,7,5,6,8]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,2,4,7,3,5,6,8]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[4,1,2,3,5,7,6,8]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,4,2,3,5,7,6,8]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,2,4,5,7,3,6,8]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[4,1,2,3,5,7,8,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[1,4,2,3,5,7,8,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,2,4,5,7,3,8,6]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,2,4,5,7,8,3,6]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[4,1,8,2,3,5,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,1,2,3,5,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,8,3,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,4,2,8,3,5,6,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,4,8,2,3,5,6,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,1,2,3,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,4,2,3,8,5,6,7]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,2,4,3,8,5,6,7]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,4,8,3,5,6,7]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[4,1,2,3,5,8,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,4,2,3,5,8,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,2,4,3,5,8,6,7]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,4,5,3,8,6,7]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,2,4,5,8,3,6,7]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[4,1,2,3,5,6,8,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,4,2,3,5,6,8,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,2,4,5,6,8,3,7]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,4,2,3,5,6,7,8]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[5,1,6,2,7,3,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,6,1,2,7,3,8,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[5,1,6,7,2,3,8,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[5,6,1,7,2,3,8,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[5,6,7,1,2,3,8,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[5,1,6,2,7,8,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[5,6,1,2,7,8,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[5,1,6,7,2,8,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[5,6,1,7,2,8,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[5,6,7,1,2,8,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[5,1,6,7,8,2,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[5,6,1,7,8,2,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[5,6,7,1,8,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[5,1,6,2,7,3,4,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[5,6,1,2,7,3,4,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[5,6,1,7,2,3,4,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[5,1,6,2,3,7,4,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[5,1,2,6,3,7,4,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[1,5,2,6,3,7,4,8]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[5,1,2,6,7,3,4,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[1,5,2,6,7,3,4,8]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,5,6,2,7,3,4,8]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,5,6,7,2,3,4,8]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[5,1,6,2,3,7,8,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[5,6,1,2,3,7,8,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[5,1,2,6,3,7,8,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[1,5,2,6,3,7,8,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,5,6,2,3,7,8,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[5,1,2,6,7,3,8,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[1,5,6,7,2,3,8,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[5,1,2,6,7,8,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[1,5,6,2,7,8,3,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,5,6,7,2,8,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,5,6,7,8,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[5,1,6,2,8,3,4,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,6,1,2,8,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,6,1,8,2,3,4,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,6,8,1,2,3,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,1,6,2,3,8,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[5,6,1,2,3,8,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[5,1,2,6,3,8,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[1,5,2,6,3,8,4,7]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,5,6,2,3,8,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[5,1,2,6,8,3,4,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,5,2,6,8,3,4,7]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,5,6,2,8,3,4,7]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,5,6,8,2,3,4,7]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[5,1,6,2,3,4,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[5,6,1,2,3,4,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[1,5,2,6,3,4,8,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,5,6,2,3,4,8,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,5,2,3,6,4,8,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,2,5,3,6,4,8,7]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,2,5,6,3,4,8,7]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[5,1,2,3,6,8,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[1,5,2,3,6,8,4,7]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,2,5,6,3,8,4,7]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,2,5,6,8,3,4,7]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[5,1,6,2,3,4,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[5,1,2,6,3,4,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[1,5,2,6,3,4,7,8]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,5,6,2,3,4,7,8]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[5,1,2,3,6,4,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[1,5,2,3,6,4,7,8]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,2,5,3,6,4,7,8]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,2,5,6,3,4,7,8]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[5,1,2,3,6,7,4,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[1,5,2,3,6,7,4,8]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,2,5,3,6,7,4,8]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,2,5,6,3,7,4,8]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[5,1,2,3,6,7,8,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,5,2,3,6,7,8,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,2,5,3,6,7,8,4]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,2,5,6,3,7,8,4]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,2,5,6,7,3,8,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,2,5,6,7,8,3,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[5,1,7,2,8,3,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,7,1,2,8,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,1,7,8,2,3,4,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,7,8,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,1,2,7,3,8,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[1,5,2,7,3,8,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,5,7,2,3,8,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[5,1,2,7,8,3,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[1,5,2,7,8,3,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,5,7,2,8,3,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,5,7,8,2,3,4,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[5,1,7,2,3,4,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,7,1,2,3,4,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,1,2,7,3,4,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[1,5,2,7,3,4,8,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,5,7,2,3,4,8,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[5,1,2,3,7,4,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[1,5,2,3,7,4,8,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,2,5,3,7,4,8,6]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,2,5,7,3,4,8,6]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[5,1,2,3,7,8,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[1,5,2,3,7,8,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,2,5,3,7,8,4,6]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,2,5,7,3,8,4,6]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,5,7,8,3,4,6]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[5,1,7,2,3,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,7,1,2,3,4,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,5,2,7,3,4,6,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,5,7,2,3,4,6,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,5,2,3,7,4,6,8]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,2,5,3,7,4,6,8]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,2,5,7,3,4,6,8]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,5,2,3,4,7,6,8]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,2,5,3,4,7,6,8]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,2,3,5,7,4,6,8]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[5,1,2,3,4,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[1,5,2,3,4,7,8,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,2,5,3,4,7,8,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,2,3,5,7,4,8,6]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,3,5,7,8,4,6]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[5,1,8,2,3,4,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,1,2,3,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,1,2,8,3,4,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,5,2,8,3,4,6,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,1,2,3,8,4,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,5,2,3,8,4,6,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,2,5,3,8,4,6,7]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,2,5,8,3,4,6,7]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[5,1,2,3,4,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,5,2,3,4,8,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,2,5,3,4,8,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,3,5,4,8,6,7]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,3,5,8,4,6,7]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[5,1,2,3,4,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,5,2,3,4,6,8,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,2,5,3,4,6,8,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,2,3,5,6,8,4,7]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,5,2,3,4,6,7,8]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,2,5,3,4,6,7,8]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[6,1,7,2,8,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,7,1,2,8,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,1,7,8,2,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,7,1,8,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,1,7,2,3,8,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,7,1,2,3,8,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,1,2,7,3,8,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,6,2,7,3,8,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,6,7,2,3,8,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[6,1,2,7,8,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,6,2,7,8,3,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,6,7,2,8,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,6,7,8,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[6,1,7,2,3,4,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,7,1,2,3,4,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,1,2,7,3,4,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,6,2,7,3,4,8,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,6,7,2,3,4,8,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[6,1,2,3,7,4,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,6,2,3,7,4,8,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,2,6,3,7,4,8,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,2,6,7,3,4,8,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[6,1,2,3,7,8,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,6,2,3,7,8,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,2,6,3,7,8,4,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,2,6,7,3,8,4,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,2,6,7,8,3,4,5]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[6,1,7,2,3,4,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,1,2,7,3,4,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,6,2,7,3,4,5,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,6,7,2,3,4,5,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,6,2,3,7,4,5,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,2,6,3,7,4,5,8]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,2,6,7,3,4,5,8]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[6,1,2,3,4,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,6,2,3,4,7,5,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,2,6,3,4,7,5,8]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,2,3,6,4,7,5,8]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,2,3,6,7,4,5,8]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[6,1,2,3,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,6,2,3,4,7,8,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,2,6,3,4,7,8,5]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,2,3,6,4,7,8,5]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,2,3,6,7,4,8,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,3,6,7,8,4,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[6,1,8,2,3,4,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,1,2,8,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,6,2,8,3,4,5,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,8,2,3,4,5,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,1,2,3,8,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,6,2,3,8,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,2,6,3,8,4,5,7]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,2,6,8,3,4,5,7]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[6,1,2,3,4,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,6,2,3,4,8,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,2,6,3,4,8,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,2,3,6,4,8,5,7]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,2,3,6,8,4,5,7]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[6,1,2,3,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,6,2,3,4,5,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,2,6,3,4,5,8,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,3,6,4,5,8,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,3,4,6,8,5,7]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,6,2,3,4,5,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,2,6,3,4,5,7,8]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,2,3,6,4,5,7,8]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[7,1,8,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,2,8,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,7,2,8,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,8,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,1,2,3,8,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,7,2,3,8,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,2,7,3,8,4,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,2,7,8,3,4,5,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[7,1,2,3,4,8,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,7,2,3,4,8,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,2,7,3,4,8,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,2,3,7,4,8,5,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,2,3,7,8,4,5,6]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[7,1,2,3,4,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,7,2,3,4,5,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,2,7,3,4,5,8,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,2,3,7,4,5,8,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,2,3,4,7,5,8,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,2,3,4,7,8,5,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,7,2,3,4,5,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,2,7,3,4,5,6,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,2,3,7,4,5,6,8]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,3,4,7,5,6,8]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,8,2,3,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,8,3,4,5,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,8,4,5,6,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,4,8,5,6,7]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,4,5,8,6,7]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[5,3,2,6,1,4,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[7,3,2,5,4,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,4,5,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,3,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,5,2,3,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,4,6,2,1,3,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[3,6,1,5,4,2,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[4,6,5,1,3,2,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[5,6,4,3,1,2,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[7,5,4,3,2,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,6,4,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,8,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,4,3,8,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[5,7,4,3,1,8,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[4,7,5,1,3,8,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,7,1,5,4,8,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[2,1,7,5,4,8,3,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[3,8,1,5,4,7,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,1,3,7,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,3,1,7,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,4,3,7,1,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,5,7,3,1,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,6,7,1,3,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,6,1,7,3,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,6,7,4,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,8,6,7,4,5,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,7,6,8,4,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[3,7,1,6,8,4,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,7,6,1,8,3,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,7,6,8,1,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,4,7,2,1,8,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,4,7,2,8,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,4,6,2,8,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,4,6,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,8,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,2,7,8,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,3,2,7,1,8,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[4,3,2,1,7,8,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[3,4,1,2,8,7,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[5,3,2,8,1,7,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,3,2,8,7,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,3,2,8,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,4,7,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,4,8,2,7,1,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,4,8,2,1,7,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,5,8,1,2,7,6,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,5,1,8,2,7,6,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[2,1,5,8,3,7,6,4]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,1,6,8,7,3,5,4]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[3,6,1,8,7,2,5,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,6,8,1,7,2,5,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[5,6,8,7,1,2,4,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,5,8,7,2,1,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,5,8,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,5,7,6,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,1,4,2,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,7,8,1,6,5,2,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,7,1,8,6,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,1,7,8,6,5,3,4]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[3,8,1,7,6,5,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,1,6,5,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,1,4,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,7,5,4,1,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,2,5,1,4,6,7,8]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[4,2,5,1,3,6,7,8]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[5,2,4,1,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[3,2,6,1,4,5,7,8]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[4,2,6,1,3,5,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[5,3,6,1,2,4,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[6,2,4,1,3,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,3,5,1,2,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,2,7,1,3,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,3,7,1,2,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,4,7,1,2,3,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[6,2,7,1,3,4,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,3,7,1,2,4,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,4,7,1,2,3,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,3,5,1,2,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,6,1,2,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,6,1,2,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,2,8,1,4,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,2,8,1,3,5,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,2,8,1,3,4,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,1,2,3,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,2,8,1,3,4,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,8,1,2,4,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,1,2,3,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,1,2,3,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,8,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,1,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,1,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,2,4,1,3,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,2,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,2,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,2,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,2,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,1,4,6,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[4,2,5,7,1,3,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[4,3,5,7,1,2,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[5,2,4,7,1,3,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,3,4,7,1,2,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,2,6,7,1,3,5,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[5,2,6,7,1,3,4,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[5,3,6,7,1,2,4,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[6,2,5,7,1,3,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,3,5,7,1,2,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[7,2,4,6,1,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,4,6,1,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,5,6,1,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,2,5,8,1,4,6,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[4,2,5,8,1,3,6,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,3,5,8,1,2,6,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[5,2,4,8,1,3,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,2,6,8,1,4,5,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[4,2,6,8,1,3,5,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,3,6,8,1,2,5,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[5,2,6,8,1,3,4,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,2,4,8,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,4,8,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,5,8,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,5,8,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,5,8,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,2,7,8,1,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[4,3,7,8,1,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[5,3,7,8,1,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,4,7,8,1,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[6,2,7,8,1,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,3,7,8,1,2,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,4,7,8,1,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,2,4,8,1,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,4,8,1,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,5,8,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,5,8,1,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,6,8,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,2,4,6,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,6,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,6,1,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,6,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,7,1,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,7,1,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,5,1,4,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[4,6,2,5,1,3,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[4,6,3,5,1,2,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[5,6,2,4,1,3,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[3,7,2,5,1,4,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[4,7,3,5,1,2,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[5,7,2,4,1,3,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,7,3,4,1,2,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[3,7,2,6,1,4,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[4,7,3,6,1,2,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[5,7,2,6,1,3,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,7,3,6,1,2,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,7,2,5,1,3,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[4,8,2,5,1,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,4,1,3,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,3,4,1,2,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,2,6,1,4,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,6,1,3,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,6,1,2,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,6,1,2,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,2,4,1,3,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,3,4,1,2,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,3,5,1,2,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,5,1,2,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,2,7,1,4,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,7,1,3,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,7,1,2,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,7,1,3,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,3,7,1,2,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,7,1,2,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,2,7,1,3,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,3,7,1,2,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,7,1,2,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,2,4,1,3,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,5,1,3,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,5,1,2,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,6,1,2,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,3,2,6,1,5,7,8]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[5,3,2,6,1,4,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[5,4,2,6,1,3,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[6,3,2,5,1,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,4,2,5,1,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,5,2,4,1,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[4,3,2,7,1,5,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[5,3,2,7,1,4,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,4,3,7,1,2,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[6,3,2,7,1,4,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,4,2,7,1,3,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,4,3,7,1,2,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,5,2,7,1,3,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,5,3,7,1,2,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[7,3,2,5,1,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,2,5,1,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,2,6,1,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,2,6,1,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,3,6,1,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,2,6,1,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,3,6,1,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,3,5,1,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,3,2,8,1,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[5,3,2,8,1,4,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,4,3,8,1,2,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,3,2,8,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,2,8,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,3,8,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,2,8,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,3,8,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,4,8,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,3,2,8,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,2,8,1,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,3,8,1,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,3,8,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,4,8,1,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,2,8,1,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,4,8,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,3,2,5,1,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,1,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,1,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,1,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,1,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,1,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,1,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,1,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,1,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,1,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,1,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,1,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,1,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,1,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,5,8,1,4,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[4,6,3,5,8,1,2,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[5,6,2,4,8,1,3,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[4,7,2,5,8,1,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,7,3,5,8,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,7,2,4,8,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,3,4,8,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[3,7,2,6,8,1,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,7,3,6,8,1,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,7,2,6,8,1,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,4,6,8,1,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,7,3,4,8,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,3,5,8,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[3,8,2,5,7,1,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,5,7,1,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,5,7,1,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,4,7,1,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,2,6,7,1,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,6,7,1,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,6,7,1,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,3,6,7,1,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,6,7,1,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,2,5,7,1,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,3,5,7,1,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,5,7,1,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,2,4,6,1,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,4,6,1,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,5,6,1,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,5,6,1,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,3,2,6,8,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[5,3,2,6,8,1,4,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,4,2,6,8,1,3,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,4,3,6,8,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[6,3,2,5,8,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,4,3,5,8,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,2,4,8,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,3,2,7,8,1,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[5,3,2,7,8,1,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,4,2,7,8,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,4,3,7,8,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[6,4,2,7,8,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,4,3,7,8,1,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,5,2,7,8,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[7,4,2,5,8,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,3,5,8,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,2,6,8,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,2,6,8,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,3,6,8,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,2,4,8,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,3,5,8,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,3,2,5,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,7,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,7,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,7,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,7,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,7,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,7,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,7,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,6,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,6,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,6,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,6,1,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[5,3,7,2,6,1,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,4,7,2,6,1,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[6,3,7,2,5,1,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,4,7,2,5,1,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,4,7,3,5,1,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,3,6,2,5,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,3,8,2,6,1,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,3,8,2,6,1,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,2,6,1,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,3,6,1,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,3,8,2,5,1,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,2,5,1,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,3,5,1,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,2,4,1,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,3,4,1,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,3,8,2,7,1,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,3,8,2,7,1,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,2,7,1,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,3,7,1,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,3,8,2,7,1,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,2,7,1,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,3,7,1,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,2,7,1,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,3,8,2,5,1,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,3,5,1,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,2,6,1,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,2,6,1,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,4,6,1,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,8,2,5,1,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,8,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,3,6,2,5,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,5,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,4,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,5,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,5,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,4,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,6,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,6,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,4,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,5,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,5,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,2,7,1,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[6,4,3,2,7,1,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,5,3,2,7,1,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,5,4,2,7,1,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[7,5,3,2,6,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,4,2,6,1,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,3,2,5,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,4,3,2,8,1,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,5,3,2,8,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,4,2,8,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,4,3,8,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,5,3,2,8,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,4,2,8,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,3,2,8,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,4,3,8,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,5,2,8,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,5,3,8,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,5,3,2,6,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,5,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,4,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,7,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,7,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,5,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,6,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,6,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,4,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,5,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,2,6,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,7,2,6,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,7,2,6,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,7,3,6,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,3,7,2,5,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,7,2,5,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,7,3,5,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,7,2,4,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,7,3,4,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,4,3,8,2,7,1,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,4,3,8,2,7,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,3,8,2,7,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,4,8,2,7,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,4,8,3,7,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,4,3,8,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,3,8,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,4,8,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,3,8,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,4,8,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,5,8,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,4,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,6,4,3,2,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,5,4,2,8,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,5,4,3,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,6,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,7,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,6,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,1,2,3,8,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[8,1,2,3,6,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,8,3,7,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[8,1,2,5,3,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,5,3,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,2,6,3,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,6,3,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,2,5,3,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,1,2,5,3,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,3,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,5,3,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,1,2,8,6,3,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,1,2,8,7,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,1,2,7,6,3,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[8,1,2,5,6,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,7,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,6,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,5,6,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,1,2,5,8,7,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[4,1,2,8,6,7,3,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[8,1,2,5,6,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,4,7,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,8,2,6,4,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,8,2,7,4,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,7,2,6,4,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[3,1,5,2,8,7,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[3,1,8,2,6,7,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,1,4,2,3,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,3,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,4,2,3,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,1,4,2,3,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,3,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[8,1,5,2,3,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,3,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,7,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,3,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,1,5,2,3,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,3,7,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,1,5,2,3,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,1,4,2,8,3,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,1,4,2,7,3,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[8,1,4,2,6,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,7,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,6,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,5,2,6,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,7,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,2,6,3,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,5,2,6,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,1,4,2,6,8,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[5,1,4,2,8,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[8,1,4,2,6,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,6,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,6,7,8,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[3,1,4,8,2,7,5,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,1,8,5,2,4,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,7,5,2,4,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[3,1,8,6,2,4,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,7,6,2,4,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[3,1,6,5,2,8,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[3,1,8,5,2,7,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,8,6,2,7,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,5,2,7,8,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[8,1,4,5,2,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,2,3,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,4,6,2,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,2,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,4,6,2,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,6,5,2,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,5,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,8,6,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,6,5,2,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,4,5,2,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,1,4,5,2,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,2,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,5,2,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,5,2,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[3,1,4,8,6,2,5,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,1,4,8,7,2,5,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,1,4,7,6,2,8,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[3,1,8,5,6,2,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,8,5,7,2,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,8,7,6,2,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,7,5,6,2,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[8,1,4,5,6,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,7,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,6,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,6,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,6,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,1,4,5,8,7,2,6]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[3,1,4,8,6,7,2,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,1,8,5,6,7,2,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,1,4,5,6,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,4,7,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,3,6,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,3,7,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,6,4,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,5,1,3,8,7,4,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,8,1,3,6,7,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,8,3,7,5,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,8,1,5,3,4,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,3,4,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,1,6,3,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,3,4,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,6,1,5,3,8,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,8,1,5,3,7,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,6,3,7,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,5,3,7,8,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[2,4,1,8,6,3,5,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,4,1,8,7,3,5,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,4,1,7,6,3,8,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[2,8,1,5,6,3,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,5,7,3,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,7,6,3,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,5,6,3,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,4,1,5,8,7,3,6]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[2,4,1,8,6,7,3,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,8,1,5,6,7,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,2,4,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,3,1,2,4,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,3,1,2,4,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,3,1,2,8,4,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,3,1,2,7,4,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[8,3,1,2,6,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,7,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,6,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,3,1,2,6,8,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[5,3,1,2,8,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[8,3,1,2,6,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,6,7,8,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[7,4,1,2,3,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,4,1,2,3,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,4,1,2,3,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,2,3,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[7,6,1,2,3,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,8,1,2,3,7,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,6,1,2,3,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,2,8,3,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,4,1,2,7,3,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[8,4,1,2,6,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,7,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,6,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,8,1,2,6,3,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,1,2,7,3,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,7,1,2,6,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,6,3,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,4,1,2,6,8,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[5,4,1,2,8,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[8,4,1,2,6,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,6,7,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,6,7,8,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[4,3,1,8,2,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,1,7,2,5,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[4,3,1,6,2,8,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[4,3,1,8,2,7,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,1,6,2,7,8,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[8,3,1,5,2,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,2,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,3,1,6,2,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,8,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,1,6,2,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,3,1,5,2,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,3,1,5,2,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,2,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,2,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[8,4,1,5,2,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,2,3,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,1,6,2,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,8,2,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,1,6,2,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,8,1,5,2,3,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,7,1,5,2,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,5,2,3,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,4,1,5,2,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,4,1,5,2,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,2,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,5,2,7,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,4,1,5,2,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,3,1,5,8,2,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[4,3,1,5,7,2,8,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[4,3,1,8,6,2,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,1,8,7,2,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,1,7,6,2,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[8,3,1,5,6,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,7,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,6,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,1,5,6,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,7,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,6,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,6,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,4,1,5,6,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,3,1,5,6,8,2,7]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[4,3,1,5,8,7,2,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[4,3,1,8,6,7,2,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[8,3,1,5,6,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,6,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,5,6,7,8,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[2,3,8,1,4,7,5,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,1,6,4,5,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,1,7,4,5,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,7,1,6,4,8,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,3,5,1,8,7,4,6]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,3,8,1,6,7,4,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,8,4,1,3,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,3,5,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,6,4,1,3,8,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,8,4,1,3,7,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,3,7,8,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[2,8,5,1,3,4,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,3,4,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,7,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,1,3,8,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,8,5,1,3,7,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,8,1,3,7,4,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,6,5,1,3,7,8,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[2,5,4,1,8,3,6,7]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,5,4,1,7,3,8,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[2,8,4,1,6,3,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,1,7,3,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,6,3,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,5,1,6,3,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,1,7,3,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,8,1,6,3,4,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,7,5,1,6,3,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,5,4,1,6,8,3,7]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[2,5,4,1,8,7,3,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,8,4,1,6,7,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,1,6,7,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,6,7,8,3]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[7,3,4,1,2,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,3,4,1,2,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,3,4,1,2,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,2,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[7,3,5,1,2,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,3,7,1,2,4,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,3,5,1,2,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,3,5,1,2,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,2,7,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,5,1,2,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[7,5,4,1,2,3,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,8,4,1,2,3,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,4,1,2,3,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,8,5,1,2,3,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,5,1,2,3,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,5,4,1,2,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,5,4,1,2,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,2,7,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,1,2,7,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,5,4,1,2,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,3,4,1,8,2,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,3,4,1,7,2,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[8,3,4,1,6,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,7,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,6,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,3,5,1,6,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,7,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,1,6,2,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,5,1,6,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,5,4,1,6,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,7,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,6,2,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,1,6,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,5,4,1,6,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,3,4,1,6,8,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[5,3,4,1,8,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[8,3,4,1,6,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,6,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,6,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,6,7,8,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[2,3,4,8,1,7,5,6]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,8,5,1,4,6,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,7,5,1,4,8,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,3,8,6,1,4,5,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,7,6,1,4,8,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,3,6,5,1,8,4,7]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,3,8,5,1,7,4,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,6,1,7,4,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,5,1,7,8,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[2,8,4,5,1,3,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,1,3,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,4,6,1,3,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,8,1,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,4,6,1,3,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,6,5,1,3,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,8,5,1,3,4,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,7,8,6,1,3,4,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,7,6,5,1,3,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,6,4,5,1,8,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,8,4,5,1,7,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,6,1,7,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,5,1,7,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,5,1,7,8,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[7,3,4,5,1,2,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,3,4,6,1,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,3,6,5,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,6,1,2,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,6,5,1,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,4,5,1,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,3,4,5,1,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,3,4,5,1,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,6,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,5,1,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,1,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,5,1,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[2,3,4,8,6,1,5,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,8,7,1,5,6]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,7,6,1,8,5]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,8,5,6,1,4,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,5,7,1,4,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,7,6,1,4,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,7,5,6,1,8,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,8,4,5,6,1,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,5,7,1,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,7,6,1,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,5,6,1,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,6,1,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[8,3,4,5,7,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,6,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,6,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,6,1,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,3,4,5,8,7,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,8,6,7,1,5]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,8,5,6,7,1,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,8,4,5,6,7,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,6,1,4,8,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[3,5,2,6,4,1,8,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[3,5,2,7,4,8,1,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[3,5,2,7,4,8,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[4,5,7,2,3,8,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[4,5,7,2,3,8,1,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[4,5,6,2,3,1,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[4,5,6,2,1,3,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[3,5,1,6,4,2,8,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[4,5,6,1,3,2,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[4,5,6,3,1,2,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[4,5,7,3,2,8,1,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[4,5,7,3,2,8,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[4,6,7,3,8,2,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[4,6,7,3,8,2,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[4,6,7,3,8,1,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[4,5,7,3,1,8,2,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[4,5,7,1,3,8,2,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[3,5,1,7,4,8,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[2,1,5,7,4,8,3,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[2,1,5,7,4,8,6,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[3,5,1,7,4,8,6,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[4,5,7,1,3,8,6,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[4,5,7,3,1,8,6,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[4,6,7,3,8,1,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[4,6,7,3,8,5,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[4,6,7,3,8,5,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[5,6,7,8,3,1,4,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[5,6,7,8,1,3,4,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[4,6,7,1,8,3,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[3,6,1,7,8,4,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[2,1,6,7,8,4,5,3]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,6,7,8,4,3,5]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,6,1,7,8,4,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[4,6,7,1,8,3,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[5,6,7,8,1,3,2,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[4,5,7,2,1,8,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[4,6,7,2,8,1,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[4,6,7,2,8,3,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[4,6,7,2,8,3,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[3,6,2,7,8,4,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,6,2,7,8,4,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,6,2,7,8,1,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,5,2,7,1,8,4,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[3,4,2,1,7,8,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[3,4,1,2,7,8,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[3,5,2,7,1,8,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[3,6,2,7,8,1,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,6,2,7,8,5,1,4]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,6,2,7,8,5,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[4,6,7,2,8,5,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[4,6,7,2,8,5,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[4,6,7,2,8,1,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[4,5,7,2,1,8,6,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[4,5,7,1,2,8,6,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[3,5,1,7,2,8,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[2,1,5,7,3,8,6,4]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[2,1,6,7,8,3,5,4]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,6,1,7,8,2,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[4,6,7,1,8,2,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[5,6,7,8,1,2,4,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[5,6,7,8,2,1,4,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[5,6,7,8,2,4,1,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[5,6,7,8,2,4,3,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[5,6,7,8,1,4,2,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[4,6,7,1,8,5,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[3,6,1,7,8,5,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[2,1,6,7,8,5,3,4]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,6,1,7,8,5,4,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[4,6,7,1,8,5,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[5,6,7,8,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[5,6,7,8,4,1,3,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[6,5,8,7,3,4,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,6,7,4,5,8,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[2,6,7,4,5,1,8,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,6,7,4,5,2,3,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,5,4,7,6,2,3,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[2,5,4,7,6,1,8,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[3,5,4,7,6,8,1,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[4,5,3,7,8,6,1,2]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[5,4,3,8,7,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,4,8,3,7,5,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,8,4,5,7,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,3,4,8,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,3,5,6,8,7,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[3,2,5,6,1,8,7,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[4,2,5,6,8,1,7,3]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[5,2,4,8,6,1,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,2,8,4,5,1,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,2,4,5,1,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,4,5,2,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,1,8,4,5,2,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,1,4,8,6,2,3,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,1,3,2,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[5,1,3,8,2,6,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,1,8,3,2,5,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,1,3,2,5,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,3,1,5,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,2,8,3,1,5,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,2,3,8,1,6,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,3,8,2,1,7,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,4,2,8,7,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,5,2,7,8,1,6,3]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[2,5,3,7,1,6,8,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,5,3,7,2,6,4,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,6,7,3,2,5,4,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[2,6,7,3,1,5,8,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[3,6,7,2,1,8,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[7,8,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,5,8,7,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,4,1,8,7,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,4,8,1,7,2,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,3,1,2,6,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,3,1,8,2,7,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,3,1,2,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,2,1,3,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[5,2,1,8,3,4,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,2,8,1,3,4,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,2,1,3,4,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,3,1,2,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[5,3,1,6,2,4,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[6,3,1,5,2,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,3,1,5,2,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,4,5,1,2,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,2,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,5,1,2,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,4,6,1,2,3,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[2,1,6,5,3,4,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[3,6,1,5,2,4,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[4,6,5,1,2,3,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[5,6,4,1,2,3,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[6,5,4,1,2,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,5,4,1,2,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,6,4,1,7,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,8,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,4,1,8,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[5,7,4,1,2,8,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[4,7,5,1,2,8,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,7,1,5,2,8,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[2,1,7,5,3,8,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,1,8,5,3,7,4,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,8,1,5,2,7,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,1,2,7,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,1,2,7,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,4,1,7,2,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,7,4,1,6,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,1,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,6,1,7,2,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,6,7,2,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,8,6,7,3,4,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,7,6,8,3,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[3,7,1,6,8,2,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,7,6,1,8,2,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,7,6,8,1,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,4,7,1,2,8,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,4,7,1,8,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,4,6,1,8,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,4,6,1,7,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,7,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,6,8,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,1,7,8,2,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,3,1,7,2,8,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[4,3,1,2,7,8,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[2,1,4,3,8,7,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[3,4,1,2,8,7,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[6,3,1,8,7,2,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,3,1,8,6,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,4,7,1,6,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,6,2,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,4,8,1,2,7,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,5,8,1,2,7,3,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,5,1,8,2,7,4,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[2,1,5,8,3,7,4,6]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,1,6,8,7,3,4,5]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[3,6,1,8,7,2,4,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,6,8,1,7,2,3,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[5,6,8,7,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[7,5,8,6,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,5,7,6,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,1,2,3,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,7,8,1,6,2,3,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,7,1,8,6,2,4,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,1,7,8,6,3,4,5]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[2,1,8,7,6,3,4,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,8,1,7,6,2,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,1,6,2,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,1,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,7,5,1,2,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,4,7,3,8,5,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,4,7,3,5,8,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,4,7,2,5,1,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,4,2,7,6,1,3,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,4,2,7,6,1,8,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[5,4,3,7,6,8,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,4,3,7,8,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[6,4,8,3,5,7,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,4,3,8,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,4,3,6,8,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,4,2,6,7,1,8,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[5,4,2,6,7,1,3,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[5,3,2,6,1,7,4,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[5,3,2,6,1,7,8,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[5,3,2,6,1,8,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[5,4,2,6,8,1,7,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,4,2,8,6,1,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,4,8,2,5,1,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,4,2,5,1,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,2,5,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,4,2,8,6,1,3,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,3,2,6,1,8,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[4,3,2,1,6,8,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[4,3,2,1,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[5,3,2,8,1,6,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,3,8,2,1,5,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,3,2,1,5,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,2,1,5,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,3,8,2,1,5,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,3,2,8,1,6,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,4,2,7,8,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,3,2,7,1,8,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,3,2,7,1,6,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[5,3,2,7,1,6,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[6,3,7,2,1,5,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,3,7,2,1,5,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,3,7,2,1,8,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,4,7,2,8,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,5,7,8,2,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,5,8,7,2,1,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,7,2,1,8,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,3,7,2,1,4,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,3,7,2,1,4,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[5,3,2,7,1,4,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[5,4,2,8,7,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[7,8,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,2,1,6,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,3,8,2,1,7,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,3,2,8,1,7,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,3,2,1,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,3,2,1,7,5,8,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[4,3,2,1,7,5,6,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[4,3,2,1,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[5,3,2,8,1,4,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,3,8,2,1,4,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,3,2,1,4,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,3,8,2,1,4,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,3,2,1,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,3,2,1,5,8,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[7,8,5,6,1,2,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,1,6,2,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,4,6,2,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,1,8,4,7,2,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,6,8,4,7,2,5,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,6,8,3,2,7,5,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,1,8,3,2,7,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,1,3,2,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,1,2,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,4,6,5,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,4,6,1,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,3,1,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,1,3,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,1,8,2,3,7,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,6,8,2,3,7,5,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,5,2,8,3,7,6,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,1,2,8,3,7,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,2,1,8,3,7,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,2,8,1,3,7,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,8,3,1,7,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,8,4,7,1,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,8,4,7,5,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,6,8,4,7,5,1,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[2,6,8,4,7,1,5,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,6,8,3,1,7,5,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,6,8,1,3,7,5,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,5,1,8,3,7,6,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,2,5,8,3,7,6,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,4,1,3,8,7,6,5]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,5,3,8,1,7,6,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,5,4,8,7,1,6,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[3,5,4,8,7,6,1,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[5,3,4,8,7,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,2,4,8,7,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,2,3,8,1,7,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,2,1,3,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,1,2,3,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,4,2,3,8,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[4,1,3,2,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,3,1,2,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[6,3,8,1,2,7,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,3,1,8,2,7,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,1,3,8,2,7,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,5,3,8,2,7,6,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,5,4,8,7,2,6,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,1,4,8,7,2,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,4,1,8,7,2,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,4,8,1,7,2,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,7,1,2,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,6,8,7,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,6,8,7,2,1,4,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,5,1,8,7,2,6,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,1,5,8,7,2,6,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[1,4,5,8,7,2,6,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,3,5,8,2,7,6,4]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[3,1,5,8,2,7,6,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[3,6,8,1,2,7,5,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,6,8,2,1,7,5,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[4,6,8,2,7,1,5,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,8,3,7,5,1,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,5,3,8,7,6,1,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,5,2,8,7,1,6,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,5,2,8,1,7,6,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,1,4,2,8,7,6,5]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[3,1,2,4,8,7,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[3,2,5,8,1,7,6,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[4,2,5,8,7,1,6,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,3,5,8,7,6,1,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[3,4,5,8,7,6,1,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[2,4,5,8,7,1,6,3]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[2,3,5,8,1,7,6,4]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[4,1,3,2,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[5,1,3,2,6,4,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[6,1,3,2,5,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,1,3,2,5,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,3,2,5,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,5,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,5,3,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,4,2,5,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,1,4,2,6,3,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[2,1,6,3,5,4,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[3,1,6,2,5,4,8,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[4,1,6,2,5,3,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[6,2,5,1,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,2,6,1,4,3,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[5,2,7,1,4,3,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,2,8,1,4,3,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,2,8,1,4,3,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,7,1,4,3,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[7,2,6,1,4,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,2,5,1,4,3,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,1,7,2,5,3,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[3,1,7,2,5,4,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[2,1,7,3,5,4,8,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[2,1,8,3,5,4,7,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,8,2,5,4,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,1,8,2,5,3,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,2,5,1,4,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,4,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,3,8,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,1,4,3,7,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,7,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,8,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,2,6,1,5,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,6,3,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,1,8,2,6,3,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,1,8,2,6,4,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,3,6,4,7,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,7,3,6,4,8,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[4,1,7,2,6,3,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[5,1,7,2,6,3,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[7,2,6,1,5,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,2,7,1,5,3,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,2,8,1,5,3,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,1,5,2,6,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,7,3,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,1,4,2,7,3,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[8,1,4,2,6,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,6,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,6,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,3,2,7,4,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[5,1,3,2,7,4,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[4,1,3,2,7,5,8,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[2,1,4,3,8,5,7,6]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[3,1,4,2,8,5,7,6]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[4,1,3,2,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[5,1,3,2,8,4,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,1,3,2,8,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,4,7,1,3,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,1,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,1,4,2,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,3,7,1,4,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,8,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,1,4,2,8,3,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[4,1,5,2,8,3,7,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[3,1,5,2,8,4,7,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[2,1,5,3,8,4,7,6]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[2,1,6,3,8,4,7,5]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[3,1,6,2,8,4,7,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[4,1,6,2,8,3,7,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[5,1,6,2,8,3,7,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[6,1,5,2,8,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,3,7,1,5,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,1,5,2,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,7,3,8,1,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,2,8,3,7,1,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,3,7,2,6,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,7,2,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,1,8,3,7,2,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,1,8,4,7,2,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,4,7,3,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,7,4,8,3,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[3,1,7,4,8,2,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[4,1,7,3,8,2,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[5,1,7,3,8,2,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[7,3,8,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,2,6,3,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,8,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,4,2,6,8,1,5,7]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[5,3,6,2,8,1,4,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,3,6,2,4,8,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[5,7,3,8,2,4,1,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,7,3,8,2,4,6,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[7,4,2,5,8,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,2,5,8,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,5,2,6,3,8,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[4,5,2,1,6,8,3,7]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[5,3,1,6,8,2,4,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,6,2,8,1,3,4,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[3,5,6,1,4,8,2,7]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[4,1,5,6,3,8,2,7]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[4,5,1,6,3,8,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[4,5,6,3,2,8,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[7,4,5,3,8,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,5,3,8,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,4,8,3,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,4,8,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,4,1,8,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,4,5,3,1,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,7,1,5,8,3,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,3,7,8,1,4,2,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[7,5,8,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,5,8,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,5,1,7,8,3,6,2]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[7,4,1,5,8,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,4,3,8,1,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,4,8,3,1,5,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,4,8,3,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,6,7,3,8,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[5,6,7,3,1,8,4,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[5,6,1,7,3,8,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[5,1,6,7,3,8,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[6,4,7,1,8,3,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,7,8,3,1,4,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,2,8,4,5,1,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,2,8,4,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,1,7,4,8,3,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,1,6,7,3,2,8,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[5,6,1,7,3,2,8,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[5,6,7,3,2,1,8,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[5,6,7,3,2,8,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[5,6,2,7,3,8,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[5,6,2,7,3,1,8,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[5,6,2,1,7,3,8,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[6,1,7,4,2,8,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,7,2,1,8,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,5,8,2,1,3,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,7,3,1,8,2,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[4,7,1,5,2,8,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[7,4,2,5,1,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,7,4,2,1,8,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,7,4,2,8,3,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,4,2,8,3,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[3,6,7,2,8,4,5,1]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[3,6,7,2,8,4,1,5]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[3,6,7,2,1,8,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[5,7,3,8,2,1,4,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,4,7,8,2,1,5,6]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[3,7,8,1,4,6,2,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,4,7,8,2,6,1,5]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[5,7,3,8,2,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,6,7,2,8,5,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[3,6,7,8,5,2,1,4]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[3,6,7,8,5,2,4,1]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[6,4,7,8,2,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,4,7,8,2,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[4,1,5,7,8,2,6,3]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[5,3,7,8,1,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[6,7,2,8,5,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,4,1,7,8,2,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,1,6,2,7,8,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[5,6,2,1,7,8,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[5,6,2,7,1,8,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[5,6,2,7,8,4,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[5,6,7,2,8,4,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[5,6,7,2,1,8,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[5,6,1,7,2,8,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[5,1,6,7,2,8,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[6,4,7,1,8,2,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[3,6,7,1,8,5,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[6,7,8,5,2,4,1,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,3,5,1,4,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[4,6,7,8,1,5,3,2]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[5,1,6,7,8,4,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[5,6,1,7,8,4,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[5,6,7,1,8,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[8,6,1,3,4,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,1,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,7,4,1,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[7,5,3,8,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,4,5,8,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,4,5,3,7,1,8,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[8,2,4,5,6,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,5,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,1,3,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,6,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,6,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,2,1,8,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[7,4,5,8,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,3,6,7,2,8,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[4,3,6,7,2,8,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[1,4,3,6,7,2,8,5]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[4,5,3,7,1,8,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[4,1,5,3,7,2,8,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[5,3,4,7,1,2,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[7,5,8,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,3,8,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,5,8,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,3,6,7,8,1,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[1,6,4,7,8,3,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[6,4,7,8,3,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[3,5,6,7,8,4,1,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[3,1,5,6,7,8,4,2]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[4,6,1,7,8,3,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[3,6,7,1,4,8,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[6,2,4,1,7,8,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[2,6,7,1,4,8,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[4,3,6,7,8,1,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[1,5,3,6,7,8,2,4]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[3,5,6,7,8,2,1,4]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[3,5,6,7,8,2,4,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[5,2,7,1,3,8,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,3,1,7,8,2,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[4,5,2,7,8,1,3,6]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[4,2,6,7,8,3,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[4,2,6,7,8,3,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[3,6,2,7,4,8,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[3,6,2,7,4,8,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[3,2,1,6,4,7,8,5]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[3,7,4,2,1,5,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,7,3,4,2,5,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,7,2,1,3,5,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[7,8,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,3,4,2,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,4,2,1,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,3,2,7,1,8,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[3,6,2,7,1,8,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[6,7,3,8,2,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,4,7,8,5,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[2,6,4,7,8,1,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[4,6,2,7,8,1,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[7,4,5,8,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,1,5,8,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,3,8,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,8,2,1,6,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,7,1,3,8,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,3,1,7,8,2,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[4,6,1,7,8,5,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[5,1,2,6,7,8,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[5,2,6,7,8,4,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[5,2,6,7,8,4,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[2,5,6,7,8,4,1,3]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,5,2,6,7,8,4,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,6,4,7,8,5,2,3]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[2,6,7,1,3,8,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[6,7,8,2,1,5,4,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,3,8,5,1,4,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,4,7,8,5,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[4,5,2,3,7,6,1,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[6,4,3,7,2,5,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[8,4,3,6,5,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,4,8,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,6,2,7,3,5,1,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[3,2,6,7,4,5,1,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[4,7,2,6,5,3,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[5,7,6,2,4,3,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,7,5,4,8,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[8,7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,2,1,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,6,2,4,1,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,2,6,5,1,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,6,5,1,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,6,5,8,7,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[5,1,6,2,4,8,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[6,1,5,4,2,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,1,5,4,8,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,1,5,4,7,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,4,5,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,7,4,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,4,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,1,7,8,2,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,1,7,2,8,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[4,1,2,7,8,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[3,2,1,7,8,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[3,2,8,7,1,5,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,8,2,7,1,5,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,2,1,4,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,7,1,2,4,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,6,1,4,2,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,6,1,4,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,4,3,5,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,6,7,8,3,4,5,2]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[8,6,7,1,3,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,3,2,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,7,8,2,1,3,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,7,2,8,1,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[3,2,6,8,4,1,5,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[4,6,2,8,3,1,5,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[5,6,8,2,3,1,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,5,8,3,2,1,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,5,8,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,5,7,3,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,8,4,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,4,3,7,8,5,6,2]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[8,4,3,7,1,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,2,1,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,5,2,3,8,1,6,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[3,2,5,4,8,1,6,7]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[4,5,2,3,1,8,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[6,4,3,1,2,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,4,3,1,8,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,4,3,1,7,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,7,6,4,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[8,5,1,3,7,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,8,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,1,3,2,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,6,1,2,3,8,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[4,6,2,1,3,8,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[3,2,6,1,4,8,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[3,2,7,1,8,4,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[4,7,2,1,8,3,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,7,1,2,8,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,7,1,8,2,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,6,1,8,3,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,6,1,7,3,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,3,5,4,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,7,8,6,5,3,4,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,7,1,6,5,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,5,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,1,7,2,5,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,1,2,7,6,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,2,1,7,6,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,1,7,6,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,8,7,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[5,1,8,2,7,6,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,1,8,7,2,5,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,1,8,6,5,2,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,1,7,6,5,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,5,8,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[3,1,6,2,4,8,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[3,1,5,2,4,8,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[4,5,1,2,3,8,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[4,6,1,2,3,8,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[1,6,5,3,4,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[6,1,5,2,4,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,5,1,2,3,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,4,1,2,3,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,4,1,2,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,4,1,2,7,3,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[6,4,1,7,2,3,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,4,1,8,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,4,1,2,8,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,1,2,8,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,5,2,8,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,7,5,3,8,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,8,5,3,7,4,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,5,2,7,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,7,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,7,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,2,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,2,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,6,1,7,2,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,2,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,3,4,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,8,3,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,1,6,8,2,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,1,8,2,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,7,1,2,8,3,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[3,1,7,2,8,4,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[3,1,2,7,8,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[1,4,3,8,7,5,6,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[4,1,2,8,7,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,1,2,8,7,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,1,8,2,7,4,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,8,7,2,4,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,7,6,2,4,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[4,7,1,6,2,3,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,8,1,6,2,3,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,7,2,3,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,2,7,3,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,2,7,3,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,1,8,2,7,4,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,5,8,3,7,4,6,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,6,8,7,3,4,5,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,1,8,7,2,4,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,1,7,2,3,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,7,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,7,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,1,2,3,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,2,3,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[7,8,1,6,2,3,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,8,6,2,4,5,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,7,8,6,3,4,5,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,8,7,6,3,4,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,7,6,2,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,2,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,6,4,8,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[3,2,5,4,7,1,8,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[4,2,5,3,7,6,8,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,2,5,3,7,1,8,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,2,5,3,6,1,8,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,2,5,1,6,3,8,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[3,1,5,4,6,2,8,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[4,1,5,3,6,2,8,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,3,5,1,6,2,8,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,3,5,2,7,1,8,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,3,6,2,7,5,8,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,3,6,2,7,1,8,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,3,6,1,7,2,8,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,3,5,1,7,2,8,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[3,1,5,4,7,2,8,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,1,5,4,7,3,8,6]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,5,4,7,6,8,2]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[4,1,5,3,7,6,8,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,3,5,1,7,6,8,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,3,6,1,7,5,8,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,3,6,5,7,1,8,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[5,3,6,4,7,2,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,3,6,4,7,1,8,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,3,6,1,7,4,8,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,1,6,3,7,4,8,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,1,6,3,7,5,8,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,1,6,4,7,5,8,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[2,1,6,4,7,5,8,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[2,1,6,4,7,3,8,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[3,1,6,4,7,2,8,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[4,1,6,3,7,2,8,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[5,1,6,3,7,2,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,3,6,1,7,2,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,3,6,2,7,1,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,3,6,2,7,4,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,2,6,3,7,4,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,2,6,3,7,1,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,2,6,1,7,3,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,2,5,1,7,3,8,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,2,6,1,7,3,8,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,2,6,3,7,1,8,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,2,6,3,7,5,8,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,2,6,4,7,5,8,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,2,6,4,7,1,8,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,2,6,1,7,4,8,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,2,5,1,7,4,8,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[3,2,4,1,7,5,8,6]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[3,1,4,2,7,6,8,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[3,2,5,1,7,6,8,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[3,2,6,1,7,5,8,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,2,6,5,7,1,8,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[4,2,6,5,7,3,8,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,2,6,5,7,1,8,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,2,6,1,7,5,8,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,2,5,1,7,6,8,3]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,1,5,2,7,6,8,3]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[3,1,5,2,7,6,8,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,1,5,3,7,6,8,4]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[2,1,6,3,7,5,8,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[3,1,6,2,7,5,8,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[4,1,6,2,7,5,8,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[5,1,6,2,7,4,8,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,2,6,1,7,4,8,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,2,6,4,7,1,8,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,2,6,4,7,3,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,4,6,2,7,3,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,4,6,2,7,1,8,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,4,6,1,7,2,8,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,1,6,4,7,2,8,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,1,6,5,7,2,8,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,1,6,5,7,2,8,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[2,1,6,5,7,3,8,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[3,1,6,5,7,4,8,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[4,1,6,5,7,3,8,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[5,1,6,4,7,3,8,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,4,6,1,7,3,8,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,4,6,3,7,1,8,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[8,3,5,2,1,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,2,4,1,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[8,3,7,5,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,7,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,7,3,1,8,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[8,2,4,6,5,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,4,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,1,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,5,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,3,2,1,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,2,7,5,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,7,6,3,2,8,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,4,6,7,3,2,8,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[5,4,7,3,1,8,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[1,7,4,5,3,2,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,7,5,1,4,2,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[5,7,4,2,1,3,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[8,5,7,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,1,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,5,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,7,1,5,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[1,7,4,8,6,3,5,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[8,4,7,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,8,7,4,1,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,1,5,8,6,7,4,2]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[4,8,1,6,7,3,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,1,8,7,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[8,2,6,1,4,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,1,4,3,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,1,6,4,8,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,3,5,6,8,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,3,6,7,5,8,2,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[3,7,6,5,8,2,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,6,8,5,7,2,4,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[2,3,5,7,6,8,1,4]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[2,1,6,5,7,8,3,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[4,2,7,6,8,3,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,2,6,8,7,3,5,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[3,8,2,4,6,7,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,4,8,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,2,6,1,4,7,8,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[5,3,7,2,1,8,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[4,7,3,2,1,5,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[8,7,6,1,3,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,7,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,6,2,1,5,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[8,7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,8,1,6,5,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[4,6,8,2,1,7,5,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[8,4,1,5,7,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,1,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,1,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,7,1,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,7,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,8,7,2,5,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[8,1,2,5,6,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,7,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,5,6,4,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[8,2,5,7,6,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,8,5,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,2,5,8,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,4,8,2,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,8,1,6,5,2,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[2,7,8,6,1,3,5,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,5,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,6,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,2,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,6,3,5,1,2,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[8,5,3,7,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,5,7,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,7,2,4,5,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,4,5,1,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[2,6,1,4,5,3,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[6,1,2,4,5,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,6,3,2,1,4,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[5,4,3,6,1,2,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[6,3,1,4,5,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[3,1,6,4,5,2,8,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[8,3,7,4,5,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,2,6,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,8,7,4,1,6,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,7,4,2,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,5,1,2,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[2,1,8,7,5,3,4,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,8,5,7,3,4]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[5,6,3,8,1,7,2,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[7,6,1,4,5,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,7,6,4,5,8,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[8,5,7,4,1,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,7,6,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,5,8,4,7,6,1,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,4,8,3,5,6,7,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,1,8,3,5,6,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,8,4,2,5,6,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,1,3,5,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,5,3,8,4,1,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,1,5,8,4,6,7,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,1,4,8,3,6,7,5]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[6,4,3,8,2,1,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,3,8,4,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,3,1,2,5,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,5,6,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,1,5,6,7,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,3,8,2,5,6,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,2,3,5,6,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,1,5,6,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,3,5,6,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,2,3,5,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,3,6,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,3,2,4,1,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,1,8,3,4,6,7,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,7,8,5,4,3,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[5,7,3,8,1,4,2,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[7,1,8,4,5,3,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,8,4,5,3,1,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,7,1,4,3,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,2,6,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,8,4,3,6,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,6,3,8,4,2,7,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,8,3,6,2,1,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,6,3,1,4,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,4,3,1,8,5,7,6]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[4,1,3,2,6,8,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[7,5,3,6,2,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,6,3,5,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,6,1,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,5,3,8,6,2,7,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,5,8,4,7,6,2,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[5,8,2,4,7,6,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,7,5,4,1,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,5,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,1,6,4,5,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,7,3,6,1,8,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[2,1,7,6,5,8,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,1,8,5,3,6,7,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,8,3,5,2,1,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,1,4,2,5,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,5,6,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,2,5,6,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,1,5,6,7,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,2,8,5,6,7,1]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[2,4,1,8,5,6,7,3]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[4,1,2,8,5,6,7,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[8,4,2,1,5,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,4,8,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,3,2,8,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,1,5,3,8,6,7,4]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[6,4,3,5,8,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,3,5,4,8,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,3,4,1,5,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,5,6,7,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,1,4,8,5,6,7,2]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[6,5,3,7,2,8,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,3,7,4,5,8,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,7,2,4,5,8,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,1,7,4,8,6,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[2,5,7,4,8,6,3,1]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[5,6,3,7,1,8,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[3,8,7,4,5,2,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,8,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[5,7,1,4,8,6,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,6,3,1,8,2,7,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[4,6,3,5,8,2,7,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,6,3,8,1,2,7,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[3,7,8,4,1,6,2,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,2,5,1,6,8,4,7]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[3,6,2,5,4,8,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[3,5,2,4,7,1,8,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[3,5,8,2,4,7,6,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[4,2,5,8,3,7,6,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,2,6,5,3,8,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[5,4,2,1,6,8,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[6,3,5,1,4,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,6,1,5,3,8,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[5,1,6,4,3,8,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[5,4,3,2,7,1,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[5,4,3,8,2,7,6,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,3,6,2,8,7,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,3,7,6,2,1,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[6,4,3,1,7,2,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[7,5,4,3,1,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,4,7,5,8,3,2,6]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[7,1,3,5,8,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,5,8,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,8,5,7,4,6,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,8,7,1,4,6,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,5,8,7,3,6,2]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,5,4,8,7,3,6,2]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[6,4,3,8,1,7,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,3,7,1,8,6,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,8,3,7,6,5,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,3,8,7,6,4,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,5,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,8,6,5,3,7,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,8,6,3,7,4,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,6,1,8,7,3,5,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[6,8,7,3,1,4,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,2,8,7,4,5,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,6,2,8,4,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,1,6,8,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,7,6,4,8,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,7,1,6,3,2,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[6,1,7,5,3,2,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[7,6,5,3,2,1,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,5,3,2,8,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,2,6,3,8,7,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,2,7,6,3,1,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[6,5,2,1,7,3,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[5,2,7,4,1,8,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[4,7,2,6,3,1,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[2,4,8,6,3,7,5,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,8,6,2,4,7,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,4,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,6,7,2,1,4,8,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[4,3,7,8,2,1,5,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[8,3,7,1,4,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,5,7,1,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,6,2,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,2,1,6,5,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,2,6,8,1,7,5,3]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[5,4,8,2,7,1,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,8,1,5,7,2,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,7,1,6,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,2,6,1,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,6,2,7,5,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,7,5,2,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,1,6,8,2,7,4,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,5,2,8,1,7,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,2,7,1,8,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,8,2,7,6,4,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,2,8,7,5,4,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,6,2,1,8,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,1,7,2,8,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,5,1,8,2,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,7,1,8,6,2,5,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[7,8,3,1,6,5,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,6,1,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,6,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,5,4,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,1,8,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,4,2,3,7,6,1,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[6,4,2,7,3,5,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[7,4,2,6,3,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,4,2,6,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,6,4,5,1,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[4,7,2,6,3,5,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[5,7,6,2,3,4,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,6,5,2,3,8,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,7,5,2,8,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,8,5,2,3,1,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,6,2,3,1,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,2,6,3,1,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,6,4,1,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,6,4,8,5,7]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[7,1,5,2,8,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,8,5,2,7,3,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,7,2,3,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,7,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,2,1,7,8,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[3,2,8,7,1,4,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[5,8,7,2,1,3,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,7,6,8,2,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,8,2,3,1,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,5,7,2,1,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,8,3,1,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,4,2,3,8,1,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[3,2,5,4,1,8,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[4,5,2,3,1,8,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[5,4,2,3,1,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[6,4,2,1,3,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,4,2,1,8,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,4,2,1,7,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,8,7,3,5,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,5,8,2,7,3,4,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[8,5,1,2,7,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,2,8,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,1,2,3,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,6,2,1,3,8,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[3,2,6,1,4,8,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[3,2,7,1,8,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[4,7,2,1,8,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[7,6,1,8,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,6,1,7,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,7,8,6,2,3,4,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,8,1,6,2,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,1,7,2,3,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,2,1,7,3,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,1,7,4,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,8,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,1,8,2,7,3,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,1,8,7,2,3,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,1,7,6,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,2,3,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,2,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,3,5,6,1,2,8,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[8,3,7,5,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,1,8,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,5,2,7,1,8,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[8,5,2,7,4,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,5,4,3,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[6,4,3,5,1,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,3,1,4,6,2,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[3,1,4,6,5,2,8,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[5,7,4,6,2,8,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[8,1,4,7,2,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,8,5,2,1,6]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[2,1,8,5,7,3,4,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,6,3,5,1,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,6,7,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,4,8,6,5,7,1,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[7,5,4,8,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,1,4,6,8,2,7,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[2,5,4,6,7,1,8,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[2,4,6,3,7,5,8,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[4,1,6,3,8,5,7,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[3,7,4,2,8,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[7,4,1,3,5,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,5,8,4,1,7,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,5,3,7,4,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,3,7,6,5]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[7,4,3,8,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,3,7,4,1,8,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[8,3,1,2,5,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,7,6,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,1,6,7,5,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,3,7,2,6,8,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,7,2,3,8,5,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[3,8,2,1,7,5,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,3,6,5,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,8,5,4,3,1,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,7,1,6,3,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,2,4,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,8,7,4,2,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,3,8,7,2,1,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,3,6,1,4,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,3,4,1,8,5,7,6]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[4,1,3,2,6,7,8,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[8,3,5,6,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,1,8,7,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,6,2,8,7,4,1,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[7,8,5,6,1,4,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,8,6,5,4,7,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,4,5,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,1,7,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,1,8,6,5,7,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,7,5,3,6,8,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[6,7,3,5,2,1,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,1,4,2,5,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,7,4,1,6,5,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,6,1,2,8,7,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[2,4,1,5,8,7,6,3]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[4,1,2,5,8,6,7,3]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[6,4,2,1,5,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,5,2,4,6,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,6,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,1,5,3,6,8,7,4]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[7,3,5,4,6,1,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,3,4,1,5,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,3,1,5,7,6,8,2]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[3,1,4,5,6,8,7,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[4,5,2,6,3,1,8,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[6,5,2,1,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,5,2,7,4,8,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[8,5,2,7,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,5,2,8,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[3,1,6,5,4,2,8,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[5,6,3,2,4,1,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[3,6,2,4,1,5,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[2,6,1,3,5,4,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[6,7,2,3,4,8,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[8,7,2,3,4,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,8,4,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[2,5,7,3,8,6,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[7,6,1,3,5,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,6,7,4,1,8,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[5,6,3,7,4,8,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[2,1,6,7,4,8,5,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[2,1,8,7,4,3,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,8,3,7,4,2,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,7,4,1,2,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,1,3,5,2,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,8,7,3,2,6,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,8,6,3,1,5,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,3,2,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,6,3,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,2,7,6,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,2,5,7,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,3,5,2,7,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,1,5,3,8,7,6,4]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[6,5,3,2,8,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,5,2,4,8,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,4,2,8,5,7,6,1]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[2,4,1,8,7,6,5,3]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[8,4,2,1,7,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,8,6,7,5,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,1,4,8,6,5,7,2]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[7,1,6,5,4,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,7,5,6,8,4,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[5,7,1,6,8,2,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[8,6,2,5,1,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,1,8,7,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[4,6,2,5,8,3,7,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[7,5,2,6,3,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,1,2,3,6,8,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[2,4,3,1,8,5,6,7]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[7,5,2,8,3,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,6,2,8,4,3,1,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,7,2,8,1,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[8,7,2,1,4,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,7,1,5,4,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,8,6,3,4,1,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[7,1,8,5,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,8,4,5,3,6,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[5,7,3,8,1,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[2,1,7,8,5,4,6,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[2,1,5,8,4,6,3,7]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[6,5,3,8,4,1,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,5,8,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,4,8,3,5,6,1,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,1,8,3,6,5,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,1,7,2,5,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[8,4,1,3,7,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,4,7,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,1,4,6,7,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,3,8,2,5,1,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,3,8,4,2,5,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,4,3,8,2,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,1,4,8,3,5,7,6]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[6,8,2,4,3,5,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,2,3,5,1,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,1,4,6,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,3,4,5,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,1,6,5,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,1,6,5,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,6,1,4,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,6,7,4,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,8,6,1,4,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,5,7,6,1,4,2,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,5,7,2,4,1,6,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[7,5,8,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,8,5,3,4,7,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,3,4,1,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,3,4,1,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,6,1,4,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,3,6,1,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,6,7,4,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,3,4,7,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,3,4,6,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,3,4,6,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,2,4,6,1,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[6,5,2,7,3,1,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,5,2,8,3,1,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,2,8,3,1,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,5,8,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,6,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,5,8,2,1,3,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,5,6,2,1,8,7,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[3,5,7,6,1,4,8,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,5,7,2,4,1,8,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,5,7,2,4,6,8,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[6,5,2,7,3,1,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[4,5,2,6,3,1,7,8]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[4,1,2,3,7,6,8,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[6,5,2,7,3,4,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,1,6,7,4,3,8,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[5,1,2,6,4,8,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[5,1,2,8,6,4,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,1,6,8,7,3,4,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,5,2,8,3,7,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,1,2,3,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,1,2,3,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,1,2,3,8,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,1,2,3,7,6,5,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[4,1,2,3,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[7,1,6,8,4,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,1,2,8,4,5,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,6,8,2,3,1,7,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,5,8,2,4,3,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,2,4,3,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,5,2,8,3,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,2,8,3,7,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,2,7,3,4,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[5,1,6,7,4,3,2,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[5,1,6,8,7,3,2,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[7,1,6,8,4,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,7,8,6,3,4,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,1,8,3,6,5,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,8,3,6,2,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,1,4,8,6,2,7,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,1,4,8,6,5,2,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[7,1,6,5,8,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,1,6,7,8,3,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[4,1,6,5,7,3,2,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[4,5,2,6,3,7,1,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[4,5,2,7,3,8,1,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[3,5,6,2,4,8,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[3,5,6,2,4,8,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[3,7,5,6,8,4,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,6,5,2,8,1,7,4]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[6,1,2,5,8,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,1,6,5,8,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,2,6,3,8,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,1,2,3,5,8,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[4,1,2,3,7,8,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[4,5,2,7,3,8,6,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[4,1,6,7,8,3,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[4,1,2,6,8,5,7,3]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[4,1,2,5,6,8,7,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[4,5,2,6,3,7,8,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[7,8,5,6,1,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,2,1,5,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,1,6,5,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,4,1,2,5,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[2,4,8,1,5,7,3,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,1,7,2,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,3,1,4,7,2,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[7,8,3,4,5,1,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,5,4,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,1,2,3,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,6,5,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,1,5,3,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,6,4,1,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,5,6,4,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,2,1,7,5,4,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[2,1,8,7,5,4,3,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,2,6,4,7,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[5,3,7,1,6,4,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,3,6,2,7,4,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[6,1,2,5,8,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,3,1,8,4,2,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,2,1,5,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,4,3,7,5,8,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[4,3,8,7,5,6,1,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,4,7,1,5,3,6,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,3,7,6,4,2,8,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,1,7,5,6,8,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[3,7,2,8,6,4,1,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,8,1,7,6,4,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,7,3,6,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,8,3,6,1,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,5,6,8,2,4,7,3]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[2,6,8,5,3,1,4,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,6,1,4,7,3,5,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,6,7,3,8,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[5,2,8,1,4,7,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,6,7,5,2,1,3,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[4,5,6,7,2,8,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[4,5,7,6,1,8,3,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[1,5,8,6,2,7,3,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,6,5,8,3,2,7,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[4,6,5,7,1,2,8,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[4,7,5,6,3,1,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[5,1,6,3,4,2,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[5,7,1,4,2,3,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,7,6,4,3,8,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,3,4,5,8,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,2,4,1,8,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,2,3,5,4,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,1,3,4,5,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,1,4,2,7,6,8,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[1,6,2,4,7,8,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,7,2,4,1,6,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,1,4,2,8,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,7,5,8,1,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,8,7,6,3,4,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,2,3,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,6,5,3,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[4,8,2,1,5,6,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,8,1,6,3,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[2,1,8,7,6,5,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,7,8,2,6,5]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[3,1,7,4,5,6,8,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[4,2,7,1,6,3,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,3,7,5,6,8,1,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,8,6,3,5,7,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,2,5,3,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,5,2,4,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,6,1,4,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,8,2,1,6,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,2,8,7,1,6,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,6,8,7,5,2,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,6,7,8,5,1,4,2]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[3,7,6,8,5,2,1,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,8,5,1,2,4,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,1,6,4,2,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[4,1,8,6,2,3,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,7,8,6,3,5,1,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,8,7,6,5,4,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,5,3,4,8]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,8,1,6,4,5,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,5,1,4,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,7,5,1,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,8,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,3,1,2,7,4,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,4,2,7,1,3,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,4,2,5,1,3,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,3,6,1,8,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,5,3,6,1,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,4,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,4,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,3,7,1,2,5,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[3,6,2,7,1,4,8,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[5,3,6,7,1,2,8,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[6,3,7,4,1,2,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[4,7,1,5,2,3,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,7,5,1,2,4,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[7,6,4,2,3,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,6,4,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,3,8,1,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,7,4,2,3,8,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[3,7,6,1,4,8,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[5,7,2,6,1,8,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,4,7,5,2,8,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[7,4,8,5,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,8,2,6,3,7,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,6,1,2,7,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,2,4,7,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,4,3,7,1,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,3,7,1,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,5,7,1,2,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,7,1,3,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,2,7,1,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,3,8,5,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,3,7,5,8,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[2,7,6,4,8,1,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,6,5,8,1,3,4,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[3,6,5,8,1,2,4,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,5,7,4,8,1,3,6]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[5,4,6,7,2,8,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[4,6,3,7,1,8,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[3,5,7,1,4,8,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[5,3,7,2,4,8,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,4,7,3,8,1,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[7,4,6,3,8,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,4,6,3,7,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,7,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,8,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,4,1,7,8,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[6,5,3,7,1,8,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,5,1,2,7,8,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,3,6,4,7,8,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[6,3,7,4,8,5,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[4,7,1,5,8,6,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[7,5,1,2,8,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,3,8,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,1,8,6,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,1,8,5,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,6,1,7,5,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,8,1,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[6,4,7,8,2,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,3,7,8,5,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[3,6,8,2,7,1,4,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[2,4,8,7,1,3,5,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,7,1,2,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,3,8,7,1,2,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,3,7,6,1,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,1,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,1,2,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,5,8,7,1,2,4,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,5,8,7,1,3,4,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,6,8,2,7,1,3,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,7,1,8,6,2,3,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[7,5,8,6,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,4,7,5,1,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,7,1,6,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,8,7,6,1,3,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,6,1,2,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,6,1,2,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,6,3,1,4,2,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[7,5,3,8,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,8,7,4,5,1,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,5,8,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[2,1,7,8,5,3,6,4]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[5,7,3,8,1,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[8,7,1,4,5,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,1,6,5,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,1,8,4,2,6,5,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,1,4,8,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,3,1,8,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,4,3,8,1,5,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,6,3,1,2,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,2,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,6,4,5,7,2,8,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[5,3,2,7,4,6,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[7,5,3,6,2,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,3,2,5,1,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,5,3,6,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,4,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,4,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,2,7,3,4,5,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[3,6,2,7,4,5,8,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[4,2,5,7,3,6,8,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[5,4,7,6,2,3,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[6,7,3,5,2,4,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[3,7,6,2,4,5,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[2,7,6,3,4,5,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,3,1,2,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,6,5,2,3,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,7,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,1,8,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,6,3,2,8,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,7,3,1,2,8,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,6,2,3,1,8,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[4,2,6,5,1,8,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[5,4,8,6,2,7,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,8,3,5,2,7,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,5,2,3,6,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,2,1,7,3,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,6,3,7,2,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,7,3,4,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,7,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,1,7,2,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,5,7,2,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,2,8,3,7,1,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,7,5,8,2,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[1,7,3,8,2,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[8,1,2,7,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,1,8,3,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[3,6,2,7,1,8,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[6,3,7,1,2,8,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[7,2,6,1,8,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,2,6,1,7,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,8,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,2,1,5,8,4,6,7]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[5,4,1,3,6,8,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[1,5,3,4,6,8,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,3,5,1,6,8,2,7]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[5,4,6,3,8,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[3,6,4,5,8,7,1,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[6,5,3,4,8,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,3,2,8,7,1,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,3,1,8,7,2,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,5,3,7,6,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,7,2,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,8,1,7,2,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,6,8,2,3,5,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,7,8,2,4,6,1,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,3,8,2,5,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,4,7,8,2,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,2,5,8,7,1,3,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[3,6,2,8,7,1,4,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,7,8,1,6,2,4,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[2,3,8,7,1,4,5,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[7,2,8,6,1,3,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,1,8,7,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,2,7,6,1,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,3,4,5,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,7,2,4,5,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,7,8,3,6,2,4,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[4,1,5,8,7,2,3,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[5,4,8,7,6,1,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,8,3,7,5,1,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,6,2,5,1,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,1,6,7,3,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,3,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,7,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,6,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,6,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,8,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,1,3,2,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,1,4,3,2,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,2,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,6,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,6,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,2,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,2,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,2,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,2,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,8,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,4,3,8,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,3,1,2,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,4,1,3,2,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,1,3,2,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,1,3,6,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,1,4,6,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,8,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,3,2,5,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,4,3,8,2,5,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,3,7,2,5,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,4,3,2,8,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,4,3,2,8,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,5,3,8,7,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,4,8,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,4,1,7,8,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,5,3,1,7,2,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,4,3,1,2,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,4,3,2,1,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[6,5,3,1,8,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,4,1,8,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,5,1,4,8,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,1,3,2,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,4,1,3,2,8,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,3,1,2,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,4,3,1,2,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,4,3,8,2,7,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,3,8,7,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,3,1,7,2,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,5,3,1,8,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,5,1,3,8,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,1,8,3,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,1,8,4,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,8,1,4,5,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,8,1,3,2,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,5,3,7,8,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,4,3,7,2,8,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,4,3,7,2,1,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[7,4,8,3,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,4,1,6,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,5,4,8,1,7,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,3,8,1,2,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,4,3,2,8,1,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,4,3,7,2,1,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,5,3,7,1,2,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,5,4,7,1,8,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,5,3,7,8,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,4,3,7,2,8,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,4,3,2,7,8,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[5,4,3,2,6,8,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[5,6,2,1,3,4,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[5,8,2,7,4,1,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,3,7,8,2,1,4,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[7,6,1,2,5,8,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,1,7,8,4,3,5,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[8,3,7,4,1,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,5,4,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,6,8,3,1,4,7,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,1,8,3,2,4,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,4,1,3,7,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,2,1,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,8,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,2,1,8,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,7,2,8,1,3,6,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[7,3,8,6,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,4,7,1,8,2,6,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[1,8,2,4,3,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,3,5,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,6,2,4,3,5,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,5,2,4,3,6,7,8]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,6,2,5,3,4,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,7,2,5,3,4,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,2,5,3,4,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,6,3,4,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,3,4,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,2,7,3,5,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,8,3,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,6,2,8,3,5,4,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,5,2,8,3,6,4,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,4,2,8,3,6,5,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,3,2,8,4,6,5,7]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,8,4,6,5,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,7,4,6,5,8]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,3,2,7,4,6,5,8]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,4,2,7,3,6,5,8]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,5,2,7,3,6,4,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,6,2,7,3,5,4,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,7,2,6,3,5,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,2,6,3,5,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,5,3,6,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,3,6,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,6,2,5,3,7,4,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,5,2,4,3,7,6,8]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,6,2,4,3,7,5,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,7,2,4,3,6,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,2,4,3,6,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,3,4,6,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,4,6,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,2,3,4,7,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,4,3,7,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,3,8,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,6,2,4,3,8,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,5,2,4,3,8,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,6,2,5,3,8,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,7,2,5,3,8,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,8,2,5,3,7,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,6,3,7,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,3,8,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,2,3,8,4,7,5,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,3,2,8,4,7,5,6]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,4,2,8,3,7,5,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,5,2,8,3,7,4,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,6,2,8,3,7,4,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,7,2,8,3,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,8,2,7,3,6,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,7,2,5,1,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[4,6,3,7,5,2,1,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[4,6,3,8,5,1,7,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,6,3,8,5,1,2,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[5,6,8,3,4,1,2,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,6,8,3,4,1,7,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,6,2,7,5,3,1,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[5,6,7,2,4,3,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[5,6,8,4,3,1,7,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,6,8,4,3,1,2,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,7,8,4,1,6,2,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,4,1,6,3,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,4,1,3,6,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,6,8,4,2,1,7,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,6,8,2,4,1,7,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,6,2,8,5,1,7,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[3,2,6,8,5,1,7,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[3,2,6,8,5,1,4,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[4,6,2,8,5,1,3,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[5,6,8,2,4,1,3,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,6,8,4,2,1,3,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,7,8,4,1,3,2,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,4,1,2,6,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,4,1,2,3,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[6,7,8,1,5,2,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,5,2,4,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,5,3,2,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,3,5,2,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[5,7,8,2,1,6,3,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,7,2,8,1,6,3,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[3,2,7,8,1,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[3,2,7,8,1,6,5,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[4,7,2,8,1,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[5,7,8,2,1,6,4,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[6,7,8,1,3,5,4,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,5,3,4,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,5,4,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,4,5,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,4,5,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,4,3,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,3,4,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[5,7,8,2,1,4,6,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,7,2,8,1,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[3,2,7,8,1,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[3,2,6,8,4,1,7,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[4,6,2,8,3,1,7,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[5,6,8,3,2,1,7,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,7,8,3,1,4,6,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,3,1,6,4,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,3,1,6,2,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,7,3,8,1,6,2,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,3,8,1,6,5,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,3,8,1,5,6,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,6,3,8,2,1,7,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,5,3,2,8,1,7,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[4,5,2,3,8,1,7,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[3,2,5,4,8,1,7,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[4,5,3,2,8,1,6,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[4,6,3,8,2,1,5,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,7,3,8,1,5,2,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,3,8,1,2,6,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,3,8,1,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[5,7,8,3,1,2,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,3,1,2,6,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,3,1,4,2,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,6,8,3,2,1,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[3,2,7,8,1,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[5,7,8,2,1,4,3,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[6,7,8,1,3,4,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,4,3,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,4,2,5,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,4,2,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,2,5,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,2,5,4,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,2,4,5,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,3,2,5,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[5,7,8,2,1,3,6,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[3,2,7,8,1,4,6,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[6,7,8,1,3,2,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,2,4,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,1,2,3,5,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[7,2,8,5,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,3,7,5,2,6,4,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,3,7,5,4,2,6,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[7,2,8,5,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,8,5,4,3,1,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,5,6,1,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,5,7,3,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,5,3,7,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,3,5,6,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,8,4,5,6,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,6,3,7,5,2,4,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[6,2,3,8,5,1,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,2,8,5,1,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,4,8,2,5,6,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,5,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,4,8,5,1,3,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,7,5,2,1,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[4,3,7,5,1,2,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,3,7,1,5,6,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[3,6,1,7,5,2,8,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[3,4,1,2,7,6,8,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[3,4,2,1,7,5,8,6]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[3,6,5,7,1,4,8,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[6,5,2,7,4,1,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[3,5,2,6,4,8,7,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[5,3,1,8,6,4,7,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,6,1,8,7,2,4,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[6,3,5,8,2,7,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,8,4,2,3,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,5,8,3,7,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,6,5,7,3,4,2,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,5,2,7,4,6,3,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[5,2,1,8,7,6,3,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[7,1,3,8,4,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,3,4,8,6,1,7,5]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,8,6,5,1,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,7,3,5,8,6,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,2,4,7,8,6,1,5]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[1,5,4,6,2,7,3,8]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[5,2,4,7,1,8,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,3,6,4,1,8,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[5,3,6,1,4,8,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[7,3,5,6,8,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,5,1,8,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,6,1,5,8,4,7,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,7,6,5,8,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,7,1,6,3,8,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[3,2,4,1,7,8,5,6]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[3,1,4,2,7,8,6,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[5,1,4,7,2,8,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[3,6,4,7,8,2,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,1,4,6,8,5,7,2]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[6,3,4,5,7,1,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[2,5,4,6,1,7,8,3]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[7,2,1,4,3,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,4,1,2,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,3,2,1,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,3,2,5,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,3,2,5,4,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,8,3,2,5,4,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,5,2,3,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,1,6,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,1,5,6,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,1,6,5,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,6,1,5,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,6,5,1,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,8,5,4,3,2,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,4,3,7,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,7,4,3,1,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,4,7,5,1,3,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,3,7,1,5,4,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,2,1,7,5,4,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[3,2,1,8,5,4,7,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[2,3,8,1,5,4,7,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,4,8,5,1,3,7,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,5,8,4,3,1,7,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,6,8,4,3,7,1,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,7,8,4,3,6,5,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,8,7,4,3,6,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,5,6,3,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,8,5,6,3,4,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,6,8,5,7,3,1,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,5,8,6,7,1,3,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,4,8,6,1,7,3,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,2,1,8,6,7,4,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,2,1,7,6,8,4,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,3,7,1,6,8,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,4,7,6,1,8,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[4,5,7,6,8,1,3,2]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[4,6,7,5,8,3,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[1,8,6,5,7,3,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,6,7,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,8,2,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,6,5,7,8,2,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[5,4,6,7,1,8,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[5,3,6,1,7,8,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[5,2,1,6,7,8,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[6,2,1,5,7,3,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,3,5,1,7,2,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,4,5,7,1,2,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,5,4,7,2,1,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,6,4,7,2,8,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[1,8,4,6,2,7,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,2,6,7,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,2,6,8,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,6,3,2,7,8,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[6,5,3,2,7,1,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,4,3,2,1,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,2,1,4,3,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,2,1,4,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,3,4,1,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[4,6,3,2,8,7,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,7,3,2,8,6,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[1,8,3,2,7,6,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,7,2,6,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,8,2,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,6,4,8,2,7,1,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,5,4,8,2,1,7,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,4,5,8,1,2,7,6]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[4,3,5,1,8,2,7,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[4,2,1,5,8,3,7,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[4,2,1,6,8,7,3,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[4,3,6,1,8,7,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[3,4,6,8,1,7,2,5]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,6,8,7,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[3,6,5,8,7,2,1,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,7,5,8,6,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,8,5,7,6,2,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,7,5,4,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,7,8,5,4,1,2]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[3,5,7,8,6,1,4,2]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[3,4,7,8,1,6,5,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[4,2,1,7,8,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[2,3,8,1,7,6,5,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,4,8,7,1,6,5,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,5,8,7,6,1,4,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,6,8,7,5,4,1,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[7,4,6,1,8,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,3,5,1,7,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,7,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,7,5,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,7,5,8,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[1,4,6,2,7,5,8,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,7,5,2,6,8,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,5,2,1,6,8,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,8,4,3,1,7,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,6,8,4,1,7,5,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,6,7,5,1,8,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[7,5,6,1,8,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,4,6,5,7,1,8,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[4,7,5,6,1,8,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[6,7,5,1,8,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,8,4,1,7,5,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,5,3,1,8,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[8,4,2,1,6,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,6,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,2,7,6,8,4]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[5,3,2,1,7,6,8,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[2,5,3,1,7,6,8,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[2,8,4,1,6,7,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,6,8,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,4,6,1,7,5,8,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[4,7,1,6,5,8,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,8,2,6,5,7,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,7,5,8,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[7,5,1,2,6,8,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,4,1,2,6,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,2,7,6,8,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[1,2,5,3,7,6,8,4]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[4,3,1,2,7,6,8,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[3,5,1,2,7,6,8,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[6,7,1,5,8,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[2,7,6,1,5,8,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,3,5,1,7,6,8,4]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[7,6,1,5,8,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,6,7,1,5,8,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[7,1,6,5,8,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,1,6,8,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,4,1,6,7,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,1,7,6,8,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[3,5,2,1,7,6,8,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[1,3,5,2,7,6,8,4]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,7,6,2,5,8,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,6,2,1,5,8,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,3,1,5,7,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,7,5,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,2,5,1,7,4,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[7,1,6,4,8,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,2,6,4,7,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,7,4,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[7,6,2,5,8,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,3,5,7,6,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,7,6,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,3,7,6,8,4]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[5,2,1,3,7,6,8,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[7,5,2,6,8,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,4,2,6,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,7,5,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[8,2,6,5,7,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,5,7,1,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[8,3,2,5,7,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,2,7,6,8,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[4,1,3,2,7,6,8,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[4,2,1,3,7,6,8,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[1,4,2,3,7,6,8,5]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[2,4,1,3,7,6,8,5]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[2,5,1,3,7,6,8,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[2,8,3,5,7,6,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,2,3,5,7,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,1,3,5,8,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[8,3,5,7,6,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,7,6,8,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[3,1,2,4,7,6,8,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[8,1,2,4,3,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,6,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,2,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,4,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,4,5,6,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,6,3,8,4,5,7,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,3,2,1,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,3,1,4,2,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,1,5,6,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,7,8,5,6,1,2,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,7,8,5,6,2,1,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,8,4,2,6,1,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,8,2,4,5,1,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,6,2,8,4,5,1,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,3,6,7,4,5,8,1]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[3,5,2,4,8,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[3,5,4,2,8,7,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[4,6,5,8,7,1,2,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[6,4,5,1,7,8,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[7,4,1,2,3,8,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,2,4,1,3,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[2,6,4,8,3,7,5,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,5,8,7,3,4,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,2,5,1,7,3,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,5,2,1,8,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,5,6,7,8,3,4,1]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[2,4,6,7,3,8,5,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[4,2,6,7,3,1,5,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[4,7,8,2,3,1,5,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,7,8,3,2,1,6,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[5,6,4,8,1,7,2,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,6,3,8,1,2,7,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,2,5,3,7,1,6,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[4,3,6,7,2,1,8,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[3,4,6,7,2,8,1,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[3,4,5,2,7,8,1,6]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[3,4,2,5,6,8,1,7]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[5,2,7,8,6,4,1,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,1,2,7,8,6,4,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[4,7,1,8,6,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,1,2,8,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,6,8,1,2,7,5,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[6,8,7,1,5,3,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,7,3,5,1,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,1,6,3,5,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,3,6,5,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,7,2,8,6,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[1,7,3,4,8,6,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[4,2,7,1,8,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[7,8,2,3,6,5,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,5,7,1,6,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,2,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,7,1,3,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,7,2,5,3,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,2,4,8,7,1,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,6,8,3,7,4,5,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,6,8,3,4,7,5,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,2,4,8,1,7,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,8,7,2,3,5,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,1,7,3,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,5,7,2,1,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,2,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,1,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,3,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,7,1,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,8,7,5,3,4,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,3,5,4,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,5,4,7,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,3,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,4,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,2,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,4,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,2,1,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,8,7,5,4,3,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,8,4,3,7,5,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,8,7,3,2,5,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,1,7,3,2,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,5,7,3,1,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,3,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,7,1,2,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,1,7,2,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,7,1,6,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,1,2,6,5,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,6,7,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,1,6,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,7,1,2,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,1,7,2,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,5,3,1,7,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,3,7,2,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,6,2,8,1,7,5,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[1,6,4,8,3,7,5,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,8,7,4,5,3,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,7,2,1,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,5,3,7,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,1,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,3,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,7,1,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,4,3,5,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,3,4,5,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,4,5,7,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,4,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,3,1,5,2,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,1,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,2,1,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,5,4,2,3,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,3,2,5,1,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,5,4,3,1,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,5,4,1,3,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,5,4,1,2,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,3,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,1,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,3,7,6,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,3,2,5,1,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,1,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,3,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,6,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,4,3,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,7,6,4,5,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,3,2,7,6,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,4,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,5,4,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,6,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,4,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,4,7,3,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,3,2,7,6,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,3,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,6,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,6,3,5,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,3,2,7,6,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,1,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,1,8,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,4,1,8,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,5,6,2,1,8,7,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[1,6,5,2,7,4,3,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[7,4,3,1,8,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,5,1,8,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,4,1,8,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,4,2,1,8,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,6,4,2,7,5,3,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,5,3,2,7,6,4,8]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[5,3,2,1,8,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[2,5,3,1,7,8,6,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[2,6,4,1,7,8,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[2,6,5,1,7,8,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[4,5,7,1,6,8,2,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[6,5,1,2,8,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,4,1,2,8,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,3,1,2,8,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[4,3,1,2,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[6,1,2,5,8,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,1,3,4,8,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,5,6,8,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,6,1,5,7,8,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[7,4,1,6,8,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,2,3,1,8,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[3,5,2,1,6,8,7,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[1,6,2,5,7,3,4,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[6,2,1,5,8,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,3,1,5,8,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,2,4,1,8,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,2,5,1,8,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,3,1,4,8,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,2,1,4,8,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,6,2,4,7,3,5,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,2,1,3,8,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[7,4,1,3,8,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,1,3,8,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,6,7,1,4,8,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[7,6,1,4,8,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,2,1,3,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[2,6,1,4,7,8,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[7,1,4,6,8,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,3,5,8,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,1,2,4,8,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,2,3,1,6,4,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[7,4,5,2,3,1,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,6,7,3,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,4,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,1,6,3,5,2,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[5,2,6,3,4,1,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[5,2,7,3,4,1,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,2,8,6,7,3,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,2,8,5,7,3,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,7,3,4,1,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[4,1,7,3,5,2,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[3,1,7,4,5,2,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[2,1,7,4,5,3,8,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[3,1,8,6,7,4,5,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,1,8,6,7,3,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,5,7,3,4,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,7,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,5,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,7,3,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,1,8,5,7,4,6,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,7,3,6,2,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[5,1,7,3,6,2,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[6,2,7,3,5,1,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,2,8,4,7,3,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,4,7,3,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,5,1,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,2,5,1,7,3,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[5,2,4,1,7,3,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[6,2,4,1,7,3,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[8,5,7,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,6,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,7,5,8,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[3,1,4,2,8,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[8,5,6,2,3,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,5,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,1,5,2,8,6,7,4]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[2,1,6,3,8,5,7,4]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[3,1,6,2,8,5,7,4]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[4,1,6,2,8,5,7,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[5,1,6,2,8,4,7,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[7,3,8,4,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,7,3,8,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,1,8,4,6,2,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,1,8,5,6,2,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,1,8,5,6,2,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,1,7,4,8,5,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[4,1,7,3,8,5,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[7,3,8,4,5,1,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,4,5,1,7,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,8,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,8,5,6,1,3,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,3,6,2,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,3,8,4,7,2,5,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,6,1,4,7,2,5,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[4,6,1,2,5,7,3,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[1,4,8,2,5,7,3,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[7,8,2,4,5,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,5,4,6,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,1,6,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,5,6,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,4,2,3,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,1,4,2,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,5,3,1,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,5,8,4,3,2,7,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,6,1,4,3,2,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[2,6,4,8,3,7,1,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,4,6,8,3,7,5,2]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,8,5,3,1,6,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,5,8,1,4,7,6,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,8,4,7,6,1,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,6,2,4,7,3,8,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,6,2,1,4,7,8,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[4,6,2,5,3,1,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[4,7,5,1,3,6,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[7,5,3,6,2,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,7,3,6,1,4,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,3,6,7,2,1,8,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[6,1,7,5,2,4,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,3,1,2,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,4,7,2,5,3,8,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[4,6,7,8,3,5,1,2]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[3,6,1,8,4,2,5,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,7,5,8,2,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[3,5,6,7,8,1,4,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[3,6,5,7,8,2,1,4]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[5,2,7,6,1,4,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[2,5,7,6,8,1,3,4]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[2,7,5,6,8,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,1,6,8,4,5,3,7]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,7,1,8,5,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,6,8,5,4,1,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[4,3,8,5,6,7,1,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,2,8,1,6,3,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,1,8,5,4,6,7,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,8,4,5,6,1,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,8,6,1,7,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,4,7,1,5,2,6,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[4,3,7,8,1,2,6,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[1,7,3,8,5,2,6,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[4,1,8,3,6,2,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,7,8,6,3,2,1,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,6,1,3,4,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[7,6,5,8,1,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,6,4,3,8,2,5,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[7,1,3,4,8,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,6,5,4,1,2,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[2,4,5,1,7,8,6,3]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[2,6,3,4,5,8,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,6,4,1,8,3,7,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[7,3,6,4,8,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,1,4,8,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,6,5,3,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,2,5,6,3,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,5,2,7,1,8,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,6,2,7,3,1,4,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[5,6,7,4,2,8,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[5,7,6,4,1,8,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,7,1,5,2,8,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,7,5,2,4,8,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,5,2,8,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,7,5,3,8,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,6,5,4,2,3,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[7,1,5,3,4,2,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,1,5,3,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,6,4,1,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,5,4,3,1,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,5,2,4,3,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,6,1,2,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,4,2,5,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,8,1,4,2,5,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,6,4,2,5,7,3,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,6,3,7,5,4,2,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[6,8,1,3,7,5,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,1,3,5,6,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,1,6,4,5,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,2,6,5,1,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,6,3,1,5,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,4,1,5,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,3,5,4,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,8,1,2,3,4,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,5,7,2,3,8,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[5,1,8,2,3,6,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,2,3,7,6,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,2,8,1,3,7,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,2,3,5,4,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,4,1,5,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,3,1,2,4,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,6,4,1,5,7,3,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[2,6,3,5,7,1,4,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[2,5,1,7,8,3,6,4]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[2,5,3,6,8,4,7,1]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[2,1,4,7,8,5,6,3]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[2,4,7,6,8,5,1,3]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[2,5,3,7,6,1,8,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[2,5,7,8,1,4,6,3]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[3,5,7,4,1,6,2,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[5,3,4,1,8,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,2,8,4,6,1,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,1,8,6,3,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,2,8,6,5,3,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,2,8,5,7,6,3,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,4,2,7,5,8,6,3]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[4,1,8,6,7,5,3,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,3,8,7,6,2,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,4,7,6,2,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,4,3,6,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,8,3,1,7,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,2,8,7,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,8,7,2,5,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,8,3,7,1,6,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,1,3,8,6,7,2,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,5,3,7,8,6,2,4]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,5,7,6,4,2,8,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[5,8,7,4,1,6,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,8,1,2,7,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,5,1,2,3,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,2,4,3,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,3,1,2,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,5,1,2,7,6,3,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[4,5,1,2,6,8,7,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[3,5,6,1,8,4,7,2]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[3,5,7,1,2,8,6,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[3,6,2,7,5,1,4,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[4,2,6,1,7,3,5,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[4,6,3,1,2,7,5,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[4,5,3,1,7,6,2,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[4,2,5,7,1,6,3,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[3,5,2,7,8,1,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[3,1,4,7,5,6,2,8]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[3,4,6,5,8,7,1,2]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[3,1,4,5,8,6,7,2]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[3,4,6,8,5,2,7,1]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,6,2,8,4,7,1]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[4,2,5,6,1,8,7,3]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[4,5,3,1,6,8,7,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[2,1,7,5,8,6,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,2,7,5,3,8,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[4,1,2,7,3,8,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[6,4,1,7,5,2,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,1,3,7,5,2,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[3,1,2,6,8,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[3,7,1,2,5,4,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,3,7,2,4,8,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,4,1,7,8,6,5,3]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,4,7,5,1,8,6,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[2,7,4,1,5,8,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,3,7,1,5,8,6,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[5,2,8,1,3,7,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,1,6,8,3,4,7,5]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,6,8,3,1,5,7,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,8,6,4,1,5,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,8,5,1,7,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[6,3,7,4,5,1,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[2,6,3,7,5,8,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,2,1,7,8,3,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[4,7,2,3,6,8,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[5,2,7,3,6,8,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,7,4,6,2,8,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,3,4,6,1,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,3,8,4,6,1,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,5,2,4,1,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,1,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,3,6,7,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,1,7,3,5,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[8,4,1,3,6,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,7,2,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,2,8,4,7,1,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,4,7,3,1,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,6,8,3,1,7,5,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[6,3,8,2,7,1,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,1,8,2,4,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,3,8,1,2,6,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,7,4,1,6,2,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[8,5,4,1,2,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,2,7,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,6,2,8,5,3,7,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,8,5,3,1,7,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,4,5,1,2,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,7,1,2,4,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[1,6,3,7,2,8,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[6,3,2,7,8,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[4,5,7,8,3,1,6,2]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[4,7,2,5,8,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[8,1,3,4,6,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,6,7,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,8,2,7,1,4]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[2,4,5,6,8,1,7,3]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[4,8,3,5,6,1,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,3,7,8,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[5,8,7,3,4,1,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,7,3,4,1,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,7,1,5,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,7,2,5,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,4,8,7,2,6,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,7,1,6,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,3,8,7,6,1,2,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,3,8,7,6,1,2,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,3,7,5,1,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,3,4,6,5,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,5,1,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,7,6,1,2,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,5,8,7,6,1,2,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,7,6,1,2,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,7,1,6,3,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,7,2,6,3,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,5,8,2,7,6,4,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,8,1,7,6,4,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,5,8,1,7,6,4,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,5,8,7,1,6,3,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,4,8,7,1,6,3,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,8,4,7,1,5,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,4,6,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,2,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,2,5,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,8,7,2,6,3,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,5,8,7,2,6,3,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,5,8,2,7,6,4,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,5,8,3,7,6,4,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,2,8,7,6,5,3]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,3,8,2,7,6,4,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,8,3,2,7,5,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,3,2,6,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,6,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,7,5,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,8,1,7,6,4,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,4,1,8,7,6,5,2]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[4,3,1,8,7,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,2,1,8,7,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,8,2,1,7,5,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,2,1,6,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,1,6,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,2,8,7,1,6,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,8,1,7,6,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,3,8,1,7,6,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,3,8,2,7,6,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,8,3,2,7,5,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,3,1,7,5,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,1,7,5,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,7,1,5,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,7,2,1,4,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,5,6,1,2,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,2,4,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,1,2,7,5,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,3,7,5,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,2,8,3,7,6,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,8,3,7,6,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,8,7,2,6,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,1,8,7,2,6,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,1,7,2,5,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,4,1,6,2,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,6,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,2,7,5,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,8,2,7,6,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,8,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[4,1,3,8,7,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,1,4,8,7,6,5,2]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[2,1,8,3,7,6,4,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,8,1,3,7,5,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,1,3,6,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,6,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,7,5,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,8,3,7,6,4,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,3,6,8,2,5,7]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,1,6,2,5,8,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[3,5,1,8,2,4,7,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[1,4,5,2,8,3,7,6]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,4,2,6,5,8,3,7]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,5,4,2,6,8,3,7]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[3,1,6,5,8,2,4,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[1,6,4,2,5,8,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,5,2,6,4,8,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,2,6,5,4,8,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,2,5,4,7,3,8,6]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[4,1,2,6,3,8,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[7,1,5,4,2,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,4,7,5,2,8,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[7,1,3,5,2,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,2,5,1,8,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,4,5,2,8,7,3,6]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,6,4,2,8,3,7,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,4,2,8,3,7,6,5]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,2,5,3,8,7,6,4]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,2,8,6,5,3,7,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,2,8,6,3,7,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,6,4,2,8,7,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[6,2,1,8,7,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,6,2,1,8,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,1,6,2,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,7,6,4,2,8,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,5,2,6,3,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,6,2,7,5,3,8,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,2,7,6,5,3,8,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,2,6,5,3,8,7,4]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,2,6,3,8,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,5,2,7,6,3,8,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,6,5,2,7,3,8,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,5,7,4,2,8,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,1,2,8,6,3,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,1,8,6,2,4,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,3,7,1,8,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[8,3,1,6,2,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,2,4,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,8,7,3,2,4,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,8,7,3,6,5]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,7,4,2,8,3,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[8,1,5,4,2,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,2,7,3,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[8,5,3,1,7,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,7,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,2,7,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,2,6,3,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,3,8,6,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,2,8,5,3,7,6,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,6,3,8,7,5,4]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,2,7,6,3,8,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,6,2,7,3,8,5,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,7,2,8,5,3,6,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,4,2,8,6,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,1,8,3,2,6,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,1,8,6,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,8,7,3,2,6,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,8,7,6,3,5]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,2,8,7,5,3,6,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,6,3,7,5,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,7,3,8,6,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[4,1,7,3,6,5,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[5,1,8,7,6,2,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,1,7,6,3,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,2,4,1,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,1,6,2,4,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,4,1,5,2,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[8,1,4,5,3,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,5,3,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,1,4,5,3,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,1,7,8,6,2,4,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[6,1,4,8,3,5,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,1,8,6,3,4,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,4,5,3,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,4,5,3,6,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,4,5,3,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,2,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,3,5,7,2,1,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,3,5,8,2,1,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,5,7,2,1,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[8,4,5,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,3,7,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,8,7,6,2,4,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,4,8,6,3,1,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,1,8,2,3,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,8,1,6,2,4,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,4,1,5,2,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,3,4,1,8,6,5,7]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[8,3,5,6,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,1,4,7,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,6,1,5,7,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,8,6,7,1,3,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,5,7,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,6,1,7,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[7,4,5,6,3,1,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,5,6,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,6,2,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,5,8,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,5,6,2,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,7,6,5,1,3,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7,6,8,1,3,5,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,6,5,8,3,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[8,7,5,6,1,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,8,5,7,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,1,3,8,5,7,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,7,1,3,6,5,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,7,6,8,4,3,1,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,6,1,8,3,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,6,1,4,3,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[7,3,5,1,2,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,4,1,5,2,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,3,4,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,4,1,8,3,2,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,3,8,6,4,1,7,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,8,6,7,4,3,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,5,7,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,1,8,7,5,6]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[2,8,6,1,7,3,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,8,1,6,4,7,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,1,4,5,7,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,8,6,1,4,3,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,3,6,5,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,4,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,5,4,2,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,6,5,2,7,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,5,4,2,1,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,6,2,4,1,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,2,6,5,1,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,6,5,1,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,7,6,4,5,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[4,1,3,7,6,2,5,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[5,1,7,3,6,2,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[6,1,7,5,3,2,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,1,6,5,2,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,1,6,5,2,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,3,4,5,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,2,8,3,7,4,5,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,1,7,2,6,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,2,6,4,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,8,2,4,7,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,1,8,3,2,7,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,1,3,8,2,7,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,2,1,8,4,7,5,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,8,7,1,6,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,8,2,7,1,6,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,2,1,6,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,7,1,3,5,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,6,1,5,3,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,6,5,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,8,2,5,6,3,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,6,7,1,4,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,4,3,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,5,8,3,2,1,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,5,8,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,5,7,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,2,7,3,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,5,4,8,2,7,3,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[8,4,3,7,1,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,1,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,4,3,1,5,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[7,4,3,1,2,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,4,3,1,2,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,2,3,6,7,8]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[8,5,1,4,2,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,2,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,1,4,3,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,6,1,3,4,2,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[4,6,2,1,5,3,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[3,2,6,1,5,4,7,8]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[3,2,7,1,4,6,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[4,7,2,1,3,6,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[5,7,1,3,2,6,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,7,1,2,4,5,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,1,2,5,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,6,1,2,5,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,6,4,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,7,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,3,5,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,1,2,4,3,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,1,3,2,4,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,2,1,3,5,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,1,4,5,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,2,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[5,1,2,4,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[6,1,2,3,5,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[7,1,2,3,4,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,1,2,3,4,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,5,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,4,5,1,8,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,4,7,6,8,1,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,3,7,8,6,1,2,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[3,8,4,5,7,1,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,6,7,1,2,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[4,5,6,7,1,8,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[3,5,6,2,7,4,8,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[3,5,6,1,7,8,4,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[2,5,6,1,8,7,4,3]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[2,5,6,8,1,7,3,4]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[8,2,4,5,1,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,2,3,7,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,5,6,8,2,3,7,4]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,5,6,2,8,4,7,3]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[2,5,6,3,4,7,8,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,4,2,6,8,5,7,3]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[8,1,3,2,5,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,5,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,5,7,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,6,8,7,5,3]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,4,1,6,7,8,5,2]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[4,3,1,7,6,8,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[5,2,7,8,1,6,3,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,3,7,2,6,4,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[6,7,3,1,5,8,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,7,2,1,8,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,2,8,1,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,8,2,1,4,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,1,2,8,4,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,1,3,4,8,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,2,7,3,4,6,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,1,7,3,4,8,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,1,7,8,2,3,6,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,1,8,7,2,3,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,8,1,2,7,4,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,5,8,6,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[3,1,4,5,7,8,6,2]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[2,1,8,3,4,7,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,2,1,3,4,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,4,5,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,8,3,4,6,7,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,6,5,8,7,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[5,2,6,1,4,8,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[5,2,6,4,1,8,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[5,2,7,4,8,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,2,7,4,8,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,7,2,3,8,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,2,3,8,1,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,6,2,3,1,8,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[5,6,2,1,3,8,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[5,1,6,4,2,8,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[5,6,1,3,2,8,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[5,6,3,1,2,8,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[5,6,3,2,1,8,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[5,7,3,2,8,1,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,3,2,8,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,7,3,8,2,1,5,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,3,8,1,2,5,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,7,3,1,8,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,1,3,8,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,1,7,4,8,2,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[1,5,7,4,8,3,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,5,7,4,8,6,3,2]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[5,1,7,4,8,6,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,7,1,3,8,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,3,1,8,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,7,3,8,1,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,3,8,5,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,8,3,1,4,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,1,8,3,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,1,7,8,4,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,6,7,8,4,5,3,2]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,6,7,8,4,3,5,2]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[6,1,7,8,4,2,5,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,7,1,8,3,2,5,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,7,2,1,8,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,7,2,8,1,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,2,8,3,1,5,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,2,8,3,5,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,2,7,8,4,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,2,7,8,4,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,2,7,8,1,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,2,7,1,8,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[4,2,1,7,8,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[4,1,2,7,8,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[6,2,7,8,1,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,2,7,8,5,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,2,7,8,5,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,7,2,8,5,3,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,7,2,1,8,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,1,2,8,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,1,7,2,8,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[1,5,7,3,8,6,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,6,7,8,3,5,4,2]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[6,1,7,8,2,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,7,1,8,2,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,8,2,4,1,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,2,4,3,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,1,8,5,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,1,7,8,5,2,4,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,6,7,8,5,3,4,2]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[6,1,7,8,5,4,2,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,7,1,8,5,3,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,8,4,1,3,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,3,8,5,2,7,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,2,8,4,7,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,4,5,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,8,4,7,5,2,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,4,7,2,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,8,7,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[3,6,4,8,5,7,1,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[5,1,4,8,6,3,7,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,4,7,1,8,6,5,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[6,3,8,4,2,7,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,6,8,7,1,4,2,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,3,7,1,6,8,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[4,3,8,5,6,7,2,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,8,1,7,6,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,7,8,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[3,6,4,2,8,7,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[6,3,7,5,2,8,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,5,2,7,4,8,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,7,1,4,8,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,8,1,4,6,7,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,3,7,4,2,8,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[5,3,8,7,4,1,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,6,1,8,7,3,2,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,4,2,7,3,6,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[7,5,3,6,4,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,4,1,5,3,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,5,2,6,4,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,4,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,5,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,2,7,4,3,5,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,7,3,6,4,2,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[3,7,6,4,5,2,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[2,7,6,5,3,4,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,4,3,1,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,6,5,4,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,7,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,8,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,6,5,2,8,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,7,4,2,1,8,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[1,6,5,3,4,8,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,6,3,1,8,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[6,5,8,4,2,7,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,8,2,6,4,7,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,6,2,5,7,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,3,1,7,2,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,6,3,7,5,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,2,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,6,3,2,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,8,1,7,3,5,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,1,7,4,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,3,7,2,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,2,8,5,7,3,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,1,7,6,8,3,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[3,7,1,5,8,4,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[6,7,3,1,8,4,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,7,3,8,4,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,2,8,5,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,6,1,8,4,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,6,1,7,4,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,3,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,8,3,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,6,1,8,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,2,6,1,7,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,7,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,8,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,2,1,5,8,3,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[5,4,2,7,1,8,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,4,3,1,6,8,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[4,7,5,6,8,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[6,5,4,8,2,7,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,2,8,7,3,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,1,8,7,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,6,4,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,7,6,2,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,1,7,2,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,5,8,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,6,8,2,4,7,5,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,8,2,6,4,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,4,6,8,2,7,3,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[5,2,6,8,7,3,4,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,7,2,8,6,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[3,6,8,1,7,2,5,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[2,3,8,7,4,5,6,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[7,2,8,6,4,3,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,1,8,7,5,6,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,2,7,6,3,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,5,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,5,3,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,2,8,7,6,3,4,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,7,4,6,2,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,5,8,3,7,6,2,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,1,6,8,7,4,2,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,8,4,7,5,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,7,2,5,4,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,7,6,4,5,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,6,5,3,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,6,5,4,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,3,4,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,6,7,3,5,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,7,4,5,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,7,4,5,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,7,4,5,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,7,4,6,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,7,4,6,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,7,3,6,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,8,3,6,4,5,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,3,7,4,5,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,3,7,4,6,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,7,4,8,5,6,1,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[4,7,3,8,5,6,1,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,2,8,5,6,1,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,1,8,5,6,2,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[3,7,1,8,5,6,2,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,2,8,5,6,1,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,3,8,5,6,1,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,4,8,5,6,1,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,8,2,7,4,6,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,2,7,4,5,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,2,6,4,5,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,6,4,5,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,1,7,4,5,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,1,7,4,6,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,7,4,8,5,6,2,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,3,8,5,6,2,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,8,5,6,1,7,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,6,2,7,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,8,4,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[4,8,1,7,3,6,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,7,3,6,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,1,7,3,5,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,2,6,3,5,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,2,7,3,5,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,2,7,3,6,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,2,7,3,6,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,8,4,6,1,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,2,8,4,6,1,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,1,8,4,6,2,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,8,4,7,3,6,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,7,3,6,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,7,2,6,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,7,2,6,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,7,2,6,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,7,3,6,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,7,3,6,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,7,3,5,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,7,3,5,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,7,2,5,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,7,2,5,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,2,4,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,5,7,1,4,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,6,7,1,4,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,6,7,1,5,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,7,1,5,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,8,6,7,3,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,5,1,8,6,7,3,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,6,1,8,5,7,3,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,2,8,5,7,3,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[3,8,5,7,1,6,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,4,7,1,5,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,4,6,1,5,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,6,1,5,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,3,7,1,5,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,3,7,1,6,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,7,1,6,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2,8,4,7,3,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,1,8,4,7,3,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[3,7,2,6,1,8,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,1,6,2,8,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[4,8,1,6,2,7,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,6,2,7,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,8,1,5,2,6,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,5,1,6,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,2,5,1,7,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,2,6,1,7,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,2,6,1,7,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,2,8,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,3,6,1,8,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,7,4,8,3,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,4,5,2,8,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,7,4,6,2,3,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,7,4,6,3,8,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,4,8,3,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[6,8,4,5,3,7,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,4,6,3,7,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,6,4,8,3,7,1,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,6,3,7,2,4,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[5,6,3,7,2,8,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[5,6,3,8,2,7,1,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,6,4,8,2,7,1,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,8,4,6,2,7,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,4,5,2,7,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,4,5,2,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,4,5,2,3,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,4,6,2,3,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,6,4,8,2,3,1,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,6,3,8,2,4,1,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,6,3,4,2,8,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[4,6,3,5,2,7,1,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[4,6,3,5,2,8,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[4,6,3,8,2,5,1,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,8,3,6,2,5,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,6,2,4,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,3,5,2,4,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,3,5,2,4,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,5,2,6,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,8,3,6,2,7,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,3,6,2,7,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,8,2,7,1,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,6,3,7,2,8,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[4,7,3,6,2,5,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,7,3,6,2,8,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,7,3,8,2,6,1,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[5,7,4,8,2,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,7,3,6,2,8,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,3,6,2,4,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,7,3,5,2,4,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,7,3,5,2,8,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,7,4,8,2,5,1,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,5,8,2,4,1,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,8,5,7,2,3,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,4,8,2,3,1,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,3,8,2,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,3,4,2,8,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,7,3,4,2,6,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,7,3,4,2,8,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,4,8,2,3,1,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,8,4,7,2,3,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,4,7,2,3,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,6,2,4,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,3,7,2,4,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,3,7,2,4,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,3,7,2,5,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,8,2,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,3,5,2,8,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,7,3,5,2,6,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,5,3,7,2,6,1,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[4,5,3,7,2,8,1,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[4,5,3,8,2,7,1,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,8,3,5,2,7,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,4,2,7,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,3,4,2,7,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,3,4,2,6,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,3,4,2,5,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,3,4,2,6,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,3,5,2,6,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,8,2,6,1,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,5,3,6,2,8,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[4,7,5,2,1,8,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,8,5,2,1,7,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,6,5,2,1,3,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[5,6,4,2,3,1,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[6,4,5,3,1,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,4,6,1,3,2,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[4,6,8,1,7,3,2,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,7,8,1,6,3,5,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[7,4,8,1,6,5,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,4,8,1,3,7,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,4,5,3,1,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,1,3,8,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,4,8,1,7,5,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,6,8,7,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[8,5,7,6,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,8,7,4,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,1,6,8,7,4,3,5]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,7,8,6,4,5,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[7,3,2,8,6,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,8,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,7,8,6,2,3,1,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,8,7,6,3,2,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,7,5,3,2,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,4,2,3,7,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,8,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,8,7,2,6,3,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,2,7,3,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,8,7,4,2,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,7,1,8,6,4,5,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,8,1,6,7,5,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,6,8,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,7,6,2,8,1,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[6,7,4,2,8,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,8,4,2,7,5,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,1,8,6,7,5,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,3,2,6,7,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,7,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,7,3,1,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,7,5,8,1,3,4,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,6,5,8,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,6,5,7,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,8,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,2,6,8,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,1,7,6,8,3,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[7,5,6,8,1,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,7,8,1,2,4,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[8,1,3,7,4,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,7,4,6,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,6,2,5,4,7,3,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[6,2,7,5,4,8,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[8,1,3,5,4,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,4,3,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,1,8,3,4,5,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,1,5,3,4,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,4,3,5,6,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,3,4,5,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,5,6,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,3,2,7,5,1,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[8,4,7,2,5,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,4,7,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,5,2,1,4,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,4,1,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,6,2,1,4,8,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[3,6,1,8,5,2,4,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,2,6,3,5,4,7,8]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[3,4,1,2,8,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[4,3,1,2,6,8,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[5,8,1,6,3,2,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,3,8,5,2,1,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,3,1,5,2,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,6,1,5,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,7,2,1,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,5,6,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,8,3,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,7,5,6,3,2,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,2,3,8,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,1,2,3,6,5,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,2,1,3,8,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,5,7,3,2,4,6,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[5,2,7,3,1,8,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,8,2,4,1,3,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,7,2,6,3,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,3,2,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,1,8,6,4,2,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,1,6,7,4,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,7,2,4,1,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[4,2,1,3,7,8,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[2,4,1,3,8,7,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,5,8,3,1,7,4,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[8,6,1,3,7,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,6,4,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,2,3,4,1,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,1,8,3,2,4,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,4,2,7,8,6,3,5]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,6,2,4,8,5,3,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,6,2,4,7,5,3,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,7,3,8,5,2,4,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,3,2,8,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[4,2,5,7,8,6,1,3]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[7,2,3,1,8,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,2,5,1,7,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,8,3,4,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,8,3,5,1,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,4,8,5,7,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,3,6,4,8,5,7,2]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,3,6,4,7,5,8,2]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[6,2,4,7,5,8,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,2,1,3,7,8,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[7,8,2,1,4,3,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,6,4,2,3,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,7,2,3,1,6,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[7,5,4,2,6,8,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,7,5,3,4,6,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[8,2,5,4,6,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,3,1,8,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[8,2,6,4,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,1,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,3,5,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,2,3,5,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,8,4,1,3,2,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,7,4,3,2,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,8,2,4,7,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,8,1,2,7,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,8,3,2,6,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,7,3,1,2,6,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,7,5,4,2,6,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,5,8,2,4,6,3,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,5,8,4,2,7,3,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,6,2,8,3,7,5]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[5,3,1,6,7,2,4,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[5,3,6,1,2,8,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[1,6,3,2,7,8,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,7,4,5,3,8,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,4,1,2,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,3,1,4,2,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,8,3,2,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,3,2,4,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,6,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,8,1,7,3]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[4,2,5,6,7,8,1,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[5,2,3,6,7,1,8,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[6,2,3,4,1,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[7,2,3,1,4,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,6,1,4,3,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,5,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,8,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,1,5,2,8,7,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[8,1,2,4,6,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,4,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,1,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,2,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,4,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,6,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,5,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,4,2,8,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,1,4,8,2,7,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,4,6,8,2,7,3,5]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,4,7,6,2,8,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[5,1,4,7,2,8,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[1,7,4,5,2,8,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,5,1,2,8,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[5,7,2,8,1,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,2,8,7,1,3,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,1,5,8,2,7,3,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[1,4,6,2,8,7,3,5]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,4,2,8,6,7,3,5]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,2,6,4,8,7,5]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[2,1,7,6,3,4,8,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[3,1,2,7,4,6,8,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[1,4,7,2,6,8,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,2,3,6,8,5,7,4]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[5,1,4,2,7,8,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[1,4,2,7,6,8,3,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,4,2,6,8,7,3,5]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[3,1,2,8,4,6,7,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,1,2,7,6,4,8,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[5,3,7,1,8,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[1,7,4,3,2,5,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,8,7,2,1,3,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,3,4,2,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,8,2,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,4,2,7,8,3,6,5]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[5,2,8,1,3,4,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,1,8,6,3,4,7,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,6,8,3,7,5]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,2,3,7,8,5,6,4]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,3,7,5,8,6,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,4,2,7,3,8,6,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,1,7,2,8,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[2,1,7,8,3,4,6,5]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,2,3,8,7,5,6,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[4,7,8,5,6,2,1,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[5,7,8,4,2,6,1,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[6,7,8,4,2,5,1,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,6,3,7,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,8,3,2,1,5,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[5,7,8,3,2,1,6,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[2,7,8,4,3,5,6,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,8,4,2,5,1,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,7,8,3,2,1,5,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[5,7,8,3,2,1,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[7,6,3,8,2,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,6,3,7,2,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,8,2,1,4,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[3,6,4,8,2,5,1,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,4,8,3,5,7,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,4,7,3,5,8,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[3,6,4,7,2,5,1,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[4,6,3,7,2,1,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[5,6,3,7,2,1,4,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[8,4,3,2,1,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,1,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[4,5,3,2,7,1,6,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[3,5,4,2,8,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[6,4,3,2,1,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,4,3,2,1,8,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,4,3,2,1,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,1,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,3,2,1,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,6,3,8,2,1,7,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[7,5,3,2,8,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,5,4,2,7,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,8,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,4,2,8,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,6,5,8,7,2,1,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[2,6,5,7,8,3,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[6,5,4,2,7,8,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[8,5,4,2,6,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,6,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,6,1,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,6,3,7,2,1,8,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[4,6,3,7,2,1,8,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[3,6,4,7,2,8,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[2,6,4,7,3,8,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[3,5,4,2,7,8,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[4,5,3,2,7,1,8,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[7,4,3,2,1,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,3,2,1,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,1,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,1,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,4,3,2,1,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[3,5,4,2,6,8,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[5,6,3,4,1,2,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[8,5,3,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,1,7,8,5,6,3,4]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[6,8,3,7,5,1,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,7,3,8,1,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,2,6,4,8,5,1,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[3,2,5,8,4,6,1,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[3,5,2,4,1,7,6,8]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[4,2,1,5,7,3,6,8]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[4,5,2,3,7,1,6,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[4,2,5,3,8,1,6,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[4,2,5,8,3,1,6,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[3,1,5,4,2,8,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[4,1,5,3,8,2,6,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[4,1,5,8,3,2,6,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,3,8,5,2,1,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,7,3,5,2,1,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,3,2,7,5,1,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[4,3,6,2,5,1,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[4,6,3,2,5,1,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[4,6,7,1,3,2,5,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[4,5,1,7,3,2,6,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[4,5,1,3,7,2,6,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[3,5,1,4,2,7,6,8]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[2,5,1,4,3,7,8,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[5,2,1,4,3,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[5,3,1,4,2,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[4,3,1,5,7,2,6,8]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[4,3,1,7,5,2,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[4,3,6,1,5,2,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[4,6,3,1,5,2,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[5,3,6,4,1,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[4,3,6,1,7,2,5,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[6,3,4,1,2,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,2,4,1,3,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[3,6,4,1,2,7,5,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[4,6,3,1,7,2,5,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[5,3,6,2,1,4,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[5,6,2,7,1,3,4,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[4,5,2,7,3,1,6,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[4,6,7,2,3,1,5,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[4,6,2,1,7,3,5,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[3,2,6,1,4,7,5,8]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[3,6,2,1,4,7,5,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[3,6,7,2,4,5,1,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[3,5,2,7,4,6,1,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[3,7,2,4,8,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[7,2,1,4,6,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,3,1,4,6,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,2,6,1,5,7,4,8]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[3,6,2,1,5,7,4,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[6,3,2,1,5,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,4,2,1,5,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[4,2,6,1,5,3,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[4,2,1,7,5,3,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[7,4,1,5,6,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,1,5,2,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,1,5,3,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,2,5,1,3,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,3,5,1,2,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,4,5,1,7,2,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[5,2,6,4,1,3,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[4,6,5,1,7,2,3,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[3,6,5,1,2,7,4,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[6,5,2,1,4,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,5,3,1,4,7,2,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[2,3,1,8,5,4,7,6]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,4,1,5,8,3,7,6]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[2,4,1,5,3,8,7,6]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[3,4,5,1,2,8,7,6]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[3,4,5,1,8,2,7,6]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[1,8,4,5,3,2,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,8,5,3,1,7,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,5,8,2,1,7,6]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,5,2,8,1,7,6]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,6,2,1,7,8,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[3,4,6,2,1,7,5,8]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[3,5,6,2,7,1,4,8]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[3,5,6,2,7,1,8,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[3,5,6,2,7,8,1,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[3,4,6,2,8,7,1,5]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[3,4,6,8,2,7,1,5]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,8,6,3,7,1,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,8,4,6,3,7,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,6,3,7,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,8,2,7,5,1]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[3,4,6,2,8,7,5,1]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,6,2,7,8,4,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[3,5,6,2,7,4,1,8]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[4,5,6,7,2,8,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[3,5,6,8,7,2,4,1]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[2,5,8,6,7,3,4,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,8,5,6,7,3,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,6,7,3,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,8,6,7,3,1,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,6,8,7,2,1,4]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,6,7,2,1,8,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[3,4,6,1,8,7,2,5]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,1,6,8,7,3,5]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[2,3,1,8,6,7,4,5]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,8,3,2,6,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,6,7,8,4,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[2,5,1,6,7,4,8,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[2,5,1,6,7,4,3,8]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[3,5,6,1,7,4,2,8]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[3,5,6,1,7,4,8,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[3,4,6,1,8,7,5,2]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[3,4,6,8,1,7,5,2]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,8,6,1,7,5,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,8,4,6,2,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,6,7,2,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,8,6,7,1,4,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,6,8,7,1,4,2]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,6,7,8,1,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,1,3,8,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[4,5,6,7,1,3,2,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[4,5,6,7,3,1,8,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[3,5,6,8,7,4,1,2]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[2,5,8,6,7,4,1,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,8,5,6,7,4,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,6,7,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,8,6,7,4,3,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[8,2,5,3,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,7,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,3,7,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,1,8,3,7]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[4,2,5,6,1,7,3,8]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[6,1,5,7,3,2,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,1,5,8,3,2,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,8,2,4,7,1,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,8,2,4,7,1,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[4,3,5,6,7,1,8,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[3,7,1,5,6,8,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,1,5,8,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[8,3,2,4,6,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,4,6,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,2,5,1,7,4,6,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[3,2,5,1,8,4,6,7]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[3,2,5,1,7,8,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[7,8,3,2,4,6,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,1,5,7,8,3,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[4,2,5,6,1,7,8,3]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[5,7,6,1,8,3,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,8,6,1,7,3,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,1,5,8,7,3,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,7,3,2,4,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,8,7,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[3,2,5,1,6,4,7,8]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[3,2,4,1,8,7,5,6]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[3,2,5,1,6,8,7,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[3,8,6,5,1,7,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,5,1,8,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[6,5,1,7,8,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[3,2,5,1,6,7,8,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[3,2,4,1,8,5,6,7]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[3,2,4,1,7,5,6,8]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[3,2,4,1,6,8,5,7]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[3,2,4,1,8,5,7,6]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[8,3,2,4,7,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,8,4,7,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[3,2,5,1,6,7,4,8]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[6,5,1,7,4,2,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,5,1,8,4,2,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,4,2,3,7,5,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,8,3,7,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[5,2,6,1,8,3,7,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[8,4,6,1,7,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,1,8,4,7,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[7,4,2,3,8,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,5,1,6,4,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,6,4,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,2,5,1,7,6,4,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[3,2,5,1,8,6,4,7]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[7,3,2,4,8,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,6,1,5,7,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,1,8,5,7,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[8,5,6,1,7,3,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,1,7,4,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[8,5,1,6,7,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,8,6,7,4]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[3,2,4,1,8,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[3,2,4,1,5,8,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[3,2,5,1,7,8,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[7,8,5,1,6,4,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,8,5,1,7,6,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,1,8,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[8,7,5,1,6,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,8,7,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[6,5,7,3,1,8,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[4,6,3,7,1,8,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[4,6,3,7,5,1,8,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[4,2,6,1,7,5,3,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[2,5,7,4,1,6,3,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[2,5,7,4,1,6,8,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[5,4,7,3,6,1,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,4,7,8,3,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,3,7,5,1,8,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[6,4,3,8,5,1,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,8,4,3,6,1,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,4,8,3,6,1,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,3,6,7,1,8,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[2,5,4,6,1,7,3,8]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[3,2,5,8,1,6,7,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[2,5,4,6,8,1,7,3]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[5,2,8,4,1,6,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,6,2,1,8,5,7,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[2,4,1,7,5,8,6,3]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[2,4,1,7,5,3,8,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[2,6,4,1,8,5,3,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,8,2,1,6,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,5,8,4,1,6,3,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,2,5,6,1,8,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[4,8,3,2,6,1,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,8,1,6,4,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,2,1,6,8,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[3,2,7,1,5,4,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[3,2,7,1,5,8,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[3,8,2,5,1,6,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,2,6,7,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,8,2,6,7,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,2,6,7,8,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[4,3,2,6,7,1,5,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[4,3,7,2,6,8,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,3,7,8,2,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[2,5,7,4,8,1,6,3]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[3,2,5,7,8,1,6,4]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[3,2,5,7,1,6,8,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[3,2,5,7,1,6,4,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[6,3,2,7,1,5,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,3,2,7,1,5,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,3,2,7,8,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[4,2,6,1,7,8,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[6,5,2,1,7,8,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[2,1,7,5,3,8,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[6,2,1,8,5,3,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,2,7,1,4,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,3,2,1,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,3,2,1,4,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[3,5,2,1,7,4,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[3,5,2,1,7,8,4,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[5,8,4,2,1,7,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,6,2,1,8,3,7,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[2,4,1,7,3,8,6,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,2,7,1,4,8,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[3,5,8,2,1,7,4,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[4,8,3,7,2,1,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,8,1,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,3,7,2,1,5,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[4,8,3,2,7,1,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,8,1,7,4,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[6,3,2,8,1,4,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,2,1,4,7,5,8,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[5,3,2,1,8,4,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[4,8,3,2,1,5,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,8,2,1,5,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,2,3,1,5,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,4,5,2,3,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,3,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,3,4,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,1,5,2,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,4,5,1,3,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,1,5,3,4,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,3,5,1,4,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,3,5,2,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,4,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,4,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,4,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,3,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,5,3,7,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,6,7,4,5,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,5,3,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,5,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,6,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,6,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,6,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,6,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,6,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,6,3,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,6,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,4,7,5,6,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,1,7,3,4,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,6,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,6,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,6,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,6,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,6,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,6,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,4,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,7,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,7,4,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,1,5,2,4,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,4,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,4,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,6,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,6,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,3,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,7,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,5,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,1,3,2,8,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[8,6,7,2,3,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,7,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,6,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,6,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,6,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,5,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,5,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,3,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,7,3,5,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,3,7,5,6,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,1,3,2,7,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,6,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,6,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,6,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,6,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,6,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,6,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,6,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,6,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,7,3,6,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,5,7,4,6,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,6,3,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,6,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,6,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,6,1,7,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,5,8,1,3,2,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,5,8,6,3,2,7,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[6,5,8,7,3,1,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,5,8,7,3,6,2,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,7,2,8,4,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,7,2,8,4,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[3,6,2,8,4,5,7,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,1,8,4,5,7,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,8,4,6,1,5,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,8,4,5,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,1,6,8,4,5,7,2]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[2,3,6,8,4,5,7,1]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[6,3,7,8,4,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,3,7,8,4,6,5,2]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,5,7,8,2,4,6,3]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[5,1,7,8,2,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[3,6,7,8,4,2,5,1]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[7,6,1,8,4,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,6,8,7,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[2,8,3,7,1,6,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,8,7,3,6,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,2,1,8,4,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,2,7,8,4,6,5,1]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[5,2,7,8,1,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[1,2,7,8,5,4,6,3]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[4,2,1,3,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[7,2,5,8,3,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,2,8,5,4,3,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,8,3,5,4,1,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,5,3,1,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,8,5,2,3,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,3,5,8,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,3,1,2,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[3,4,2,1,8,5,6,7]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[2,7,6,8,4,3,5,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,7,1,8,3,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,7,5,8,1,4,6,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,5,8,3,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,6,8,5,4,3,2,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,6,8,5,1,3,2,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[5,6,8,1,4,3,2,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[7,5,8,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,4,8,3,6,5,1,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,8,4,1,5,6,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,8,3,5,6,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,6,8,4,1,3,2,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,6,8,1,5,3,2,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[1,6,8,4,5,3,2,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,7,3,8,5,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,1,8,5,4,6,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,3,8,4,6,5,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,1,3,8,4,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,7,8,4,3,6,1,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[2,8,7,4,1,6,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,4,3,1,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,8,4,2,3,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,1,3,2,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,4,3,2,8,5,6,7]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[7,3,2,8,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,4,8,2,5,3,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,8,4,3,5,1,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,4,5,1,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,8,4,5,3,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,3,8,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,2,3,1,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[3,2,1,4,8,5,6,7]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[5,1,3,2,4,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[2,8,1,5,3,4,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,8,4,5,3,7,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,2,8,5,3,6,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,8,4,2,5,3,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,5,3,2,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,2,4,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,1,4,8,2,6,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[1,5,2,8,4,3,6,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,2,8,5,4,3,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,4,3,8,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,4,8,5,3,7,6]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,7,4,8,5,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,5,2,7,8,4,3,6]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[5,1,2,7,4,8,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[8,3,5,1,4,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,5,4,7,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,8,5,7,4,3,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,8,7,5,3,6]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,8,1,4,3,7,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,8,7,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,1,2,8,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,6,4,8,1,7,2,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[7,6,1,4,2,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,6,2,8,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,6,7,2,8,4,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[6,7,1,4,2,8,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,3,7,1,4,8,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[3,7,8,1,5,2,4,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[7,1,2,8,5,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,7,2,8,4,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,4,2,7,8,5,3,6]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[6,1,2,8,4,3,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,1,2,8,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,6,1,3,2,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,1,3,2,4,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,2,7,3,5,8,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,2,7,5,8,3,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[5,8,1,3,7,2,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,2,5,8,7,3,4,6]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,5,8,3,7,4,6]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,8,1,7,3,5,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,1,3,2,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,7,3,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,8,1,7,4,3,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,8,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,2,8,4,7,5,3,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,7,4,5,3,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,8,1,7,5,3,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,7,1,5,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,4,7,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,1,4,2,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,7,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,8,6,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,1,2,8,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,7,4,8,1,6,2,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,4,8,7,1,6,2,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[4,2,8,1,7,6,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,8,1,7,6,4,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,3,4,1,5,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,4,1,6,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,3,4,1,7,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,3,4,1,8,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,7,3,4,1,8,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,8,3,4,1,7,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,3,4,1,6,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,3,4,1,5,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,3,4,1,5,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[5,7,3,4,1,6,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,6,2,8,3,4,1,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,6,2,7,3,4,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[4,6,2,8,3,5,1,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,7,3,5,1,6,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,8,3,5,1,6,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,5,1,7,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,5,1,8,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[5,6,2,3,1,7,4,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[5,6,2,4,1,8,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[5,6,2,4,1,7,3,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[4,6,2,5,1,7,3,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[4,6,2,5,1,8,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[4,5,1,8,3,7,2,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,5,1,7,3,8,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[4,6,2,7,3,8,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[5,6,2,7,3,8,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[5,6,2,7,4,8,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[5,6,3,8,4,7,1,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,6,2,8,4,7,1,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,6,2,8,3,7,1,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,6,2,8,3,7,1,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,5,1,7,3,6,2,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[4,5,1,8,3,6,2,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[6,5,3,2,1,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,6,3,5,2,1,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[8,7,3,5,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,5,7,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,7,2,4,5,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,4,5,2,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[8,3,7,4,5,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,4,5,7,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,8,7,4,3,6,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,8,7,4,3,6,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,7,4,3,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,8,5,7,4,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[6,8,3,5,1,7,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,1,8,4,7,6,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,5,8,4,7,6,3,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,3,8,1,5,6,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,1,3,5,6,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,4,1,6,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,3,6,1,4,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,3,6,1,2,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,4,1,6,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,2,5,6,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,4,2,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,2,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,5,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,5,1,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,2,4,1,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,2,4,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,6,3,2,1,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,6,2,1,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,4,2,6,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,6,8,4,5,7,1,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,1,8,4,5,7,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,3,5,1,7,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,1,5,8,3,6,7,4]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[5,8,3,6,1,2,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,1,8,2,5,6,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,1,5,6,7,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,8,2,1,5,6,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,2,5,6,7,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[5,8,1,4,7,6,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,3,1,6,2,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,5,3,8,6,1,7,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,4,1,8,5,6,7,2]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[4,5,7,6,2,3,8,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[3,5,7,2,6,4,8,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[2,5,7,3,6,4,8,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,5,7,3,6,8,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[8,4,3,7,6,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,3,5,4,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[5,2,7,3,6,4,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[8,3,4,7,6,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,1,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,7,6,8,5,2]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[4,1,3,7,6,8,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[5,1,7,3,6,8,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,7,1,3,5,8,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,8,7,3,6,1,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,3,7,6,1,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,7,6,1,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,7,1,6,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,4,7,2,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,1,7,6,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,1,7,6,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,8,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[8,2,3,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,7,6,8,5,2]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[1,4,2,7,8,6,5,3]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[8,4,2,7,1,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,8,6,4,3]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[2,5,7,1,8,6,4,3]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[3,5,7,1,6,8,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[6,7,4,5,8,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[5,4,7,6,8,1,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[2,5,7,8,1,6,4,3]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,5,7,8,2,6,4,3]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[8,5,7,1,2,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,2,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,7,2,6,5,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,7,6,1,5,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,7,6,1,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,3,7,8,6,1,4,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[6,7,2,8,1,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,2,7,8,1,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,2,8,7,1,6,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,2,8,1,7,6,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,2,7,6,5,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[8,3,1,2,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,7,6,5,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,3,7,6,5,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,8,7,2,6,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,1,7,8,2,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[6,7,1,8,2,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,8,7,1,2,6,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,1,7,2,6,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,2,7,6,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,3,7,6,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,3,7,6,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,2,3,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,8,4,5,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[3,7,1,5,8,2,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,1,5,8,3,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,6,5,1,8,3,7,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[3,6,5,1,8,2,7,4]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[4,6,5,1,8,7,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[5,6,4,1,8,7,2,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[8,1,4,5,7,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,8,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,4,6,1,8,7,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[4,5,6,1,8,7,2,3]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[3,5,6,1,8,2,7,4]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[2,5,6,1,8,3,7,4]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[2,4,6,1,3,8,7,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,4,6,1,2,8,7,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[4,3,6,1,2,8,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[5,3,6,1,8,2,7,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[7,3,1,5,8,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,1,3,5,7,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,7,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,5,8,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,2,5,1,8,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,2,6,1,3,8,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[2,3,6,1,4,8,7,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[4,2,5,3,1,8,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[6,2,4,1,3,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,2,1,4,3,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,1,2,4,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,2,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,3,4,1,2,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,6,3,1,2,8,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[3,6,4,1,2,8,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[2,6,4,1,3,8,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,7,1,4,3,8,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,1,4,2,8,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[4,7,1,3,2,8,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[8,1,6,7,2,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,2,3,8,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,7,1,2,4,8,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,1,3,4,8,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,6,3,1,4,8,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[3,6,2,1,4,8,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[5,6,2,1,8,3,7,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[6,5,2,1,8,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,1,5,2,7,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,3,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,2,1,3,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,4,2,3,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[3,5,2,4,1,8,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[6,3,2,1,4,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,3,1,2,4,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,1,3,2,4,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,4,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,2,3,1,4,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[2,4,3,6,1,5,8,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[2,4,3,6,5,8,1,7]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,4,6,3,5,8,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[2,4,6,3,5,8,1,7]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[2,4,6,3,5,1,8,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[2,4,6,3,1,5,8,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[2,4,1,6,5,3,8,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[2,4,6,1,5,3,8,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[4,2,6,5,3,1,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[4,2,6,5,1,3,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[4,2,6,5,1,8,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[4,2,6,5,8,1,7,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,2,6,5,8,1,3,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,2,6,5,8,3,1,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,1,5,8,3,7]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[2,4,1,6,5,8,3,7]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,1,4,6,5,8,3,7]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[2,4,1,6,5,8,7,3]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,4,6,1,5,8,7,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[4,2,6,5,3,8,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[4,2,6,5,8,3,7,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[2,6,4,3,8,7,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,4,3,8,7,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[4,2,6,8,5,3,7,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,1,5,7,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,1,8,5,7,3]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,1,6,8,5,7,3]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[2,1,4,6,8,5,7,3]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,4,6,8,5,3,7]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[2,4,1,6,8,5,3,7]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[2,4,6,1,8,5,3,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,8,1,5,3,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[4,2,6,8,5,3,1,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,2,6,8,5,1,3,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,2,6,8,5,1,7,3]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,3,5,7,1]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,3,5,1,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,3,1,5,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,3,1,8,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[2,4,6,3,8,1,5,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,3,8,5,1,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,3,8,5,7,1]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,3,6,8,5,7,1]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[2,4,3,6,8,5,1,7]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[2,4,3,6,8,1,5,7]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[2,4,3,6,1,8,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,4,3,1,6,8,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[2,4,1,3,6,8,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[2,4,3,6,1,8,7,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,4,3,6,8,1,7,5]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[4,6,5,2,8,7,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,6,5,2,8,7,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,6,2,5,8,7,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,6,2,5,8,7,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[2,4,6,3,8,1,7,5]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,3,1,8,7,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[2,4,1,6,3,8,7,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,1,4,6,3,8,7,5]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[2,1,4,6,8,3,7,5]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[2,4,1,6,8,3,7,5]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[2,4,6,1,8,3,7,5]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,8,1,3,7,5]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,3,1,7,5]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[4,6,2,8,5,7,3,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,6,2,8,5,7,1,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[6,2,4,8,7,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,2,8,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,6,4,8,1,7,5,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,4,1,8,7,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,1,4,8,7,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,1,6,4,8,7,5,3]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[2,1,6,4,8,7,3,5]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[2,6,1,4,8,7,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,4,1,8,7,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,4,8,1,7,3,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,4,2,8,7,5,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,4,8,7,3,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,4,8,7,3,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,6,4,7,3,8,2,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,3,7,4,5,8,2,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[5,2,4,7,3,6,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[1,7,6,3,4,8,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,1,6,3,7,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,3,8,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,2,7,4,8,3,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[6,1,7,3,4,8,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[2,1,7,4,5,8,3,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[5,1,4,7,3,8,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[4,3,1,7,5,8,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[2,8,6,3,7,1,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,1,3,7,2,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,2,1,7,3,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,8,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,7,1,3,8,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[5,1,2,4,8,3,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[4,3,6,1,5,8,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[2,6,1,4,5,8,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[6,5,1,3,4,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,6,2,4,8,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[8,5,1,3,7,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,8,4,6,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[6,4,2,1,5,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[2,5,3,4,1,8,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,3,5,2,1,8,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[2,6,4,8,7,1,3,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,4,8,7,2,3,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,7,8,3,6,1,4,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[4,3,2,8,7,1,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[5,2,4,8,7,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,2,8,3,7,1,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,1,4,8,7,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,8,2,5,1,3,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,1,3,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,7,2,1,5,4,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[3,8,2,1,5,4,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,2,1,5,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,6,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,1,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,5,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,4,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,4,5,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,4,5,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[3,2,7,1,4,6,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[3,2,8,1,4,6,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,8,1,4,7,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,8,2,1,4,7,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,1,5,7,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,5,1,7,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,1,8,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,7,2,1,5,8,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,2,1,4,8,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,2,1,7,5,8,6,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[3,2,7,1,6,8,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[4,2,7,6,1,8,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,3,7,6,8,1,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,3,8,6,7,1,2,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,2,8,6,1,7,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,2,8,1,6,7,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,8,7,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,8,2,1,7,4,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,1,7,4,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,8,1,6,4,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,7,1,6,4,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[4,2,7,6,1,3,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,2,8,6,1,3,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,2,8,7,1,3,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,7,8,3,4,1,2,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,2,7,8,1,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[4,2,6,8,1,3,7,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,2,6,7,1,3,8,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[3,2,6,1,8,4,7,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[3,7,2,1,8,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,2,1,8,5,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,7,3,8,5,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,3,7,8,6,1,2,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[3,2,7,1,8,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[3,2,1,6,8,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[3,2,6,1,8,7,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[4,2,6,8,1,7,3,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,3,6,8,7,1,2,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,2,6,7,1,8,3,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[3,2,6,1,7,8,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[3,4,6,8,7,5,1,2]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[5,3,6,4,8,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[1,4,6,2,7,8,5,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[3,1,8,5,4,2,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,7,5,4,8,6,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[6,3,7,5,4,8,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[7,3,8,5,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,8,7,5,4,6,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,7,8,5,1,2]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[4,5,6,3,8,7,1,2]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[3,6,8,5,4,7,1,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[6,8,3,5,4,7,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,6,3,5,4,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,6,2,5,4,8,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[7,1,2,5,8,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,8,2,5,7,3,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,5,4,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,1,6,2,8,7,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[7,8,1,2,4,6,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,1,4,2,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,3,6,1,8,2,7,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[2,3,8,5,4,1,6,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,8,1,5,2,3,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,4,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,8,1,6,4,3,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,1,5,7,4,3,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,5,8,6,4,3,2,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,4,6,1,5,8,2,7]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[7,8,4,1,5,3,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,1,6,3,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,6,1,5,7,3,8,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,6,8,7,4,3,2,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,8,1,7,4,3,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,6,1,7,4,3,2,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[5,1,7,6,4,3,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[6,1,7,8,4,3,2,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,1,8,6,4,3,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,8,7,6,4,3,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,5,6,3,8,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[3,1,6,7,5,8,2,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[7,8,1,6,5,3,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,1,4,5,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,8,1,5,4,6,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,4,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,2,8,5,6,3,7,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,5,7,3,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[4,2,1,5,6,3,7,8]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[4,3,6,1,5,7,2,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[5,1,6,3,7,8,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[1,3,6,8,5,7,2,4]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,4,6,3,7,1,8,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,3,6,4,8,7,2,5]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[4,1,6,7,3,8,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[5,4,6,1,3,7,2,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[6,4,1,5,2,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[4,1,7,5,2,3,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[1,2,4,5,8,3,7,6]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[7,2,3,5,4,1,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,8,3,5,4,1,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,8,1,7,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[7,8,2,3,4,1,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,4,6,3,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,1,6,4,7,8,2,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[1,8,5,7,4,3,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,8,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,1,8,7,4,3,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,5,1,8,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,7,1,4,3,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,5,8,1,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,8,7,1,4,3,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,5,7,8,4,3,2,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[2,4,7,5,1,3,8,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[7,8,4,6,1,3,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,5,6,4,1,8,2,7]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[2,6,4,5,1,3,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,6,5,8,4,3,2,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,8,5,1,4,3,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,6,5,1,4,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,4,6,2,7,1,5,8]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[3,6,2,5,4,1,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[3,2,7,5,4,1,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[4,3,6,2,8,1,5,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[6,1,2,5,4,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,2,4,5,1,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[4,2,8,5,1,3,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,6,8,1,7,2,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[5,3,6,4,1,7,2,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[6,2,1,5,8,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,6,7,4,8,3,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,4,6,3,7,5,8,2]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[4,6,7,2,5,8,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[2,4,6,1,7,5,3,8]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[2,7,5,4,1,6,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[7,5,4,6,2,8,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,7,5,4,3,8,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,4,6,3,5,8,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,5,8,4,3,6,7,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,4,6,2,7,8,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[2,5,4,1,6,7,3,8]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[5,6,3,2,7,1,4,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[5,6,3,2,7,1,8,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[8,5,6,3,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,2,8,1,7,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[2,4,1,7,8,5,3,6]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[2,5,4,1,6,3,8,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[5,6,3,2,1,8,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[3,5,2,1,6,4,7,8]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[6,8,4,3,2,1,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,3,8,2,1,6,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,7,5,8,2,1,4,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[7,3,2,8,5,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,4,6,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,2,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,8,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,4,7,2,1,8,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[7,5,8,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,7,3,2,1,6,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,7,3,2,1,6,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,3,7,2,5,1,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,7,8,3,5,2,1,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,2,5,7,8,4,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[2,1,5,7,8,6,3,4]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,6,7,2,8,1,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[6,3,7,2,8,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[3,2,6,1,7,4,5,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[3,5,2,1,4,7,6,8]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[7,3,5,2,1,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,5,4,1,3,7,8,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[2,5,8,4,1,3,7,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,4,1,7,8,3,6,5]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[3,7,2,8,6,1,4,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,6,8,2,1,7,4,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,3,8,2,1,4,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,8,7,3,2,1,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,1,5,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[8,4,7,3,2,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,1,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,6,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,5,2,1,4,6,8,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[7,8,3,5,4,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,3,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,3,2,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[5,4,1,6,2,3,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[5,7,1,6,2,8,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,1,6,2,8,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[2,7,6,5,1,8,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,6,5,1,8,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,3,6,5,1,4,8,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,3,6,4,1,5,8,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,3,6,1,5,4,8,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,7,6,1,4,8,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,6,1,4,8,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,3,5,1,8,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,5,1,8,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,7,6,1,5,8,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,6,4,1,8,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,1,7,6,3,8,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,1,7,6,3,8,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[5,7,3,6,2,8,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[2,7,6,4,1,8,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,3,5,1,8,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,5,1,8,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,3,4,8,7,6,1,5]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,8,5,7,1,6]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[7,3,5,4,8,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,4,3,5,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,1,4,5,8,7,3,6]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[6,4,3,5,8,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,3,5,4,8,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,3,4,8,7,5,6,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,8,7,5,1,6]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,7,6,5,4,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,3,5,6,8,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,5,6,8,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,5,6,8,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,4,1,5,8,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,4,1,5,8,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,4,1,5,8,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,7,1,6,3,8,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,4,1,5,8,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,4,1,5,8,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,1,5,8,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,5,7,8,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,3,5,7,8,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[2,7,6,4,5,8,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,7,3,6,1,8,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[2,1,4,5,8,6,3,7]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[7,3,5,4,8,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,3,4,8,5,6,1,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,8,7,1,6,5]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,8,1,7,6,5]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,8,1,6,7,5]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,8,5,1,7,6]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[6,3,5,4,8,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,4,3,5,8,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,1,4,5,8,3,7,6]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[7,4,3,5,8,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,5,4,8,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,3,4,8,5,1,6,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,8,1,6,5,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,8,1,5,7,6]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[7,8,2,6,1,5,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,6,2,5,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,8,6,7,2,5,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,7,2,6,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,7,2,6,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,2,7,1,6,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,8,6,7,1,5,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,7,1,6,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,7,5,6,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,7,5,6,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,7,4,6,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,7,4,6,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,7,1,6,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,7,1,6,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,7,2,6,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,7,2,6,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,7,5,6,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,7,5,6,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,7,5,6,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,7,5,6,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,7,4,6,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,7,4,6,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,7,2,6,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,7,2,6,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,7,1,6,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,7,4,6,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,7,5,6,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,7,5,6,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,7,5,6,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,7,5,6,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,7,5,6,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,7,5,6,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,7,4,6,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,7,1,6,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,7,3,6,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,8,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,1,8,6,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,8,6,1,5,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,8,4,5,2,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,1,7,4,2,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,6,7,4,2,8,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,6,7,3,8,5,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[7,1,8,3,5,6,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,2,8,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,1,8,4,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,8,4,1,5,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,3,5,1,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,3,4,6,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,5,7,8,2,6,3,4]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[6,2,3,8,5,7,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,4,8,5,3,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,1,4,8,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,6,3,7,8,5,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[2,6,3,7,8,4,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[2,4,7,3,5,6,8,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[2,4,7,3,6,8,5,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[2,5,3,7,8,1,6,4]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[3,1,5,4,7,8,2,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[5,3,1,4,8,2,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,2,4,8,6,1,3,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,2,3,8,4,6,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,8,2,3,6,1,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,3,5,7,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,8,3,6,2,5]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[4,8,1,3,6,7,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,3,8,2,4,7,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,3,8,1,2,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,4,2,8,1,3,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,8,2,5,1,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,8,1,4,7,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,8,1,3,6,2,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,2,6,8,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[5,8,1,4,2,6,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,1,2,7,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,8,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,3,1,4,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,3,1,6,4,2,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[5,2,6,4,1,7,3,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[4,6,1,7,5,2,8,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[4,5,1,7,2,6,3,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[3,5,6,1,2,8,7,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[3,5,7,1,8,6,2,4]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[3,6,2,7,5,1,8,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[4,2,5,7,1,8,6,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[3,4,7,2,8,6,1,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[3,4,5,8,2,7,1,6]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,6,2,8,1,5,7]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,2,6,8,1,7,4]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[4,2,5,6,1,3,8,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[4,3,1,2,5,6,8,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[5,3,6,8,4,7,2,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[3,7,2,5,4,8,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[8,4,2,5,7,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,5,8,3,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,2,6,8,4,3,7,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[3,1,6,5,4,8,2,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[4,1,6,5,8,3,2,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[5,1,6,8,4,3,2,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,8,4,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[2,7,1,5,4,3,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[8,2,1,5,4,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,7,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,1,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,7,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,4,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,4,3,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,7,8,5,1,3,2,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[5,7,6,8,2,3,4,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,7,2,8,4,3,6,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[6,7,8,2,4,3,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[4,7,6,2,8,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[8,3,6,2,4,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,2,4,8,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[5,7,3,8,4,6,2,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,7,3,5,8,6,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[8,7,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,4,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,1,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,1,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,1,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,5,7,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,8,4,1,2,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,7,6,5,8,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[3,7,6,5,1,8,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,6,4,8,7,5,1,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[5,6,4,3,8,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[1,6,2,4,7,8,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[3,6,2,4,8,1,5,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,4,7,2,8,1,6,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[1,4,7,2,5,8,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[7,3,8,4,5,6,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,5,6,4,8,7,1,2]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[4,6,8,5,3,7,1,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[6,8,5,3,4,7,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,6,5,4,2,8,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,8,5,2,7,3,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,1,8,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[7,8,1,4,2,6,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,3,6,4,8,2,5,7]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[4,1,7,5,3,2,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[6,5,1,3,4,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,8,5,3,1,7,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,3,2,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,8,3,6,1,4,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,5,8,6,4,1,3,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,6,2,5,8,3,7]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,6,2,5,8,1,7,4]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[1,6,8,7,4,2,3,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,1,7,8,2,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,1,8,6,3,4,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,1,4,5,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,2,8,3,6,5,7,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,2,7,5,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,6,3,8,5,7,2,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,4,1,7,5,8,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[7,6,5,8,1,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,8,6,7,3,2,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,7,2,8,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[2,6,3,4,8,7,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[7,1,3,4,5,2,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,8,3,5,4,2,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,3,8,2,7,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[7,8,2,4,6,3,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,2,6,4,7,8,1,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[2,8,5,7,4,3,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,8,3,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,3,8,7,1,2,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,5,3,8,2,1,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,5,8,4,1,2,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,8,7,4,1,3,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,5,7,8,4,1,2,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[1,4,7,5,3,8,2,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[2,4,6,7,3,1,8,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[7,8,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,6,4,5,3,8,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[3,6,5,8,4,2,1,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[5,6,8,4,2,3,1,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,8,5,4,3,1,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,1,4,2,8,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,8,6,5,3,2,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,6,5,1,2,4,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,8,2,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,7,5,8,2,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,3,8,5,7,6,2,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[6,3,8,5,7,1,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,3,1,5,6,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,1,4,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,2,5,6,1,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,5,6,3,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,2,5,6,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,7,6,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,8,6,2,7,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,5,8,6,1,7,3,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[8,6,1,5,7,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,5,7,1,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,8,1,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,1,7,6,8,4,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,1,3,7,8,6,2,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[7,2,5,8,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,2,8,5,7,6,1,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,2,1,5,7,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,6,1,7,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,2,8,6,5,7,3,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,3,6,7,8,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[8,2,5,6,3,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,5,4,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,3,5,4,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,1,5,3,4,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[7,5,6,2,4,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,5,2,6,3,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,2,6,7,8,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[8,1,6,5,7,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,6,2,7,1,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[5,8,1,6,3,7,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,8,5,6,3,7,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,5,4,2,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,7,6,1,4,2,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[7,1,4,2,6,5,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,1,7,3,5,6,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[2,7,4,1,5,6,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,7,6,4,1,2,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[4,7,6,1,5,2,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[1,7,6,4,5,2,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,3,6,5,7,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,6,5,7,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,3,5,7,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,4,1,6,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,1,5,4,3,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[7,5,6,4,2,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,3,2,6,5,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,5,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,4,3,5,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,1,3,4,5,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[7,2,6,4,5,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,3,6,5,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,3,6,8,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[3,4,7,8,5,6,1,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[3,4,7,2,5,1,6,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[1,4,7,2,5,8,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,2,4,7,1,5,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[6,8,3,4,5,7,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,3,6,7,5,8,1,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[6,3,7,5,8,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,3,8,6,4,5,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,2,7,6,5,1,4,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[1,2,7,6,5,8,3,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[4,8,2,6,1,5,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,3,8,6,4,1,5,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,3,6,2,5,1,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[7,8,3,2,5,1,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,2,5,6,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,1,6,2,5,7,3,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[6,1,2,5,8,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,1,8,6,4,7,3,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[7,1,3,6,8,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,8,3,6,7,4,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,8,3,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,1,8,7,2,3,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,1,5,7,4,2,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[3,1,6,4,7,2,5,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[2,4,7,5,1,8,3,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[6,5,7,1,4,2,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[5,6,8,1,3,2,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,8,5,1,3,4,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,3,4,5,1,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,4,3,1,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[4,2,8,3,1,7,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,3,7,4,8,2,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[5,3,7,4,1,6,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[2,4,7,3,6,1,8,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[5,8,7,6,3,1,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,5,6,8,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,4,7,1,6,5,3,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,2,7,8,5,4,3,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[6,3,1,2,8,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,2,1,3,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,8,1,4,5,6,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,4,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,2,6,1,8,5,3,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[7,8,2,1,4,5,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,1,5,3,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,4,6,1,5,8,7,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[7,5,1,6,4,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,8,1,6,3,4,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,5,1,8,2,7,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,8,1,7,5,2,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,6,1,8,5,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,6,1,7,4,8,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[3,6,1,5,7,4,2,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[2,5,6,1,7,4,8,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[3,1,7,5,6,4,8,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[5,1,7,6,4,8,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,1,7,8,5,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,1,8,6,5,4,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,6,5,7,3,4,8,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,6,4,7,5,8,2,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[8,5,3,6,2,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,6,8,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[4,7,5,6,3,2,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[1,7,6,5,4,8,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,1,6,5,7,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,8,3,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[6,1,7,5,3,8,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[2,1,7,5,6,8,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[5,4,1,7,6,8,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[4,8,5,6,2,7,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,4,2,7,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,8,6,3,7,4,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,1,6,2,4,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,1,4,7,2,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,4,1,7,2,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,1,8,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[3,7,4,1,8,5,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[6,7,1,4,8,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[2,7,1,8,4,5,3,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,2,8,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,1,4,3,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,6,2,5,8,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[8,5,1,3,7,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,7,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,1,8,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,5,4,2,8,3,6,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[6,4,3,1,5,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[3,7,6,8,4,5,2,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,6,8,5,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,6,8,5,4,2,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,4,8,6,7,5,2,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,6,7,3,5,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[7,3,8,5,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,4,8,5,6,7,2,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[6,3,5,8,4,7,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,4,3,8,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,4,2,8,7,3,6,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,2,5,8,7,3,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,2,8,5,7,4,6,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,7,5,6,2,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,7,4,6,3,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,8,5,7,6,2,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,8,7,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,4,1,8,7,6,2,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,8,6,7,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,7,5,6,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,6,3,5,8,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[6,2,1,4,3,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,2,1,4,3,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,2,1,4,3,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,3,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,1,3,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,2,4,1,3,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,2,6,1,3,5,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[2,1,6,4,3,5,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,6,1,4,3,5,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,6,4,1,3,5,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[4,6,2,1,3,5,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[6,4,2,1,3,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,4,2,1,3,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,6,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,1,8,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,6,2,1,8,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[2,6,1,4,3,8,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,1,6,4,3,8,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[2,1,8,4,3,6,5,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,8,1,4,3,6,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,1,3,6,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,1,3,6,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,1,6,3,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,8,2,1,4,3,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,6,2,1,4,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,4,6,3,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,8,4,6,3,5,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,4,8,3,5,7]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[2,6,1,4,8,3,5,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,4,1,8,3,5,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,4,8,1,3,5,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[4,6,2,8,1,3,5,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,2,6,1,3,8,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[4,2,6,1,8,3,5,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[6,2,4,1,8,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,2,4,1,6,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,6,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,4,8,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,2,1,6,8,3,5,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[4,2,1,6,3,8,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[4,2,1,3,6,8,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[2,1,4,3,8,6,5,7]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,4,1,3,8,6,5,7]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[4,2,1,3,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,2,1,8,3,6,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,2,1,8,6,3,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[6,2,1,8,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,2,1,6,4,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,4,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,4,3,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,2,8,1,6,3,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,2,8,1,3,6,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,1,3,6,5,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,1,8,3,6,5,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,1,4,8,3,6,5,7]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,4,8,6,3,5,7]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,4,8,1,6,3,5,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,6,1,3,5,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,2,8,6,1,3,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,2,8,4,1,3,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,2,6,4,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,1,3,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,6,8,2,1,3,5,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[2,6,8,4,1,3,5,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,6,8,1,4,3,5,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,6,1,8,4,3,5,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,1,6,8,4,3,5,7]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,8,6,4,3,5,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,8,1,6,4,3,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,4,1,3,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,2,1,3,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,8,4,2,1,3,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,2,6,1,5,4,8,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[5,2,4,3,8,1,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,2,4,1,5,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,3,6,1,5,2,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[4,3,5,2,8,1,7,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[4,3,7,2,6,5,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,3,8,2,6,1,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,1,7,2,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,1,5,2,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,1,8,3,4,2,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,1,3,2,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,1,5,4,8,3,7,6]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[5,1,7,6,8,3,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[4,3,7,6,8,1,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,3,7,1,8,5,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,3,6,5,8,1,7,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[6,3,5,4,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,3,5,4,8,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,1,6,3,8,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,6,5,8,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,1,8,4,6,3,7,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,4,6,1,3,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,4,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,7,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,7,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,6,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,2,6,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,6,3,5,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,5,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,5,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,7,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,6,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,4,6,1,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,8,1,5,4,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,7,6,8,1,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[3,2,7,1,8,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[3,2,6,5,8,1,7,4]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[6,5,7,2,4,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,5,8,2,4,1,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,4,1,8,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,8,2,4,1,5,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,8,1,5,2,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,1,7,3,8,5,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[7,1,3,2,8,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,8,5,6,2,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,8,2,6,4,5,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,1,5,4,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,7,4,5,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,4,7,2,6,3,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,4,8,2,6,1,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,5,8,1,7,2,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,1,6,5,8,3,7,4]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[6,5,7,4,8,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,5,7,1,8,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,1,7,4,8,3,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,4,7,1,8,3,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,4,6,3,8,1,7,2]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[2,8,3,1,5,4,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,3,4,7,1,8,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[2,4,8,3,5,7,6,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,2,5,3,1,8,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[4,2,1,8,5,3,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[5,4,1,3,8,2,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,1,4,8,3,2,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,5,8,4,3,2,6,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,8,5,4,3,2,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,3,8,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,5,7,3,8,4,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[5,1,4,7,8,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[4,8,1,5,7,3,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,1,5,3,7,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,6,5,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,8,5,3,7,4,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,8,1,7,4,3,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,4,8,1,7,3,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,7,1,5,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,6,4,1,3,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,7,5,6,3,2,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,2,1,7,8,5,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[2,7,4,6,3,1,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,6,8,4,3,7,5,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,2,4,8,3,7,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,2,6,3,4,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,6,7,3,1,4,8,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[2,7,1,8,3,5,4,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,1,7,3,5,8,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[8,7,1,3,6,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,3,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,3,1,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,2,6,3,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,7,4,5,6,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,3,7,1,5,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,7,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,7,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,2,6,7,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,8,6,7,4,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[2,8,5,7,6,4,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,8,5,2,6,4,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,8,1,6,4,2,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,6,1,5,3,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,3,8,6,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,6,1,5,3,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,4,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,6,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,1,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,3,5,7,2,8,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[8,5,2,7,4,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,6,1,2,8,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[3,5,1,4,6,2,8,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[8,3,4,5,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,6,3,8,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[2,8,4,6,3,7,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,4,7,3,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,5,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,7,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,5,7,4,3,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,7,1,8,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,5,1,4,7,8,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,3,4,7,5,8,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,1,4,6,8,3,7,2]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[4,7,1,3,5,8,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,8,3,7,1,2,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,4,1,7,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,2,5,7,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,5,4,1,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,2,6,4,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,4,2,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,8,4,2,3,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,3,7,8,2,4,6,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[8,3,6,2,1,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,6,2,1,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,3,6,2,8,7,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,7,8,6,4,2,1,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[2,6,7,5,4,8,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[6,1,7,4,5,8,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,7,3,5,1,8,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[2,1,6,7,5,8,3,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[2,1,5,7,3,6,8,4]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[5,7,3,6,1,2,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[4,1,7,2,5,6,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[2,4,7,1,6,5,8,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[4,6,2,1,8,7,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[3,4,6,2,7,8,5,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[4,6,1,2,5,8,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[5,6,1,4,8,2,7,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,6,3,1,8,7,2,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[3,5,6,4,7,1,8,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[3,4,6,1,5,7,8,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[3,4,1,5,7,6,8,2]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[3,8,2,7,1,6,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,7,6,1,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,7,6,5,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,7,6,5,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,2,6,5,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,2,6,5,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,2,6,1,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,2,1,6,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,3,1,6,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,3,2,1,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,3,2,6,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,3,2,6,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,3,6,2,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,3,6,2,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,3,6,1,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,3,6,5,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,3,6,5,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,3,4,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,3,1,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,3,2,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,2,4,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,2,1,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,4,2,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,4,2,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,4,1,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,4,3,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,1,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,5,2,6,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,5,2,6,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,3,5,2,7,4,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[7,2,1,5,6,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,5,1,6,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,6,1,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,4,5,7,3,2,8,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,4,6,7,3,8,2,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[6,4,5,7,3,1,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,4,5,7,1,3,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,3,5,1,7,4,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,2,1,5,7,4,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[3,2,1,5,7,4,8,6]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[2,4,6,7,3,8,1,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,4,6,7,3,8,5,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,5,6,7,8,3,4,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[2,5,6,7,8,3,1,4]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[3,2,1,6,7,8,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[5,2,1,6,7,8,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[5,3,6,1,7,8,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[5,4,6,7,1,8,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[1,5,6,7,8,3,2,4]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[6,4,5,7,2,1,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,4,6,7,2,8,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[5,3,6,2,7,8,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[5,3,6,2,7,8,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[6,3,5,2,7,1,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,3,4,2,1,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,3,4,1,2,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[4,3,6,2,7,8,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[4,3,6,2,7,8,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[1,3,6,2,7,8,5,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,4,6,7,2,8,5,3]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[3,4,6,7,2,8,5,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[3,4,5,7,2,1,8,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[4,2,1,5,7,3,8,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[4,2,1,6,7,8,3,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[4,3,6,1,7,8,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[1,5,6,7,8,2,4,3]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,5,6,7,8,4,2,3]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[3,4,6,7,1,8,5,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[4,3,6,1,7,8,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[4,2,1,6,7,8,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[2,3,6,1,7,8,5,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[2,4,6,7,1,8,5,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[2,5,6,7,8,1,4,3]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,4,3,6,2,5,7,8]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,4,3,7,2,5,6,8]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,4,3,7,6,8,2,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,4,3,7,5,8,2,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,4,3,7,2,6,5,8]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,5,3,7,4,8,2,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,3,2,6,5,8,4,7]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,5,4,8,2,6,3,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,5,4,8,3,7,2,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,2,3,6,5,8,4,7]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[6,8,2,4,5,7,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,7,8,4,5,2,6,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[7,8,1,4,5,3,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,8,7,4,1,6,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,6,1,5,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,1,6,4,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,1,4,7,6,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,5,1,8,6,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,1,8,2,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,8,4,2,6,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,6,3,8,5,2,4,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,1,3,8,5,2,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,1,8,3,6,2,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,1,8,4,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,8,4,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,3,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,3,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,8,2,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,2,8,3,5,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,5,2,3,8,4,7,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[5,1,2,3,8,4,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,2,3,8,1,4,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,2,8,1,3,5,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,4,1,8,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,3,1,4,2,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[3,1,6,4,2,8,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[2,6,3,8,7,1,5,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,3,8,5,1,4,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,5,1,8,3,4,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,5,1,3,8,4,7,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,2,5,3,8,4,7,6]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,2,4,8,3,7,6,5]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,4,8,1,3,7,6,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,3,7,1,6,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,3,7,6,1,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,5,3,8,1,7,4,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,5,4,1,3,8,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[3,1,5,4,8,2,7,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[5,3,1,4,8,2,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,2,3,8,4,7,1,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,8,2,3,7,6,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,3,7,1,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,2,3,7,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,4,8,2,3,7,6,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,4,8,3,7,2,6,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,3,8,1,5,2,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,3,8,1,2,4,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,3,8,2,4,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,5,3,8,2,4,7,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,5,4,8,2,7,6,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,1,4,8,2,7,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,4,8,1,2,7,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,5,1,2,8,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,3,1,6,4,2,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[5,1,6,2,8,7,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[4,1,5,8,2,7,6,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,1,2,5,8,7,6,3]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[1,4,2,5,8,7,6,3]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,3,5,2,8,7,4,6]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[3,5,1,2,8,7,4,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[3,6,2,8,7,5,1,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,2,6,1,8,7,3,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,3,1,5,8,2,7,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[3,5,2,8,7,1,4,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,4,8,7,2,6,1,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,7,1,2,6,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,1,7,2,6,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,3,4,8,7,2,6,5]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,3,4,8,2,7,6,5]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[3,4,8,1,2,7,6,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,2,7,1,6,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,2,7,6,1,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[4,2,5,8,1,7,6,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,3,1,2,5,8,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[3,1,4,2,5,8,7,6]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[2,3,5,1,8,7,6,4]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[7,8,2,1,5,3,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,4,1,2,7,3,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[2,3,7,5,4,1,8,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[6,3,1,5,4,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[7,8,1,5,4,2,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,5,4,1,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,5,4,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,5,4,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,2,1,5,4,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[5,3,6,1,4,7,8,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[5,3,6,2,4,7,1,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[6,4,2,1,7,3,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[4,3,7,5,8,6,1,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,2,7,1,8,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[3,2,6,7,4,8,1,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[3,1,6,7,4,8,5,2]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[1,7,6,5,3,8,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,6,5,3,8,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,6,5,2,4,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,7,6,5,3,1,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7,1,4,8,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,6,4,8,5,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[5,7,6,3,8,4,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,1,6,2,4,8,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[4,7,6,5,2,1,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,7,6,5,2,8,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,7,6,5,1,8,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,7,6,5,2,8,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,6,5,3,2,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,7,6,5,1,2,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[4,7,6,5,3,1,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[6,1,3,5,4,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,2,6,3,4,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[5,1,6,2,4,7,8,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[1,2,6,3,4,8,7,5]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,7,2,4,8,3,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,4,2,8,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,1,8,2,6,3,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,7,2,1,5,3,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,7,1,6,2,3,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[1,7,2,6,8,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,2,6,7,4,8,5,3]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[3,1,6,7,4,2,8,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[3,2,8,5,4,6,1,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,7,6,3,5,8,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,7,1,2,5,3,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,7,6,5,2,4,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,6,5,1,4,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[3,7,6,5,2,1,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,7,6,5,8,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,6,5,8,1,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,6,5,1,2,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,1,6,8,4,2,5,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[4,7,6,8,3,5,1,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[2,7,6,5,1,4,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7,6,5,8,1,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,6,5,8,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,2,1,7,4,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[4,2,1,7,3,5,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[7,3,1,5,4,2,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,1,5,2,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,1,3,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,1,5,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[6,3,7,4,2,1,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[4,7,2,5,3,1,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[2,7,5,4,1,3,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[7,5,4,3,2,1,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,5,3,2,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,8,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,6,3,2,8,1,5,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[5,7,4,3,2,8,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[1,7,6,2,4,8,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,3,6,4,8,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,7,5,3,8,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[7,1,8,5,3,6,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,8,1,6,2,7,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,8,6,2,3,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,3,2,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,2,7,1,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,7,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,4,3,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,7,2,4,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,1,7,2,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,6,7,1,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,2,8,5,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,3,7,5,8,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[3,7,2,6,8,4,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,6,5,8,1,4,2,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,5,8,4,1,3,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,5,4,8,3,2,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,4,3,7,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,8,1,4,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,3,6,8,2,1,5,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[6,3,5,1,8,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,4,1,5,7,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,5,8,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,4,1,6,8,2,3,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[6,5,2,1,7,8,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,3,7,4,8,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[4,7,2,5,8,6,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[6,3,1,8,4,7,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,2,8,7,3,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,3,8,7,4,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,5,3,7,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,7,6,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,8,1,7,3,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,4,8,2,1,7,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,6,8,1,4,7,5,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,8,1,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[6,4,7,8,1,5,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,3,7,8,5,2,4,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[2,5,8,7,1,3,6,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,3,8,7,2,1,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,3,7,6,1,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,5,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,6,2,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,7,6,1,3,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,5,8,7,2,6,1,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,3,8,6,5,1,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[7,5,8,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,8,7,3,6,4,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,7,6,2,5,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,6,5,1,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,1,2,4,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[3,7,5,8,2,4,1,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,8,5,7,2,4,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,8,4,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,1,2,6,4,3,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[6,1,2,5,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,1,2,4,6,3,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[4,1,2,6,5,3,8,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[4,1,5,7,8,3,2,6]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[4,1,5,8,7,3,2,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,7,1,8,3,6,2,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,1,7,8,5,2,3,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[5,1,7,4,8,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[7,5,3,8,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,1,5,8,7,3,4,6]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[5,1,8,4,7,2,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,1,8,7,5,2,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,7,1,6,3,2,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[6,1,2,3,7,5,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[7,1,2,3,8,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,2,3,5,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,8,1,4,3,7,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,7,3,2,4,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,3,4,8,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[7,8,3,2,4,1,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,7,1,4,3,8,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[8,1,2,3,5,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,6,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,6,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,2,3,8,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,1,2,3,7,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,6,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,5,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,8,2,6,3,4,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,2,7,3,4,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,2,8,3,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[3,8,7,1,4,2,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,8,1,4,2,6,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,6,8,1,4,2,7,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,5,7,8,2,4,1,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[3,6,7,1,4,2,8,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[7,6,2,8,3,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,6,2,7,3,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,4,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,5,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,1,4,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,4,6,8,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[6,7,3,2,4,1,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[8,7,2,4,3,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,5,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,2,3,8,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,1,2,3,7,8,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[5,1,2,3,8,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,1,2,3,8,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,1,2,3,5,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,6,2,4,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,2,4,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,1,6,3,4,8,7,5]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[8,6,3,2,4,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,3,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,2,3,5,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,1,2,3,6,8,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[7,8,1,2,6,3,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,4,8,2,7,3,5,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,2,8,5,4,7,3,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,5,4,2,7,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,6,8,4,7,1,5]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,3,6,8,4,7,5,2]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,4,8,1,7,3,6,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,5,7,6,1,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,2,6,8,4,5,7,3]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[7,5,1,2,4,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,6,1,5,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,4,2,6,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,8,1,4,7,2,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,6,4,2,8,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,6,3,8,5,4,2,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,8,1,7,3,5,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,1,3,6,5,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,1,6,5,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,1,4,6,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,3,6,5,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,2,3,6,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,8,1,2,7,3,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,6,2,3,8,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,5,8,2,7,6,3,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,1,8,2,7,6,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,2,7,6,3,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,2,8,1,7,3,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,2,1,7,4,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,6,4,1,2,8,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[2,1,6,3,8,5,4,7]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[2,5,1,8,7,6,3,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,5,3,8,7,4,6,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,2,5,3,8,7,4,6]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[2,4,8,7,6,5,1,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,5,3,8,7,1,6,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,5,8,4,1,7,6,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,8,7,1,4,2,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[5,3,8,4,1,7,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,2,8,7,6,3,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,2,8,7,6,5,3,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,8,7,6,5,3,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,7,6,5,1,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,3,1,8,7,2,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,8,3,7,6,1,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,1,3,8,7,6,2,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,5,3,8,7,6,2,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,5,8,4,7,2,6,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,1,8,4,7,2,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,7,4,6,1,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,5,1,2,4,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,6,3,1,2,4,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[5,6,2,4,3,1,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[5,6,1,2,4,3,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[4,5,8,1,7,2,3,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,1,7,2,6,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,3,2,5,8,7,4,6]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[3,5,1,8,7,4,6,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,5,1,8,7,2,6,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,6,1,2,8,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[4,5,8,3,1,7,2,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,2,8,7,1,3,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,2,5,8,7,1,6,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[3,4,8,7,6,2,1,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,1,4,8,7,6,2,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,4,8,7,6,5,1,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,3,4,8,7,6,2,5]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[3,4,8,7,6,2,5,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,2,5,8,7,4,6,1]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[4,5,8,3,1,7,6,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[2,1,3,5,8,7,4,6]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,7,5,8,6,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[7,1,4,8,2,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,8,1,3,7,5,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,7,8,1,2,6,5,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,3,7,8,2,6,5,4]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,3,7,8,1,6,5,4]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,7,8,1,3,6,5,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,1,2,6,7,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,7,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,1,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,6,7,3,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,8,3,7,1,5,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,8,6,4,7,1,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,3,4,1,7,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,3,7,4,1,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,6,8,3,7,5,1,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,8,1,6,7,5,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,5,7,1,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,3,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,4,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,7,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,3,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,4,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,4,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,6,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,3,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,7,2,5,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[8,3,5,7,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,3,6,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,5,4,7,1,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,1,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,7,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,8,2,7,5,3]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,6,5,8,2,7,4,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[8,5,6,3,1,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,8,1,7,4,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[1,8,4,5,7,2,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,3,6,1,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,3,5,7,1,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,3,7,5,2,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,3,8,2,7,5,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,4,2,7,1,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,6,4,7,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,7,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,7,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,4,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,4,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,7,1,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,3,4,5,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,3,6,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,7,2,3,4,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,6,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,5,4,7,6]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[4,2,8,5,3,7,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,2,1,8,4,3,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,2,8,4,3,7,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,8,4,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,4,8,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,3,4,8,2,7,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,3,4,1,8,2,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[8,1,4,5,2,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,3,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,2,8,1,7,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[4,5,3,2,8,7,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[6,4,3,2,8,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,3,2,1,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,6,3,2,7,8,4,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[4,1,6,3,2,7,8,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[3,6,4,2,7,8,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[8,1,6,4,3,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,3,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,3,6,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,4,2,6,1,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[4,1,7,3,2,6,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[5,7,3,2,6,4,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[6,7,3,2,5,4,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,3,2,1,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,7,5,6,2,3,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,1,7,5,6,2,4,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[2,7,5,6,1,3,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,6,5,7,1,3,8,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[4,6,5,7,2,8,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[5,6,4,7,2,8,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[6,5,4,1,7,2,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[7,5,4,6,2,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,4,5,7,1,8,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,4,6,1,7,8,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[8,1,5,6,7,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,6,8,7,3,5]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,4,6,8,7,1,2,5]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[4,3,1,6,8,7,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[5,3,6,8,7,2,4,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,3,5,1,8,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,3,5,8,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,8,5,6,3,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,8,5,1,7,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,2,1,8,6,7,3,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,3,2,8,6,7,4,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,3,8,6,7,1,4,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[8,1,3,2,6,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,1,6,5,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,2,8,7,6,1,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,2,8,7,6,4,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,2,1,8,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,6,1,8,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,7,8,5,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,3,7,8,6,4,1,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,3,1,7,8,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[3,4,7,8,6,1,5,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[8,1,5,7,6,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,6,8,1,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[4,5,7,6,8,3,1,2]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[5,4,1,7,6,8,3,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[6,4,7,5,8,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,4,6,5,1,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,6,4,3,1,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,5,1,7,4,3,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[4,6,7,5,3,8,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[3,6,7,5,1,4,8,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[8,1,6,7,5,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,1,5,4,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,6,5,1,4,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[4,7,6,5,3,1,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[8,6,4,3,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,5,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,3,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,7,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,5,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,7,2,4,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[8,7,1,2,4,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,4,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,6,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,4,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,6,4,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,3,4,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,2,4,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,5,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,7,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,5,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,2,3,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,1,4,2,7,3,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[7,1,5,8,2,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,7,8,1,2,4,6,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,1,3,4,6,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,8,1,7,3,4,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,1,5,7,2,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,7,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,8,7,5,6]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,4,2,7,6,3,5,8]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[6,1,2,8,7,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,1,2,4,8,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,1,8,4,6,7,5,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,7,6,4,8,5,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[7,1,2,4,6,8,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,2,6,8,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,1,2,7,8,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,1,2,7,4,8,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[3,1,6,4,7,8,5,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[5,7,1,3,8,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,1,8,4,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[7,1,5,3,2,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,4,5,2,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,7,3,1,5,8,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,8,7,3,1,5,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,1,7,4,5,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,3,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,2,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,4,7,5,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,1,2,8,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,1,7,2,6,4,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[1,4,2,3,8,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,4,2,3,8,5,7,6]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[5,8,1,7,2,4,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,1,3,4,7,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,1,8,6,4,7,5,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,1,2,6,7,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,7,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,2,3,5,8,4,7,6]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,3,5,8,6,4,7]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[7,1,2,8,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,2,8,6,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,1,7,8,4,6,5,2]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[3,1,8,7,6,4,5,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,1,2,7,4,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,3,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,5,8,7,4,6]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,3,6,8,5,4,7]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[7,8,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,5,6,3,1,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,8,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,8,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,5,8,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,6,3,4,1,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,6,3,1,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,6,3,1,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,3,6,1,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,3,1,4,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,3,1,6,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,3,6,1,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,3,6,4,1,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,3,6,4,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,3,8,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,3,8,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,3,1,8,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,3,1,8,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,3,1,6,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,3,1,6,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,3,1,8,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,3,1,8,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,3,6,1,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,3,6,4,1,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,3,8,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,8,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,6,8,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,6,3,8,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,3,4,1,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,6,3,1,8,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,6,3,1,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,6,3,8,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,6,3,8,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,3,6,8,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,3,6,8,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,3,6,1,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,3,1,6,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,3,1,6,8,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,3,1,2,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,3,1,2,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,3,1,4,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,3,4,8,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,3,4,1,6,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,3,1,4,6,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,6,2,5,4,1,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[3,5,2,8,4,7,6,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[5,4,7,3,2,8,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,4,8,3,2,7,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,4,5,3,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,3,2,6,4,1,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[4,5,8,3,2,7,6,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,3,8,5,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,8,6,3,7,5,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,3,2,7,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,3,2,7,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,3,2,8,4,7,6,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[2,1,5,8,4,7,6,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[5,3,2,7,4,8,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,7,4,3,2,8,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[4,7,5,3,2,8,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,7,8,3,6,5,2,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,6,8,3,7,5,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[7,6,4,3,8,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,2,6,8,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,1,8,6,7,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,3,2,6,7,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,8,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,7,2,6,8,5,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,8,2,6,7,5,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,5,4,7,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,8,6,5,4,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,6,2,8,7,5,4,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[6,4,7,3,8,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,4,8,3,7,5,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,4,8,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,5,3,2,8,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,4,3,2,8,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,2,5,4,8,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,1,7,5,4,8,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[7,3,2,8,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,8,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,5,7,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,3,7,5,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,3,2,8,7,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,2,7,8,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,7,4,3,8,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[4,6,8,3,5,7,1,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[6,8,1,2,4,5,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,5,8,2,4,7,1,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[8,3,5,2,4,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,3,6,1,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[4,5,2,8,3,1,6,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,2,5,8,3,7,1,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[2,1,6,8,4,7,3,5]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,5,8,3,6,7,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[5,3,6,8,4,7,1,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,6,5,8,2,4,7,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[3,1,2,6,8,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[1,4,3,8,2,6,7,5]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[5,4,8,3,2,1,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,3,7,2,6,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,3,6,2,7,5,1,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[4,6,3,2,1,8,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[4,1,7,3,2,5,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,3,1,7,8,2,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[3,5,1,2,7,8,6,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[7,5,1,4,8,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,4,7,3,8,6,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,8,4,7,6,3,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,1,4,2,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,3,5,1,2,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,7,2,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,3,5,2,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,1,5,2,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[4,7,3,6,5,2,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[5,3,7,6,4,2,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[1,6,3,4,2,8,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,8,3,6,2,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,8,7,4,2,5,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,4,8,7,5,3,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,6,4,3,8,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,7,6,2,8,4,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,1,3,2,6,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,5,3,2,7,4,8,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[6,3,2,1,8,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,3,2,7,4,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[5,2,6,3,7,4,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[2,8,5,3,1,6,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,8,5,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,2,3,7,8,5,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,6,7,2,8,4,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,7,1,8,2,4,6,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,1,2,7,8,3,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[2,4,1,7,8,6,3,5]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[4,2,1,7,3,8,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[6,2,8,4,3,1,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,3,2,1,8,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,8,3,2,5,6,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,8,2,4,5,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,6,1,2,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,2,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,5,1,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,3,6,5,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,5,2,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,6,2,5,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,4,1,6,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,7,5,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,2,4,1,7,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,6,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,5,4,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,1,6,7,5,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,6,4,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,7,5,4,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,8,6,4,3,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,7,2,6,4,3,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,2,7,5,4,3,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[2,1,8,6,5,4,3,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,7,5,4,3,8,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,7,2,4,3,8,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,2,8,3,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,8,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,3,8,6,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,8,7,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,7,3,2,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,3,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,1,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,1,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,7,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,4,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,7,5,1,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[1,4,3,7,2,5,8,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[7,4,8,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,5,8,3,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,7,4,1,8,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,4,3,1,8,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[1,8,7,2,5,4,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,3,7,2,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,8,7,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,4,8,6,3,5,2,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[7,4,6,3,5,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,3,5,6,8,4,2,7]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[3,5,4,8,7,1,2,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,1,4,6,8,7,2,5]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[1,6,3,8,7,2,5,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,2,4,8,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[8,4,1,6,7,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,4,8,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,6,8,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,3,7,2,6,8,4,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[3,6,5,2,8,1,4,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,6,5,7,2,4,1,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[4,2,6,3,8,1,5,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,2,6,7,3,5,1,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[3,6,2,4,7,5,1,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[3,6,2,4,1,8,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[7,3,8,2,1,6,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,5,2,1,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,1,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,1,4,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,7,1,5,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,8,2,1,5,4,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[2,4,8,1,6,5,3,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,2,8,1,5,7,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,5,7,6,1,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,3,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,5,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,8,7,3,5,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,8,2,4,6,7,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,4,7,1,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,8,6,4,3,7]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[7,2,5,6,4,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,2,5,7,8,4,3,6]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,7,4,8,6,3,5]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,2,7,8,3,6,5,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[7,1,8,6,3,5,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,8,7,6,3,5,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,4,6,3,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,8,3,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,6,4,2,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,6,2,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,5,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,4,5,8,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,1,6,4,5,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,4,5,6,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,4,6,5,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,2,3,8,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,5,4,3,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,3,4,2,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,5,4,6,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,5,6,4,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,6,5,4,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,6,2,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,7,4,3,6,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[2,5,1,4,7,8,6,3]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[3,5,1,4,8,6,2,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[3,6,2,4,7,8,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[5,6,2,4,8,7,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[6,3,8,2,4,7,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,7,2,3,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,7,8,2,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,3,4,2,8,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,4,7,2,5,8,1,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[4,6,8,1,3,5,2,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,3,8,1,2,7,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,6,4,1,7,2,5,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[2,8,3,1,5,6,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,1,5,4,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,6,8,2,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[3,4,1,7,5,6,8,2]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[3,4,1,5,7,6,2,8]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[3,7,4,1,6,2,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[8,4,7,2,5,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,1,2,3,6,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[2,8,6,1,5,3,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,3,8,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,5,1,3,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,2,6,4,1,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,5,2,1,3,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[8,4,5,3,7,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,2,8,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[2,6,4,3,1,5,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[7,3,8,4,1,5,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,3,4,1,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,2,8,3,6,1,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,8,5,7,2,1,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,5,2,7,1,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,2,1,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,8,5,3,1,4,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,6,5,4,2,8,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,6,4,7,2,5,3,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,6,4,8,2,5,3,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,5,8,2,4,3,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,8,2,4,3,7,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,6,2,4,3,7,8,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,5,6,2,4,7,3,8]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,5,6,2,4,7,8,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,5,8,2,4,7,3,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,5,7,2,4,8,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,6,5,7,2,4,3,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,6,7,2,4,3,8,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,5,6,7,2,4,8,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,5,8,2,4,6,7,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,5,7,2,4,6,8,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,5,7,8,3,2,4,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,5,8,3,2,4,6,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,5,6,2,4,8,3,7]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,7,6,2,8,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,3,4,2,8,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,6,2,4,3,8,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,5,6,2,4,8,7,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,5,8,7,3,2,4,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,2,3,5,8,7,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,5,2,3,4,8,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,6,5,2,3,8,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,7,4,2,8,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,6,5,2,8,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,6,7,5,2,3,8,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,7,5,2,8,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,5,6,2,8,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,5,7,6,2,4,8,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,5,8,3,2,4,7,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,6,5,2,3,7,4,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,6,5,2,3,7,8,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,6,8,4,2,3,7,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,7,4,6,2,8,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,3,5,2,8,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,6,8,5,2,3,7,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,6,4,2,3,7,8,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,6,4,2,3,7,5,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,5,8,6,2,4,7,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,5,7,3,2,4,8,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,7,3,4,2,8,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,4,2,8,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,6,7,4,2,3,8,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,6,4,2,3,8,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,7,6,4,2,8,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,5,2,8,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,6,4,2,3,8,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[7,3,5,6,1,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,7,5,6,1,4,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[8,2,4,1,6,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,2,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,4,2,8,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,6,7,4,3,5,8,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[6,7,1,4,3,5,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,6,1,4,3,5,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,5,4,1,6,7,8,2]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[4,7,1,6,3,5,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,1,4,7,6,5,8,2]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[6,1,7,4,3,5,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[7,1,6,4,3,5,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,7,6,4,3,5,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[8,1,6,4,2,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,7,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,3,8,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[7,4,1,3,8,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,3,6,4,2,8,5,7]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[4,7,3,1,2,8,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,7,8,1,2,6,5,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[6,8,1,4,2,7,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,6,4,2,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,3,7,2,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,3,6,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,3,2,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,4,3,7,2,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,4,7,6,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,8,4,6,2,1,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,4,6,8,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[2,4,3,7,8,6,1,5]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,4,7,3,8,2,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[5,7,6,8,3,2,1,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[2,5,3,4,8,6,1,7]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[3,7,5,4,8,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[7,1,3,4,2,8,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,1,4,3,8,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,1,7,3,8,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[8,1,4,3,7,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,7,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,7,8,6,1,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[5,2,3,4,8,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[2,7,5,6,3,8,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,7,2,6,3,8,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,2,6,8,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[7,2,5,6,8,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,2,3,8,5,6,1,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[5,2,3,8,7,6,1,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,2,3,7,5,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,7,2,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,7,8,4,2,6,5,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[4,7,1,8,2,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[3,7,4,8,5,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,4,3,8,5,6,1,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,4,8,3,6,2,5,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[7,5,8,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,5,8,7,3,2,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,5,7,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,3,8,7,6,1,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[3,7,5,8,6,2,1,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,8,6,5,2,1,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,8,7,3,6,2,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,7,5,3,2,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,7,6,8,3,4,1,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,7,6,8,4,5,1,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,5,4,7,6,8,2,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,7,4,6,5,8,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,4,6,5,8,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,5,4,8,6,7,1,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,8,4,6,5,7,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,7,5,8,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[1,6,2,7,5,8,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,6,4,8,5,7,2,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,8,4,6,5,7,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,8,6,7,2,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[7,8,1,5,4,6,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,5,2,4,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,8,2,6,5,7,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,8,5,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,2,6,5,8,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,5,2,7,6,8,3,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,7,6,8,2,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,6,8,4,5,2,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,7,6,8,1,4,2,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[7,8,5,6,1,3,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,8,6,7,1,3,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,3,2,7,6,8,4,5]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,7,6,8,2,4,3,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,8,1,3,2,6,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,6,2,4,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,8,6,7,2,4,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,1,4,2,6,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,4,2,5,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,2,4,3,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,3,6,5,8,7,1,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[3,4,6,5,7,8,1,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[1,6,2,3,8,7,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,7,4,3,2,8,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,4,7,6,2,5,8,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,2,6,5,3,7,4,8]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,2,6,5,3,7,8,4]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,3,7,5,2,6,8,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,3,7,4,2,6,8,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,2,6,4,3,7,8,5]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,2,6,4,3,7,5,8]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,4,7,3,2,5,8,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,4,3,2,5,8,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,5,3,2,4,8,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,7,5,3,2,8,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,5,3,2,4,8,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[7,6,5,4,3,1,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,8,5,4,3,2,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,1,5,4,3,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,6,5,4,8,1,7,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[6,8,1,4,3,2,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,5,4,3,7,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,4,3,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,6,5,8,3,1,7,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[6,8,5,1,3,2,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,2,4,3,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,4,7,2,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,1,3,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,6,3,4,8,7,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,4,5,8,3,7,6,2]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[6,8,5,4,1,2,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,5,2,3,7,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,2,4,3,7,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,3,4,7,2,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,8,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,8,5,7,3,2,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,6,8,4,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[6,4,8,5,2,7,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,1,8,6,7,4,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,4,7,5,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,2,1,7,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,4,5,8,1,2,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,4,6,5,2,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,6,5,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,6,1,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,8,4,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,1,8,7,4,2,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,8,6,7,4,3,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,4,1,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[5,2,3,6,4,1,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[6,1,4,5,3,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[3,8,7,1,4,6,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,4,3,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[4,3,7,6,8,2,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[5,3,6,8,1,7,2,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[3,2,6,8,5,7,1,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[6,3,7,2,4,8,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[7,4,8,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,8,2,5,4,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,5,3,7,4,1,8,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[3,6,4,7,5,1,8,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[8,4,7,6,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,2,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,3,5,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,1,7,4,2,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,4,1,5,8,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,5,8,7,3,6,1,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,1,5,8,7,4,6,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[8,3,5,6,7,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,2,8,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,2,7,1,8,5,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,1,7,2,8,5,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[2,4,8,7,3,5,6,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,7,8,3,1,5,6,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,4,7,2,8,5,6,1]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[3,7,1,4,8,5,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[7,2,3,4,8,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,1,8,5,2,7,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,1,7,4,5,8,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,1,8,3,6,7,5,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,2,1,6,4,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,6,4,1,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,6,3,5,8,7,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[7,6,2,1,5,8,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,5,2,7,6,1,8,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[5,1,6,8,4,7,2,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[3,6,8,7,5,2,1,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[7,4,8,6,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,1,6,4,7,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,2,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,6,4,8,5,3,7,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[7,3,5,8,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,2,5,8,4,1,7,6]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[8,4,7,1,5,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,5,6,1,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,8,7,3,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,2,8,4,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,7,8,1,3,5,6,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[8,7,3,4,1,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,7,3,5,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,1,8,7,2,5,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,8,1,7,2,5,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,3,7,1,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,1,3,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,8,4,6,7,3,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,8,2,7,6,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,8,4,2,1,3,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,2,4,3,5,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,8,3,7,1,5,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,2,7,3,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,3,2,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,3,8,6,2,1,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,6,5,2,8,3,1,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,3,7,5,1,8,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[6,8,5,2,7,4,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,2,5,4,3,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,6,8,1,4,5,2,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[6,8,1,2,4,5,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,1,6,2,4,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,2,5,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,6,2,3,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,1,6,5,8,2,3,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,3,8,6,2,5,1,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,3,6,1,4,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,4,5,1,7]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,7,5,4,3,8,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,3,8,7,4,2,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,8,4,3,7,6,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,8,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,1,5,3,4,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,8,6,1,7,4,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,5,7,2,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,8,2,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[6,1,8,7,4,3,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,5,4,3,1,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,3,4,7,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,5,8,6,3,4,7,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,1,3,8,5,6,7,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[6,5,8,4,3,1,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,6,5,2,8,1,7,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[7,2,8,1,3,6,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,8,5,2,3,6,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,2,5,6,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,1,5,6,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,2,5,6,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,2,3,1,5,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,5,6,7,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,8,2,3,6,7,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,1,2,7,8,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[7,5,1,8,2,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,5,8,1,2,4,7,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,1,2,3,7,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,2,7,1,8,6,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[3,8,4,1,2,6,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,8,2,3,6,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,3,6,7,4,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,8,4,7,5]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[2,4,3,7,1,8,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,4,7,3,2,8,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[2,7,1,4,3,8,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,4,1,8,6,3,7,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[8,4,1,3,6,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,7,2,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,3,6,5,8,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,3,5,8,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,5,8,7,3,6,1,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,5,2,8,6,1,7,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[8,2,5,6,1,4,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,1,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,3,7,5,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[4,7,1,6,2,8,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[6,1,5,3,8,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,8,6,3,7,1,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,5,8,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,6,8,5,1,2,7,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[6,5,2,4,8,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,1,4,8,2,6,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,8,2,5,1,6,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,5,2,6,7,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[4,2,1,8,5,6,7,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,5,4,8,2,6,7,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[7,2,1,5,8,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,8,4,5,1,6,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,8,3,7,6,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,1,5,8,6,2,7,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[6,3,4,8,5,1,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,3,4,8,1,6,7,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[7,6,1,2,8,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,8,4,1,2,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,5,4,8,7,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,4,8,1,2,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,5,1,6,2,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,1,6,8,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,4,1,8,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,4,7,1,2,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,5,4,7,8,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,5,3,7,1,4,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,5,3,1,8,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,5,1,4,8,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,1,6,4,7,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,8,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,3,7,1,4,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,4,3,1,5,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,4,1,5,3,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,1,5,4,3,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,3,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,3,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,4,1,5,3,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,1,5,4,3,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,2,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,2,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,5,3,8,1,4,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,6,8,1,4,3,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,1,7,2,5,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,5,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,2,5,4,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,5,3,8,1,4,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,3,1,2,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[7,5,1,4,2,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,6,4,2,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,3,2,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,4,3,1,5,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,4,3,1,5,7,2,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[7,4,1,5,3,6,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,1,5,4,3,6,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,3,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,3,6,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,4,3,1,5,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,7,3,8,4,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,4,5,1,8,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[4,7,5,6,2,3,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,7,5,6,1,8,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,7,5,6,3,8,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,7,5,8,4,6,1,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[4,5,3,8,6,7,1,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,8,3,6,5,7,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,1,8,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[5,6,1,7,3,8,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[5,6,1,8,2,7,3,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,6,1,8,4,7,2,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,8,1,6,5,7,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,8,6,7,2,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[7,8,4,5,1,6,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,8,2,3,1,6,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,8,1,4,3,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,6,3,4,1,8,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[3,6,4,5,2,7,1,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[3,6,4,5,1,8,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[2,6,4,8,1,5,3,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,8,3,6,1,5,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,4,1,6,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,2,5,3,4,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,5,3,6,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,5,3,8,6,7,2,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,8,3,6,2,7,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,8,2,7,3,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,4,7,3,5,1,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[2,7,3,6,4,5,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,3,6,4,8,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,2,8,4,6,3,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,5,8,4,6,2,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,5,8,2,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,5,6,3,8,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,5,6,3,4,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,7,2,5,3,4,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,7,1,5,3,8,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,7,5,8,1,4,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,8,6,7,2,3,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,1,8,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,7,2,8,1,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[3,4,2,7,5,6,1,8]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[3,4,1,7,5,8,2,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[2,7,5,8,1,4,3,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,3,1,7,5,8,4,6]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[2,3,1,8,4,7,5,6]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[7,8,2,3,1,6,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,6,1,4,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,8,6,7,1,4,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,4,3,7,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,5,4,6,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[4,5,2,7,3,6,1,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[4,5,1,8,2,7,3,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,4,1,8,2,7,5,6]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,4,1,8,6,7,2,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,4,2,5,1,8,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[3,4,2,8,1,6,5,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,8,2,5,1,6,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,8,1,6,3,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,5,3,6,1,8,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[7,1,5,8,4,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,6,7,1,4,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,5,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,3,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,8,3,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,1,3,8,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,8,2,4,5,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,2,8,3,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,2,3,8,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,7,1,5,2,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,2,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,3,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,4,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,4,1,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,7,2,5,1,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,4,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,7,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,1,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,1,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,3,1,4,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,3,1,4,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,5,7,2,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,1,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,2,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,2,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,1,7,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,1,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,7,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,2,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,1,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,1,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,2,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,7,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,8,4,2,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,8,3,6,4,1,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,2,8,6,4,1,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,4,7,5,1,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,1,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,1,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,5,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,3,5,1,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,3,1,5,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,4,7,2,1,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,1,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,7,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,4,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,6,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,2,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,2,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,4,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,7,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,1,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,1,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,1,2,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,2,1,6,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,3,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,3,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,4,1,2,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[3,8,5,6,7,4,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,8,6,2,1,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[2,5,7,8,6,3,4,1]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,8,5,7,6,3,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,6,3,2,1,5,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[6,2,1,5,3,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,8,1,3,7,6,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,7,2,3,6,1,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,7,4,2,8,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,2,6,8,5,7,3,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[6,4,2,7,3,8,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[8,1,6,7,5,3,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,8,7,6,3,4]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,1,4,7,6,3,8,5]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[6,4,7,8,5,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[4,1,3,7,6,2,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[8,5,1,6,3,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,5,2,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[3,2,6,8,4,7,5,1]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[8,4,6,1,3,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,7,3,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[7,4,3,8,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,7,5,8,1,6,3,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[6,4,3,2,7,8,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[4,2,5,1,6,7,8,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[2,4,8,5,7,1,3,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,1,4,6,8,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[7,8,2,5,6,1,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,4,3,8,7,5,6,1]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,6,7,3,5,1,8,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[7,6,8,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,5,7,1,6,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,2,8,4,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[3,4,8,6,5,2,1,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[2,7,6,1,4,5,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,8,2,1,7,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,4,3,5,1,6,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,1,6,3,5,8,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[6,2,5,8,4,3,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,6,7,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,8,4,7,3]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[2,1,6,8,5,4,3,7]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[4,1,8,5,6,2,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,6,4,8,7,3,5,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,2,8,4,3,5,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,8,2,7,6,1,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,1,8,2,7,5,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,8,1,2,6,7,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,3,2,7,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,4,8,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,8,4,7,2,1,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,1,8,4,3,7,5,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,8,2,4,5,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,8,4,2,3,6,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,2,4,3,1,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,8,3,1,6,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,1,3,4,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,2,6,3,5,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,2,7,3,5,4,8,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,2,3,8,4,5,7,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,8,3,4,5,7,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,2,6,4,5,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,5,7,2,3,6,4,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,7,2,3,5,4,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,3,8,2,4,5,7,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,8,4,6,7,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,8,2,3,5,4,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,8,2,3,6,4,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,6,7,8,2,3,5,4]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,7,8,2,5,3,6,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,8,2,4,5,3,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,2,8,3,6,4,5,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,8,2,3,6,4,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,8,3,5,4,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,7,8,3,6,4,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,5,2,7,8,3,6,4]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,3,2,8,4,6,7,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,8,2,3,4,6,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,8,2,4,3,6,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,6,3,1,5,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,3,1,5,2,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,8,3,1,5,2,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,5,1,2,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,4,5,1,2,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,2,1,6,5,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,6,1,5,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,6,5,1,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,5,4,1,2,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[5,8,6,4,1,7,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,7,6,4,1,8,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,6,7,4,1,8,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[6,5,7,4,1,2,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,4,7,5,1,2,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,2,1,7,5,3,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,3,8,1,5,2,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,5,1,2,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,4,1,2,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,6,8,4,1,7,2,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,6,8,5,7,1,2,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,5,8,6,7,1,2,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,4,8,6,1,7,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,3,8,1,6,7,2,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,1,8,6,7,3,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,2,1,7,6,8,3,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,4,7,6,1,8,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[4,5,7,6,8,1,2,3]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[4,6,7,5,8,1,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[4,8,6,5,7,1,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,6,7,1,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,8,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,6,5,7,8,1,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[5,7,4,6,1,8,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,8,4,6,1,7,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,3,1,6,7,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,7,3,1,6,8,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,6,3,1,7,8,2,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[6,2,1,4,3,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,8,3,1,7,6,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,7,4,8,1,6,2,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,2,1,6,8,7,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,4,6,8,1,7,2,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,5,6,8,7,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[4,7,5,8,6,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,8,5,7,6,1,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,7,5,1,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,8,5,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,6,7,8,5,1,2,3]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[4,5,7,8,6,1,2,3]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[5,4,7,8,1,6,2,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,3,7,1,8,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,2,1,7,8,6,3,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,3,8,1,7,6,2,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,7,1,6,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,6,8,7,5,1,2,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,7,8,6,5,1,2,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,8,7,6,5,1,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,7,3,6,1,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[2,4,6,3,7,5,1,8]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[4,2,7,3,6,5,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[4,2,6,3,1,5,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[2,5,3,1,6,4,8,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[2,5,3,7,6,4,1,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[2,6,5,3,7,4,1,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[4,2,7,6,3,5,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[2,7,5,3,6,4,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,6,3,7,5,4,1,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,7,5,2,3,8,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,1,3,7,5,4,8,6]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[2,3,1,8,6,5,4,7]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,5,3,1,8,6,4,7]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,8,3,1,6,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,3,2,6,4,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,1,4,5,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,5,2,8,3,4,7,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,2,6,3,8,7,4,5]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,2,8,3,6,4,7,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,7,6,3,4,8,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[2,1,3,8,7,5,4,6]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,8,6,4,7,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,7,4,8,6,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,2,7,6,3,8,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,2,3,6,4,8,7,5]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,2,3,7,6,4,8,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[2,6,3,1,8,5,4,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,1,3,8,5,4,7,6]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[7,1,8,4,2,3,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,1,8,4,3,5,7,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,6,3,1,8,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[5,4,2,8,3,1,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,5,8,2,4,1,6,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,5,4,8,3,1,6,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,1,8,3,5,7,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,8,7,4,2,3,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,8,7,3,4,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,2,7,3,6,4,8,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,2,8,6,3,7,4,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,7,3,8,6,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,2,3,8,4,7,6,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,7,3,4,8,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,2,6,3,8,4,7,5]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,2,3,8,7,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,2,1,8,3,7,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[8,3,2,1,7,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,7,3,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,8,6,3,4,7,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,7,3,8,4,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,2,3,8,7,4,6,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,8,7,6,4,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,5,3,8,1,6,4,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,6,4,7,1,5,3,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[2,6,5,7,1,4,3,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[3,8,5,7,1,2,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,7,2,6,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,6,2,5,7,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,6,1,2,5,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[2,5,7,1,4,8,6,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[2,4,8,1,5,7,6,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,3,8,1,6,5,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,8,1,7,5,6,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,8,1,6,5,7,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,4,8,1,3,5,7,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,5,7,6,1,2,4,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,5,7,6,2,4,8,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[4,8,6,7,2,3,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,7,1,2,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,7,1,3,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,6,1,5,7,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,8,5,7,1,6,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,5,6,1,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,8,5,7,2,1,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,6,2,1,5,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,5,7,6,2,1,4,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[4,8,6,7,2,1,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,7,3,5,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,3,4,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,2,1,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,2,1,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,6,7,2,1,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,7,5,2,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[4,3,2,8,5,1,7,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,8,5,1,6,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,6,7,1,5,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,1,4,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,2,3,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,2,4,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,1,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,2,3,8,5,1,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,2,8,5,1,7,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,4,2,8,5,6,1,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,4,8,6,1,5,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,2,5,7,6,1,4,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[4,8,6,7,1,3,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,7,1,2,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,7,2,5,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,8,5,2,6,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,5,1,2,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,2,6,7,5,1,3,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[3,8,5,7,1,4,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,7,1,5,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,8,4,6,1,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,5,1,7,4,6,2,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[3,8,4,7,2,5,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,8,5,2,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,1,2,6,7,5,3,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[4,2,6,7,5,3,8,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[4,8,6,7,3,2,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,7,3,1,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,7,6,2,4,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[3,4,1,7,5,6,2,8]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[4,1,7,5,2,8,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,1,6,7,5,2,3,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[4,8,6,7,2,3,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,3,2,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,4,2,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,4,1,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,4,1,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,3,1,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,6,7,3,1,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,5,3,8,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[4,1,7,5,3,2,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,2,8,5,3,1,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,2,1,6,7,5,3,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[4,8,6,7,3,2,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,4,2,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,7,4,3,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,3,5,8,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,8,7,6,1,4,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,8,3,6,7,2,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,4,7,8,5,6,2,3]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,4,7,1,5,8,6,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,1,4,7,8,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[1,6,8,4,7,5,2,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,8,1,3,5,7,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,6,1,4,3,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,8,1,6,5,4,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,5,8,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[6,1,7,3,8,4,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,1,8,6,3,5,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,1,7,6,5,8,4,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[8,2,7,6,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,7,5,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,6,8,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,3,8,6,2,7,5,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,2,7,8,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,8,6,2,5,3,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,8,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[8,7,3,6,4,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,2,1,4,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[2,7,4,1,6,8,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,2,4,5,1,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,6,4,5,2,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,6,5,1,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,7,5,2,6,8]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[7,5,8,6,1,2,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,6,8,7,3,1,4,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[2,5,4,3,6,8,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[3,8,5,4,6,2,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,1,3,7,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,2,7,5,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[4,1,8,3,6,7,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,3,7,4,5,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,8,5,1,6,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[5,4,8,2,7,6,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,2,7,3,6,5,8,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[2,8,7,6,3,4,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,6,3,4,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,8,6,2,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[5,1,7,8,4,3,6,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[8,2,7,5,4,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,1,4,7,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,8,4,5,6,1,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,5,7,8,2,6]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[6,5,8,7,1,3,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,6,7,2,4,8,1,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[1,5,2,7,4,3,8,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[2,8,5,6,4,3,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,5,4,3,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,8,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,6,1,8,5,7,2,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,7,1,2,8,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[1,4,7,2,8,5,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,7,3,5,8,6,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,3,5,8,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,6,8,1,5,7,2,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,4,6,5,8,1,7,2]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[6,8,1,5,7,2,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,1,2,5,8,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,7,2,5,8,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,6,8,2,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,6,8,1,2,3,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,1,5,8,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,4,7,1,8,5,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[4,7,5,8,3,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,2,1,8,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[7,6,8,2,1,3,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,2,7,6,8,3,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[3,7,6,8,2,1,5,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[7,4,2,1,6,8,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,7,4,1,8,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,4,3,1,8,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[2,7,4,1,6,8,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,3,7,6,8,1,5,4]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[7,4,2,6,8,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,2,5,8,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,1,7,6,8,2,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[3,7,6,8,1,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,3,7,6,8,2,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,7,4,2,6,8,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,4,1,2,6,8,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,4,2,8,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,8,2,5,4,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,4,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,1,6,4,5,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,6,8,5,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,2,6,8,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,7,2,6,8,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,6,8,3,2,5,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,6,8,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,5,8,6,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,5,8,6,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,6,7,1,8,5,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[7,2,6,8,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,8,2,3,1,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,6,8,3,1,5,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,1,6,8,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,7,3,1,8,5,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,1,8,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,2,1,6,8,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,8,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,7,8,5,6,1,3,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,6,5,8,7,1,3,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[5,6,4,8,1,2,7,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[8,1,5,6,7,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,8,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,4,6,7,1,2,8,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[4,3,6,7,2,1,5,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[5,3,6,7,1,4,2,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[8,1,4,6,7,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,7,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,6,8,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,2,6,7,1,4,8,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[4,2,6,7,3,1,8,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[6,2,4,1,5,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,2,1,5,4,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,1,4,5,3,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,4,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,3,4,1,5,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,3,4,2,1,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[4,3,5,2,7,1,6,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[5,6,3,8,1,4,2,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[8,1,7,2,4,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,2,4,5,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,7,8,2,3,1,6,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[5,6,2,8,1,4,7,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[6,5,2,1,3,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[7,5,1,3,2,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,6,3,2,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,3,5,2,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,4,2,3,1,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[7,3,1,4,5,6,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,1,4,3,5,6,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,1,5,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[7,8,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,2,1,5,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,2,3,4,8,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,2,3,4,7,8,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[7,8,3,4,6,2,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,6,4,2,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,5,6,2,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,2,3,8,7,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,3,7,8,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,2,6,3,8,1,7,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[6,3,2,5,8,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,3,2,8,4,7,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,3,8,7,5,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,3,7,8,5,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,2,4,1,7,3,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,3,2,7,4,8,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,3,2,5,7,8,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,7,2,3,6,1,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,8,2,3,6,1,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,7,5,8,3,2,1,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,5,6,8,3,2,1,7]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[4,6,8,5,3,2,1,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[5,6,1,4,2,3,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[5,6,8,4,3,7,1,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,6,1,4,2,3,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[5,2,8,3,4,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,5,8,6,3,2,1,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,6,5,8,3,2,1,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,7,5,6,3,2,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[6,2,3,4,5,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,1,4,3,6,2,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[5,1,4,3,7,2,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[5,1,4,3,8,2,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,6,2,4,1,7,8,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[5,6,2,4,1,8,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[5,7,2,4,1,8,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,1,4,2,8,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,1,4,2,7,8,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,8,2,4,1,7,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,1,6,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,4,1,3,7,2,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[5,1,4,3,6,2,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[5,8,6,4,3,7,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,1,4,2,3,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,1,6,3,4,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[4,8,6,5,3,2,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,6,3,2,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,8,3,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,4,8,7,3,2,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,6,8,7,3,2,1,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,7,8,3,2,1,5]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[4,7,6,8,3,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,8,5,3,2,1,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[5,7,1,3,4,2,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,1,8,4,2,3,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,7,4,2,3,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,8,1,3,4,2,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,7,5,3,2,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,8,6,3,2,1,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,8,7,6,3,2,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,6,3,7,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,3,6,7,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,1,6,7,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,8,1,6,2,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,4,8,7,3,5,2,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,7,2,5,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,8,4,3,7,1,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,1,4,7,2,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,1,7,4,2,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,1,2,4,3,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,7,1,3,4,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,7,6,3,1,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,7,3,1,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,3,8,2,7,5,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,4,8,3,7,5,6,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,4,3,8,2,6,5,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[4,3,2,8,1,6,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,1,3,8,2,6,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,1,8,3,7,5,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,8,7,3,5,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,7,8,1,5,4,2,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[7,3,8,1,5,4,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,4,8,1,6,2,5,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,7,2,5,1,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,2,7,5,6,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,2,4,8,3,6,5,7]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,4,3,8,6,5,7]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[3,4,2,1,8,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[3,4,1,8,2,6,5,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,6,7,8,4,1,2,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[4,1,7,8,5,3,2,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[4,1,2,8,3,6,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,4,3,2,8,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[4,2,3,1,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[3,7,6,8,4,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[4,7,1,8,5,2,3,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[2,6,8,7,4,3,1,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,7,8,6,2,4,1,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,8,2,6,4,5,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,2,3,8,1,6,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,1,8,2,6,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,4,7,8,5,3,2,6]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[4,3,7,8,5,2,1,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[3,7,2,8,4,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[4,2,8,6,3,1,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,6,8,4,7,3,1,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,4,8,6,3,1,5,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[7,3,6,8,4,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,2,8,3,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,7,3,8,4,6,5,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,3,4,8,2,6,5,7]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[3,2,4,8,1,6,5,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[7,3,8,6,2,4,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,2,6,4,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,4,8,3,6,1,5,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,2,8,7,4,3,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,4,1,8,5,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,2,8,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,4,3,1,8,6,5,7]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,3,4,2,8,6,5,7]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,3,2,4,8,6,5,7]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[3,2,1,4,8,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[3,1,2,4,8,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[3,1,4,2,8,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[3,1,4,8,2,6,5,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[7,3,4,8,5,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,7,4,8,5,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[6,7,2,8,3,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[2,3,1,4,8,6,5,7]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,1,3,4,8,6,5,7]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,4,8,6,5,7]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[4,8,3,6,2,1,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,5,8,2,6,1,4,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,6,5,8,2,4,1,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,8,7,2,4,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,8,4,5,7,3,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,7,3,8,1,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[6,2,4,5,8,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,8,1,2,5,6,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,1,3,5,2,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,3,8,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[6,2,5,1,8,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,6,1,5,8,4,2,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[6,1,4,5,8,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,6,4,8,1,3,2,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[6,5,4,3,8,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,4,3,7,2,8,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,8,4,3,7,2,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,6,8,3,7,2,5,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[7,4,6,3,2,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,4,3,6,2,7,8,5]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,5,4,3,7,2,8,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,7,8,5,3,1,2,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[5,7,3,4,1,2,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[8,5,4,7,6,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,6,7,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,7,8,3,6,1,5,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[5,3,8,6,7,4,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,3,8,6,4,7,5,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[8,6,2,7,4,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,1,4,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,1,3,4,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,5,7,3,2,6,8,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,6,7,3,2,5,8,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[3,2,6,8,5,7,4,1]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[5,8,2,3,6,7,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,1,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,6,4,7,2,3,8,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[3,1,7,5,2,8,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[2,5,7,4,1,8,3,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,2,6,1,7,8,3,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[4,2,7,6,3,8,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[6,4,8,7,2,3,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,2,6,8,7,4,5,1]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[3,2,7,4,1,6,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[6,3,2,1,7,8,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[3,7,1,8,4,2,5,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[4,2,1,3,7,5,8,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[8,1,3,7,4,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,7,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,8,7,1,5,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[7,3,2,8,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,8,7,2,6,5,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,8,6,1,5,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[6,8,2,4,7,1,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,2,1,8,7,3,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,2,1,6,3,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,7,5,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,1,6,7,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,2,8,1,5,7,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,7,8,2,6,1,4,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[8,7,2,5,6,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,8,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,2,7,8,5,6,4,3]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[7,4,8,1,6,2,5,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,7,1,8,2,6,5,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,1,7,3,8,6,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[8,2,1,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,6,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,8,4,3,2,1,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,2,1,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,4,7,3,2,1,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[6,5,3,7,2,1,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[5,8,3,6,2,1,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,3,7,8,2,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,3,7,6,2,1,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[3,8,7,6,2,1,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,2,6,1,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,7,2,5,1,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,2,6,1,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,3,2,5,1,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,5,1,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[3,8,7,2,5,1,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,5,1,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,3,2,7,5,1,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[5,3,2,6,7,1,4,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[3,8,2,6,5,1,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,8,5,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,2,7,6,8,1,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[4,2,7,6,5,1,3,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[2,8,7,6,5,1,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,1,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,4,7,3,1,5,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,4,7,3,1,8,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,4,3,7,1,5,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,4,3,6,1,8,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[6,3,7,8,1,4,5,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,3,7,6,1,4,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[4,3,7,6,1,5,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[3,8,7,6,1,4,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,2,1,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,4,7,2,1,5,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[4,8,7,2,1,5,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,2,1,4,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,3,2,1,5,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,1,4,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[3,8,7,2,1,4,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,1,4,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[5,8,2,6,1,4,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,2,7,1,5,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[5,4,2,6,1,8,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[4,3,2,6,1,5,8,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[6,2,7,8,1,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[4,2,7,6,1,5,3,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[3,2,7,6,1,4,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[6,5,4,1,8,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,8,4,1,6,7,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,5,8,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[5,4,7,1,6,8,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[4,8,7,1,5,6,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,6,8,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[4,8,3,1,5,6,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,1,5,4,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,1,6,4,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,3,2,1,5,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,3,2,1,6,4,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[3,8,2,1,5,4,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,5,4,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[5,2,7,1,6,4,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[4,2,7,1,5,6,3,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[3,2,7,1,5,4,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[2,8,7,1,5,4,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,8,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,8,1,6,7,4,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,5,8,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,4,1,6,7,8,3,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[4,8,1,6,5,7,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,7,5,4,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,3,1,6,7,4,8,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[4,3,1,6,5,7,8,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[3,8,1,6,5,4,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,1,6,7,4,3,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[4,2,1,6,5,7,3,8]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[2,8,1,6,5,4,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,8,5,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[4,1,7,6,5,8,3,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[3,1,7,6,5,4,8,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[4,5,8,1,2,6,3,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,4,5,7,2,6,3,8]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,7,3,5,6,2,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,1,3,5,7,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,7,2,4,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,4,5,6,8,1,7,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[4,5,8,2,6,7,1,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[8,2,3,5,6,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,5,4,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,1,2,3,5,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,1,3,5,4,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,7,8,3,5,6,1,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,4,5,7,8,1,6,3]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[4,5,8,1,7,6,3,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,7,2,1,6,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[8,7,3,5,6,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,3,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,7,2,1,5,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[8,6,4,1,7,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,1,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,3,6,7,8,1,5,4]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[3,6,8,1,2,5,4,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,3,6,7,2,5,4,8]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[7,4,1,8,5,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,4,2,8,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,8,2,5,3,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,1,7,5,4,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,6,5,4,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,6,3,2,5,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,6,3,1,2,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,3,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,6,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,7,5,4,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[8,2,6,7,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,6,3,1,5,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,7,8,1,6,5,4,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,3,1,8,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,6,3,7,4,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,6,1,5,2,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,4,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,4,3,8,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[2,1,8,4,5,3,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,7,8,3,6,5,4]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[2,1,8,5,7,6,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,8,5,7,3,6]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,5,4,6,8,3,7]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[8,5,3,1,6,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,4,6,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,1,5,2,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,3,7,5,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,6,8,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,8,3,7,6,2,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,2,4,8,6,3,1,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,2,6,3,8,5,1,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,6,3,2,7,8,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[3,8,2,4,7,5,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,8,7,5,4,1,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[8,5,2,7,4,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,7,6,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,3,8,1,5,7,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,3,2,4,1,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,3,1,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,2,4,3,1,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,8,3,1,5,4,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,2,8,1,4,6,5,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,3,1,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,6,1,4,3,2,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[5,7,1,8,3,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[6,8,1,4,5,3,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,1,5,4,3,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[8,7,5,1,3,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,1,3,8,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[8,2,6,1,4,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,3,7,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,3,5,6,1,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,8,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,6,5,4,1,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,3,6,4,5,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,5,8,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,3,5,4,1,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,6,3,5,1,4,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,7,8,5,1,6,4,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,7,3,6,5,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,6,1,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,6,1,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,4,7,2,8,1,5,6]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[4,3,2,5,7,1,8,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[4,2,3,5,8,1,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[3,2,8,4,7,1,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,2,4,7,5,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,1,6,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,6,1,5,8,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[8,3,4,5,7,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,5,7,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,8,4,6,7,1,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,5,8,7,1,6]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,2,4,5,6,8,1,7]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[5,6,8,1,4,2,7,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,5,7,8,4,6,2,3]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,3,5,7,8,6,2,4]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[3,5,7,8,6,1,2,4]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[3,5,1,6,8,2,7,4]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[3,1,5,6,8,2,7,4]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[2,3,5,6,8,1,7,4]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[5,6,4,8,2,1,7,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,1,6,3,8,4,7,2]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[2,5,1,6,8,3,7,4]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[5,1,2,6,8,3,7,4]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,7,1,8,6,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[1,5,2,7,8,6,3,4]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,6,7,5,2,8,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[6,1,7,5,2,8,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[2,6,7,5,1,8,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,7,2,8,6,1,3,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,5,7,8,6,2,1,4]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[5,1,7,8,6,3,4,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,1,3,7,8,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,2,7,8,4,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[3,2,5,7,8,6,1,4]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[6,2,7,5,1,8,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,2,6,7,5,8,3,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[6,2,7,5,4,1,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,7,5,2,4,1,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,7,2,5,3,8,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,7,4,5,2,1,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[5,1,7,8,6,4,3,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[2,5,7,8,6,3,1,4]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[5,1,7,8,6,3,2,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[6,3,7,5,1,8,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,6,7,5,3,8,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,6,7,5,4,2,8,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[6,7,5,1,4,2,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[5,7,8,6,4,1,2,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,1,7,2,6,5,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[2,4,7,1,5,6,8,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[6,7,4,1,5,2,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,6,7,4,5,2,8,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,6,3,7,5,8,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[6,3,1,7,5,8,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[2,5,3,7,8,6,1,4]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[6,7,5,4,2,1,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,3,2,7,5,8,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,7,4,2,5,1,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,2,7,4,5,1,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,2,3,7,5,8,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[4,5,1,6,3,2,8,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[7,5,1,6,3,8,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,1,6,3,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,6,1,3,8,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,6,1,3,8,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,3,5,1,8,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,5,1,8,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,7,5,1,8,6,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[2,6,7,1,5,8,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[2,6,7,4,1,8,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[2,1,6,7,3,8,5,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[2,6,7,4,1,8,5,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[2,6,7,1,5,8,4,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[3,6,5,1,8,4,7,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,6,5,1,8,4,2,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,7,5,4,8,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,5,4,8,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,6,1,5,8,7,3,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,6,1,5,8,7,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,6,1,5,8,2,7,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[7,5,1,6,2,8,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,1,6,2,8,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,6,1,5,8,2,3,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,7,1,5,8,3,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[2,3,4,7,8,1,6,5]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[6,8,5,4,3,2,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,4,3,7,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,4,3,2,1,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,1,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,6,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,1,8,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[3,5,2,6,8,4,1,7]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[7,5,3,2,8,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,3,2,8,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,4,5,7,3,8,6,1]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[4,2,5,6,8,3,1,7]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[4,2,8,1,5,6,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,5,6,1,8,4,3,7]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[5,3,6,8,1,4,2,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,5,6,8,1,3,2,7]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[1,4,5,6,8,3,2,7]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[4,5,6,3,8,2,1,7]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[4,5,3,7,2,8,6,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[6,4,7,3,2,8,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,1,4,7,3,2,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,7,8,4,5,3,2,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[5,1,7,3,8,4,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[2,5,1,7,4,3,8,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[2,5,7,4,1,8,6,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[5,3,7,1,4,8,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,4,3,1,7,8,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,4,1,7,3,8,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,6,3,7,8,4,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[5,1,6,3,7,8,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[5,6,1,3,7,8,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[5,6,1,7,8,3,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[1,6,3,7,4,8,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[6,7,2,4,1,8,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,7,2,1,4,3,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,4,7,3,1,2,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,6,3,1,2,7,8,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[5,6,1,3,2,7,8,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[5,6,3,2,1,7,8,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[2,5,6,3,7,8,4,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[2,5,6,3,1,7,8,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[2,6,4,7,3,1,8,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[6,3,7,2,8,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,3,7,2,8,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,3,2,7,1,8,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[7,5,3,2,1,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,8,4,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,7,2,1,3,8,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,3,7,8,6,4,2,5]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[7,3,8,4,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,7,3,8,2,1,6,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[6,3,7,8,5,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[4,6,2,7,8,5,3,1]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[4,6,2,1,7,8,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[7,4,5,8,1,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,5,1,7,3,8,6,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[6,7,2,1,3,8,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,1,6,7,8,2,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[6,3,7,1,8,5,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,2,1,7,3,8,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,2,7,1,8,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,3,1,7,8,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[4,1,3,6,8,2,5,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[4,2,3,6,8,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[5,3,2,1,8,4,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[3,6,5,8,2,1,7,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,5,2,1,3,8,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[3,2,6,4,5,8,1,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[2,4,6,5,8,1,3,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,6,2,4,5,8,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,2,1,6,8,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[6,2,4,5,8,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,3,4,6,5,8,2,7]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,6,3,4,5,8,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[3,4,1,8,5,2,7,6]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[2,8,4,1,7,6,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,4,2,7,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,8,7,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[8,2,1,7,5,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,5,8,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,8,7,4,1,2,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,4,6,2,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,4,2,5,8,6,7,1]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[4,1,3,5,6,8,7,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[2,4,8,6,7,1,3,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,3,6,2,8,1,7,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[3,7,4,8,2,1,6,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,3,5,8,6,7,1,4]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[3,2,5,6,8,7,1,4]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[2,1,8,5,6,7,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,3,5,6,7,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,7,1,8,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[3,2,6,4,8,1,7,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[8,2,1,6,7,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,5,4,1,3,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,5,3,8,4,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[4,7,5,3,1,2,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[7,2,4,8,5,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,8,3,1,2,7,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,4,1,8,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[8,4,2,3,7,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,1,3,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,4,6,7,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,3,6,7,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,7,6,1,8,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[1,6,3,2,5,8,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,8,3,2,1,6,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,3,4,6,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,2,7,4,1,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,1,4,2,8,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[4,7,6,5,8,2,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,3,7,1,6,2,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,2,6,8,7,1,3,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,3,2,1,8,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,7,5,4,1,8,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[4,2,5,6,8,7,1,3]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[1,8,4,2,5,6,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,1,5,6,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,8,5,6,7,1,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,2,4,7,1,8,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,3,4,7,1,8,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[8,6,4,1,3,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,5,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,6,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,1,8,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[8,3,2,4,6,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,6,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,6,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,1,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,4,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,8,5,7,2,6]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[5,8,4,7,6,2,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,5,8,2,6]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,3,5,2,4,8,7,6]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[2,6,5,1,3,8,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[4,7,1,6,5,8,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[5,4,8,7,6,3,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,8,5,1,4,7,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,5,8,6,7,2]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[4,1,3,5,8,6,7,2]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[6,5,3,8,4,7,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,4,2,1,6,8,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[6,8,4,3,2,7,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,4,7,8,2,1,6,5]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[5,1,3,2,8,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,3,1,2,8,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,2,3,1,6,8,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[5,3,2,1,8,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,2,1,3,6,8,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[2,4,7,3,8,1,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[6,3,8,2,7,4,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,2,1,3,6,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,7,8,4,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[2,7,4,5,8,3,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,8,4,3,7,2,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,7,2,1,6,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[5,4,7,8,3,6,2,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[6,4,3,8,7,2,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,8,7,4,1,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,5,7,2,4,8,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[8,4,7,2,3,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,3,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,1,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,3,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,7,2,6,1,8,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[6,1,3,8,5,7,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,8,3,2,6,7,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,5,3,6,2,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,5,4,7,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,8,7,4,6,2,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,1,7,6,4,5,8,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,7,2,4,6,5,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,5,1,7,6,8,2,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[5,8,2,6,1,3,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,3,5,8,7,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,5,7,8,4,1,6,3]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,2,8,1,5,6,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,5,2,6,8,7,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[3,4,5,1,6,8,7,2]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[4,2,8,5,1,6,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,8,5,2,6,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,7,1,8,5,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,8,6,2,1,3,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,2,4,1,5,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,8,1,7,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[1,7,8,3,5,4,6,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,4,5,1,8,6,7,2]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[3,8,1,4,5,6,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,7,8,2,6,1]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,6,2,8,5,1,7]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[3,4,6,8,1,5,2,7]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[3,4,7,2,1,8,6,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[3,4,7,8,1,5,6,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[3,4,8,2,1,5,6,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,5,2,7,8,4,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[3,5,6,2,8,4,1,7]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[3,5,6,8,4,1,2,7]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[3,5,7,2,4,8,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[3,5,7,2,8,4,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[3,5,7,8,4,1,6,2]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[3,6,2,1,7,8,5,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[3,6,2,1,8,5,4,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,6,7,2,8,5,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[3,6,8,2,4,5,1,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,7,2,1,4,8,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,2,8,4,5,6,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,8,2,4,5,6,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,8,2,1,4,5,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,6,7,8,3,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[4,1,5,7,3,8,6,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[4,1,6,3,7,8,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[4,1,6,3,8,5,2,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,1,6,7,3,8,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[4,1,6,7,8,5,2,3]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[4,1,6,8,3,5,2,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,1,7,3,2,8,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,1,8,3,2,5,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,5,2,6,8,1,3,7]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[4,5,7,3,8,1,6,2]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[4,5,8,3,2,1,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,6,2,3,7,8,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[4,6,2,3,8,5,1,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,6,2,7,8,5,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[4,6,7,3,2,8,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[4,7,8,3,2,5,6,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,8,2,3,1,5,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,8,4,3,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,1,2,7,4,8,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,1,2,8,4,3,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,1,6,3,8,4,2,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,1,6,7,4,8,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[5,6,2,3,8,4,1,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,6,2,7,8,4,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[5,6,8,3,4,2,1,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,7,2,3,4,8,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,8,3,4,2,6,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,8,2,3,4,1,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,1,2,3,7,8,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,1,2,3,8,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,1,2,7,8,5,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,1,7,3,8,5,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,1,7,8,4,5,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,1,8,3,4,5,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,7,2,3,8,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,2,8,4,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,1,2,3,4,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,2,8,4,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,8,3,4,5,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,4,1,8,2,3,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,8,1,2,4,3,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,2,6,4,8]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[3,5,8,6,1,2,4,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,1,6,8,2,4,7,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[3,6,2,8,1,5,7,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,1,3,8,4,7,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,7,5,2,3,4,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7,5,1,3,8,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,2,5,7,4,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,7,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,1,3,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,3,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,5,4,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,2,4,8,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,8,2,5,3,1,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,8,6,3,2,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,1,5,3,2,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,6,7,5,3,2,4,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[6,5,1,2,4,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,8,1,6,4,2,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,4,1,2,5,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,6,5,2,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,1,3,7,2,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,5,1,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,8,4,2,5,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,2,7,4,5,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,6,5,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,5,7,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,5,4,6,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,6,7,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,6,4,3,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,4,5,6,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,6,5,3,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,6,3,4,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,6,5,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,8,6,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,5,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,3,2,8,5,1,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,4,7,2,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,3,1,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,6,4,1,3,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,6,1,5,3,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,8,5,2,7,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,4,1,2,8,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[6,8,3,5,4,1,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,2,5,8,3,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,7,5,6,3,4,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[7,2,6,8,5,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,3,8,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,6,4,8,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,5,7,4,2,6,3,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,2,3,1,7,8,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[5,2,8,4,1,7,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,6,3,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,5,1,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,6,3,2,5,8,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[8,3,2,1,5,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,5,8,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[2,5,1,8,4,3,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[6,2,5,4,8,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,3,1,6,5,8,2,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,3,5,4,6,8,2,7]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[6,1,3,4,5,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,3,4,1,5,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,6,8,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,2,6,4,1,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,5,2,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,5,1,8,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,7,3,2,5,4,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[8,7,2,1,5,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,5,8,7,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[8,3,6,4,5,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,8,1,2,7,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,4,7,2,3,5,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,8,4,1,3,5,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,4,7,8,6,2,5,1]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[4,1,3,5,7,8,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[6,5,1,8,4,7,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,3,1,8,4,7,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,2,7,4,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,8,1,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[6,3,1,4,7,2,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[8,7,3,6,1,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,6,8,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,4,7,3,8,5,6,1]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[2,8,6,1,5,7,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,2,5,4,3,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,8,3,4,2,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,5,3,7,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,2,4,1,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[2,8,3,4,7,1,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,7,8,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[1,7,6,3,2,5,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,8,1,5,6,2,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,5,6,1,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,8,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,4,8,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,8,6,4,5,2,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,3,6,2,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,7,5,8,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[2,5,4,1,8,7,6,3]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,7,2,6,5,8,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[6,8,1,4,2,7,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,3,4,7,1,8,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[3,4,7,8,2,5,6,1]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,8,2,4,5,6,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,1,6,8,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[3,2,5,7,6,1,8,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[4,3,5,6,1,8,7,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[5,3,4,1,7,6,8,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[3,1,4,6,5,7,8,2]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[1,4,7,3,5,6,8,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[5,1,3,6,4,8,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[1,3,2,7,5,8,6,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,4,2,5,8,3,7,6]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,4,2,7,8,5,6,3]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[5,1,2,6,8,4,7,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[3,1,2,6,5,8,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[4,1,2,6,8,5,3,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[1,5,2,4,8,7,6,3]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,2,6,4,8,7,5,3]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,2,7,4,8,6,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,3,2,7,5,8,4,6]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[2,3,1,7,5,4,8,6]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,3,2,8,5,7,4,6]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,4,2,5,8,7,3,6]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,5,2,4,8,7,3,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,2,6,4,8,7,3,5]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,2,7,8,5,6,3,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,2,6,8,5,7,3,4]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,6,8,2,7,3,4]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,3,8,2,6,7,4,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,4,7,2,8,6,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,6,7,8,2,5,3,4]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,2,6,8,3,7,5,4]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,7,8,2,3,6,4]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,5,2,7,8,4,6,3]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,4,7,2,8,3,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,3,6,2,4,8,7,5]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,6,7,3,4,8,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,5,3,7,4,8,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[2,8,4,1,5,3,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,1,5,7,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,2,8,7,5]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,3,7,4,2,8,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,3,8,4,2,7,6,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,4,7,3,6,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,7,4,8,3,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,2,6,4,8,3,7,5]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,2,4,8,3,7,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,8,4,5,7,2,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,5,2,7,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,5,1,4,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,8,6,1,4,7,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,6,2,7,4,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,4,8,6,7,2,3,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,5,6,8,7,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,2,6,8,5,3,7,4]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,7,8,5,3,6,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,2,5,8,7,3,6,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,6,8,7,3,5,4]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,7,8,6,3,5,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,6,7,8,5,2,3,4]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,5,7,8,6,2,3,4]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,4,7,6,8,2,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,3,7,6,2,8,4,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,3,8,7,4,1,6,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,4,7,6,3,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,8,7,6,3,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,6,8,7,5,3,4]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,7,8,6,5,3,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[5,2,6,7,3,4,8,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[5,2,4,7,6,3,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[5,6,2,1,7,8,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[5,6,2,1,4,8,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[2,6,1,4,5,8,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,2,7,6,3,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[2,3,7,6,4,5,8,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,1,7,5,8,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[2,6,1,7,4,8,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,1,2,7,8,4,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[2,6,1,7,4,8,3,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[3,6,4,1,7,8,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[5,4,6,1,3,8,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[3,6,4,1,5,8,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[2,6,1,5,4,8,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,6,1,4,7,8,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,1,2,4,8,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,1,2,4,8,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,1,2,4,8,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,2,3,8,5,4,7,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[4,3,1,2,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,5,3,8,6,4,7]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,2,3,8,5,6,4,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,8,6,4,5,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,8,6,5,4,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,8,5,4,6,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,6,1,5,4,8,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,2,4,8,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,1,2,4,8,3,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,6,3,1,4,8,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[2,5,4,3,1,8,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[5,4,6,3,1,8,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[3,6,4,5,1,8,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[3,6,5,4,1,8,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,6,1,7,8,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[5,1,6,2,8,7,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[2,1,3,7,8,6,4,5]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,3,7,8,5,6,4]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[5,2,4,1,7,8,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[4,3,1,2,8,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[5,1,4,2,8,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[2,1,3,6,8,5,7,4]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,3,8,6,7,4,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,8,7,5,4,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,8,7,4,5,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,8,5,7,4,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,6,8,7,4,5]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[5,4,1,2,8,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[3,1,6,2,8,7,5,4]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[1,2,8,4,5,3,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,8,3,4,2,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,3,2,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,6,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,6,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,6,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,6,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,5,3,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,5,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,5,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,3,2,5,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,1,4,2,5,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,3,6,1,4,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,5,3,6,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,5,1,4,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,4,3,6,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,8,1,4,3,7,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,2,5,1,4,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,5,3,7,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,5,4,7,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,5,4,7,6,8,1,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[2,5,3,7,6,8,1,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[2,5,1,4,3,7,6,8]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[2,6,1,4,3,7,5,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[2,6,5,8,1,4,3,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,1,5,3,7,4,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[2,6,3,7,4,8,1,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[2,6,4,7,5,8,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,8,3,6,4,7,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,2,6,4,7,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,2,6,3,7,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,5,3,7,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,5,2,6,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,7,1,5,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,8,3,7,1,4,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,1,3,2,6,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,7,1,3,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,4,7,1,3,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,7,1,3,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,7,6,8,2,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,7,6,8,1,3,2,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,5,8,1,3,2,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,1,3,2,6,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[3,7,1,4,2,6,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,5,8,1,4,2,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,6,8,1,4,2,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,6,8,2,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[4,7,6,8,2,5,1,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,5,8,3,6,1,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,5,8,2,6,1,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[3,7,5,8,2,6,1,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,4,8,2,6,1,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,4,8,1,5,2,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,1,5,2,6,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,2,6,1,5,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,2,6,5,8,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[4,7,3,6,5,8,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,6,5,8,4,7,1,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,5,8,4,7,1,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,5,8,3,7,1,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,3,7,1,5,4,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[7,6,4,2,8,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,4,3,8,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,4,8,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,8,4,3,7,2,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,4,3,5,1,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,7,3,5,4,8,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,8,3,7,5,2,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,6,8,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,3,5,8,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,3,5,2,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,4,2,5,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,2,8,4,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,3,8,2,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,3,4,8,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,8,3,7,4,5,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,3,5,8,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[5,7,8,3,6,2,1,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,8,3,6,7,2,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,3,4,8,7,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,8,4,7,2,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,8,4,1,7,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,7,4,1,5,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,3,4,7,5,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,3,5,7,8,4,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,7,3,6,8,2,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,6,8,3,7,2,1,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,6,7,3,4,1,8,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[4,6,7,8,3,5,2,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[4,6,8,3,5,7,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,7,3,5,6,8,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,7,3,5,8,2,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,3,4,7,8,2,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,3,8,2,4,1,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,3,4,8,2,6,1,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,8,3,6,2,5,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,5,7,2,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,5,6,7,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,8,3,5,6,2,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,7,8,3,6,2,5,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,8,3,6,7,2,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,7,2,5,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,3,4,8,2,7,6,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,3,8,2,4,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,8,4,1,7,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,4,2,5,1,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,4,3,5,8,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,3,5,8,7,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,8,3,7,2,6,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,8,2,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,8,4,2,3,1,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,2,3,1,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,8,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,4,8,5,3,7,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,3,8,5,7,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,2,8,5,3,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,2,7,3,1,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,4,3,7,8,5,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,4,5,3,7,1,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[5,7,4,2,3,1,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,6,3,7,1,8,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[5,6,3,4,7,1,8,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[5,6,3,4,8,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[6,3,5,7,4,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,3,5,4,7,8,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,4,3,5,7,1,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,4,2,5,1,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[5,3,7,2,4,1,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,3,4,7,2,6,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,7,3,6,2,5,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[4,7,3,6,8,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,6,7,3,5,8,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[4,5,7,8,3,6,2,1]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[4,5,8,3,6,7,2,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,3,7,2,6,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,3,4,6,8,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,3,6,8,2,1,4,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[5,3,6,7,1,8,2,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[5,3,4,6,7,1,8,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[4,6,3,5,7,8,2,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[4,5,7,3,6,8,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[4,5,6,8,3,7,2,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[5,7,4,8,6,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,2,6,5,1,8,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[3,5,6,7,2,8,4,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[1,6,2,5,3,4,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,3,8,2,4,6,5,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,3,6,4,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,6,8,2,5,3,7,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,8,2,5,3,4,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,3,6,4,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,2,8,4,7,6]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,2,7,3,5,4,6,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,8,2,7,3,4,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,8,2,3,7,4,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,6,8,2,3,5,4,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,3,6,1,2,4,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[7,1,5,8,4,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,1,5,7,4,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,8,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,1,6,2,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,4,1,7,2,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,5,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,7,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,5,8,3,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[7,1,5,4,8,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,4,8,5,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,4,1,7,2,3,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,8,3,1,2,4,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,1,6,4,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,4,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,8,4,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,8,1,2,4,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,3,7,1,2,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,2,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,1,2,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,1,8,4,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,8,1,7,4,2,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,1,8,5,4,2,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,8,4,5,2,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,1,7,8,5,3,4,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[7,6,3,1,2,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,2,3,8,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,8,1,4,2,3,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,3,1,2,7,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,3,1,2,8,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,7,1,4,2,3,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[4,3,6,8,5,7,1,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[6,1,2,5,4,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[3,2,8,5,4,1,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,8,2,1,4,6,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,2,1,5,8,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,4,8,5,1,3,6,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,5,6,1,8,4,2,7]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[1,3,6,8,7,4,2,5]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,2,8,5,7,3,4,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,5,8,3,4,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,7,1,6,8,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[4,8,1,2,5,7,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,4,6,2,5,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,4,7,2,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,8,4,6,2,5,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,4,8,5,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,1,6,5,4,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[2,7,3,1,5,8,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,4,6,8,1,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,5,8,6,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[8,2,6,7,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,1,6,4,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,8,2,7,4,1,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,5,2,8,7,4,6,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[3,4,2,7,8,1,6,5]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[4,1,3,7,5,6,8,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[6,3,8,1,7,4,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,7,1,4,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,1,7,3,8,5,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[3,6,1,4,5,8,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,6,7,4,5,3,8,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[6,1,7,3,5,4,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,3,1,2,5,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,4,7,2,8,5,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[5,6,8,7,2,4,1,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,8,5,7,1,2,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,4,1,7,5,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,4,3,7,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,1,5,7,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,2,8,4,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,2,4,8,6,5,3,7]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[7,1,5,6,8,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,7,8,1,4,6,3,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[4,8,2,5,7,1,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,8,5,3,7,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[5,2,6,4,8,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[6,7,1,3,4,5,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,7,3,2,4,8,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,3,6,5,2,8,4,7]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[7,1,6,5,3,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,3,4,2,8,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,3,8,7,5,2,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,8,7,4,2,3,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,6,4,5,2,8,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[8,6,1,3,5,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,6,1,2,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,5,6,3,4,8,7,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[2,5,3,6,8,7,4,1]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,8,7,3,5,2,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,2,6,4,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,4,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,3,8,6,1,5,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,7,6,2,5,3,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[7,5,2,6,8,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,5,2,7,1,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,3,6,2,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,4,3,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[1,5,3,4,8,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[5,4,1,3,8,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,1,8,6,3,4,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,5,2,8,3,7,6,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[8,2,3,7,6,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,7,6,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,2,5,3,4,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,2,5,6,4,8,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,6,7,4,8,2,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[7,1,3,5,8,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,2,1,3,5,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,7,5,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[4,1,3,8,2,6,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[2,8,3,6,7,5,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,8,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[3,6,1,4,7,2,8,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[1,5,8,4,7,2,3,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[7,1,3,6,2,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,2,7,4,5,8,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[2,1,8,4,5,7,3,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,8,5,7,3,2,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,8,5,4,3,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,7,4,1,5,3,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[7,4,8,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,1,4,6,3,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,7,5,6,8,1,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[7,1,3,2,8,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,8,5,4,1,3,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,4,2,3,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[3,8,6,5,1,4,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,8,6,5,2,7]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[4,1,8,6,5,3,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,5,2,7,3,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,2,8,5,3,6,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,2,8,4,3,7,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,4,7,5,2,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,8,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,7,4,3,6,2,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[6,7,5,1,2,8,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,2,6,8,3,4,7,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[7,6,2,4,5,8,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,6,8,4,7,2,5,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[7,6,3,8,4,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,6,3,8,4,7,5,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[7,2,3,6,5,8,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,2,7,5,8,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[2,8,3,6,4,5,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,6,8,3,7,4]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[5,8,1,2,6,4,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,6,8,3,2,7,4,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,5,7,2,8,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,5,1,2,8,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,4,8,3,6,2,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,2,7,4,3,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,5,8,2,7,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,7,3,6,4,8,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[1,5,6,4,8,2,7,3]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[3,1,5,6,4,8,7,2]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[1,3,6,2,5,7,8,4]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,4,6,3,5,7,8,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[3,5,1,6,4,7,8,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[3,6,1,4,2,7,8,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[2,4,6,3,1,7,8,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,3,6,5,2,7,8,4]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,2,6,4,3,8,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,2,6,3,5,8,7,4]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[2,3,5,1,8,4,7,6]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,3,6,1,8,5,4,7]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,2,7,4,6,8,3,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,3,7,5,1,8,4,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[4,7,2,5,3,8,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,1,7,5,4,8,6,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[1,2,7,6,4,8,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,2,7,3,6,8,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,3,6,1,8,5,7,4]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[3,1,5,4,8,7,6,2]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[1,2,5,8,4,7,3,6]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,6,8,5,4,7,3]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,3,6,8,5,2,7,4]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[3,5,7,4,8,2,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[2,4,7,6,8,3,1,5]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,4,6,8,3,5,2,7]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,3,6,8,5,2,4,7]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,2,6,8,5,4,3,7]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,5,8,4,3,7,6]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,3,5,8,2,4,7,6]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,3,6,8,2,5,4,7]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,4,6,8,3,2,5,7]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,7,4,8,1,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,1,7,5,8,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[2,3,6,7,5,8,1,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,3,7,5,6,8,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,3,6,5,8,1,7,4]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[3,4,6,2,8,1,7,5]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[3,5,4,6,8,2,1,7]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[3,5,4,6,8,1,2,7]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[1,2,4,7,5,8,3,6]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,2,6,7,4,8,3,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[3,6,4,7,1,8,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[1,2,6,7,3,8,5,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,2,5,7,3,8,6,4]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[3,1,5,7,6,8,4,2]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[3,5,4,6,8,2,7,1]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[4,2,6,1,8,7,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[3,1,6,5,8,7,4,2]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[2,3,6,5,8,7,1,4]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,2,7,4,6,8,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,2,7,5,6,8,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[3,1,6,7,5,8,4,2]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[4,6,2,7,5,8,3,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[3,5,7,4,8,2,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[2,4,7,6,8,3,5,1]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,4,6,8,3,5,7,2]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,3,6,8,2,5,7,4]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,3,5,8,2,7,4,6]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,2,5,8,4,7,6,3]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,4,8,7,3,6,5]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,5,8,7,4,3,6]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,3,5,8,7,2,4,6]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,3,7,6,8,5,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[5,7,1,2,8,6,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[3,1,7,6,8,5,4,2]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[1,2,6,8,5,7,4,3]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,5,8,7,4,6,3]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,4,8,7,6,3,5]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[6,4,5,7,2,8,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,3,4,7,2,8,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[3,2,7,4,6,8,1,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[5,3,6,2,7,1,4,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[2,6,3,4,7,1,5,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[2,7,3,4,5,8,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,4,5,6,8,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[2,5,7,3,6,8,1,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,7,6,2,3,8,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[7,3,5,2,4,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,2,4,5,8,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,5,2,3,4,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,3,1,2,8,4,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,5,2,3,7,1,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[5,2,1,7,3,4,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,2,1,8,3,4,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,3,2,8,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,3,1,2,8,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,4,1,3,8,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,2,3,1,8,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,3,5,2,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,7,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,6,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,2,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,2,3,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,7,3,4,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,3,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,4,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,2,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,2,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,2,3,6,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,2,1,8,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,8,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,7,8,3,4,5,6,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,4,5,8,3,6,7,2]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[2,5,7,1,8,3,6,4]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[6,2,7,1,8,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[4,7,1,3,8,5,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[1,6,2,8,4,5,7,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[4,1,3,6,8,2,7,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[5,3,4,6,8,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[4,6,3,8,7,1,2,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[6,4,5,8,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,3,4,8,7,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,2,8,7,1,4,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,8,7,2,4,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[5,3,7,6,1,2,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[1,8,3,7,2,4,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,7,2,4,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,2,3,5,1,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,7,8,2,6,1,3,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[6,2,8,7,1,4,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,8,7,1,4,5,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,1,3,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,1,3,4,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,6,2,3,4,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,6,2,3,4,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,3,4,5,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,2,4,5,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,3,6,2,4,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,5,8,7,2,3,6,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[8,7,6,1,3,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,4,7,1,8,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[3,4,7,2,5,1,8,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[2,1,6,4,8,5,3,7]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[4,1,8,5,3,2,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,6,2,5,7,1,4,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[1,2,8,3,7,5,4,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,2,8,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,6,1,2,8,4,3,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[1,6,3,8,7,4,2,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[4,3,8,1,2,6,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,6,8,7,1,2,5,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[6,2,8,5,4,7,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,7,2,4,8,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[3,4,1,6,5,8,7,2]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[3,5,1,2,4,8,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[3,7,5,2,1,4,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,8,5,2,7,4,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,8,4,7,3,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,7,4,1,3,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[4,3,5,1,2,8,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[3,1,4,6,2,8,7,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[1,4,6,5,2,8,7,3]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,4,5,6,1,8,7,2]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[3,4,5,8,7,2,1,6]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[1,4,7,2,6,3,5,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[8,4,7,5,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,2,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,3,4,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,5,1,7,4,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,1,4,8,7,3,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,8,5,7,1,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,4,8,1,6,3,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,4,8,6,3,7,2,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[5,4,7,6,3,8,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[4,6,3,7,5,8,1,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[4,1,3,5,8,6,2,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[5,7,4,3,8,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[1,4,8,3,7,6,5,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,2,1,6,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,8,4,2,7,1,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,7,6,4,8]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[1,8,2,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,6,7,5,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,6,8,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[7,2,3,8,5,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,2,1,7,5,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,5,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,3,6,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,5,4,3,6,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,8,4,5,3,2,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,6,3,4,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,8,7,1,4,2,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,6,1,4,2,7,5,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[3,4,1,8,5,7,6,2]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,6,5,1,2,8,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[3,8,5,6,7,2,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,7,6,2,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,4,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,7,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,5,7,2,3,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[8,3,6,1,7,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,5,7,3,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,6,8,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,4,1,6,5,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,1,5,8,7,6,3,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[1,2,5,8,6,7,3,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[4,2,1,5,8,7,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[5,2,4,6,1,7,3,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[1,5,3,6,8,7,4,2]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[3,5,4,6,1,8,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[3,1,5,7,6,8,2,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[1,4,5,6,8,7,2,3]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,4,6,3,7,2,8,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,7,3,6,5,2,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[8,6,2,5,4,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,6,5,4,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[7,6,2,5,4,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,7,5,2,6,3,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[3,2,6,4,7,5,1,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[6,2,3,7,5,4,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,3,4,7,6,2,8,5]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,8,3,6,1,7,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,2,5,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,6,5,1,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,2,5,4,1,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,8,5,2,6,1,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,3,7,2,8,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[6,1,3,7,5,2,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,1,3,6,2,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,1,3,6,2,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,3,8,6,5]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[7,1,8,2,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,1,8,6,2,7,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,1,7,8,2,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[5,6,1,8,2,7,4,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,2,7,8,1,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[3,2,8,6,1,7,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,2,8,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,8,7,2,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,1,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,1,6,5,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,5,1,6,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,7,8,5,1,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[5,6,3,8,4,1,7,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[7,3,8,5,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,4,8,6,5,1,7,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[8,3,7,5,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,2,7,5,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[8,4,6,7,1,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,8,1,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[3,4,6,5,1,2,8,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[7,3,5,1,2,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,4,6,2,3,8,7,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,3,2,7,4,8,6,5]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[7,2,1,6,3,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,3,1,7,6,4,8,5]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[4,5,2,1,7,3,8,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[5,6,7,1,2,8,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[4,7,5,1,2,8,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,7,1,6,2,8,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[7,6,1,2,8,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,7,1,3,8,6,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[8,6,1,2,7,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,8,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[8,7,1,2,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,6,5,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,8,1,6,2,7,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,1,2,7,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,6,8,1,2,7,4,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[2,1,3,7,4,8,6,5]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[4,2,7,3,6,8,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[5,3,6,4,2,8,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[4,1,5,3,8,2,7,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[5,2,6,4,7,3,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[2,6,3,4,7,5,1,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[2,6,3,5,4,8,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,7,4,3,5,8,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,3,6,4,2,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,4,5,2,8,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,4,3,1,8,2,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,5,4,2,7,3,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[5,4,1,7,2,6,3,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,4,1,8,3,2,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,5,2,8,3,4,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,4,2,1,8,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,3,4,8,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,1,5,3,8,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,6,3,1,8,2,7,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[5,8,4,2,7,3,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,2,6,4,7,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,7,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,6,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,2,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,4,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,6,2,5,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,1,7,3,5,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,4,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,2,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,3,2,4,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,1,5,8,4,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,8,4,5,2,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,5,3,4,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,8,4,3,2,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,1,7,4,2,5,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,2,7,3,4,6,5,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,7,8,4,3,5,6,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,6,2,8,3,5,7,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,1,7,3,5,4,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[3,1,5,8,4,2,6,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[4,3,1,6,8,2,7,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[5,7,4,8,3,2,1,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,4,8,2,7,3,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,8,7,3,4,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,4,7,5,3,2,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,8,3,7,6,2,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,2,6,4,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,2,4,7,5,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,3,8,2,6,4,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,6,8,2,7,3,1,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[2,6,8,7,3,4,1,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[7,2,8,6,3,5,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,1,7,2,5,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,7,4,5,6,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,4,3,5,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,5,4,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,6,5,2,4,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,6,5,3,2,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,4,6,2,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,7,6,2,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,1,8,6,5,2,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,4,7,5,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,4,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,5,4,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,5,2,3,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,5,7,8,4,3,6,2]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[6,3,8,1,5,4,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,1,8,5,4,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,6,3,1,7,5,4,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[2,6,5,7,4,1,3,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[2,5,6,8,4,3,7,1]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[2,4,7,5,8,1,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[2,5,4,7,1,8,6,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[5,2,1,8,7,6,4,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,8,5,7,6,1,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,7,5,3,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,5,6,2,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,8,2,1,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,8,4,7,2,6,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,8,2,6,3]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,5,7,3,2,8,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[5,8,3,2,7,6,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,2,1,4,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[3,5,7,4,2,6,1,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,6,4,5,1,2,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[4,2,1,6,5,3,7,8]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[4,2,1,5,7,6,3,8]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[4,3,5,1,7,6,2,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[3,5,4,7,1,6,2,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[3,4,7,5,6,1,2,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[3,4,5,8,6,7,1,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[3,5,4,6,1,8,7,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[4,3,5,1,6,8,7,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[4,2,1,5,6,8,7,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[2,1,7,3,8,4,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[4,1,8,2,7,3,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,7,2,8,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[7,1,3,2,8,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,8,2,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,1,7,2,5,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,8,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,1,7,2,8,3,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,1,8,2,7,3,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,8,2,4,3,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,1,6,2,4,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,4,3,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,1,8,2,5,3,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,1,6,2,5,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,7,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,2,7,3,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,1,7,2,8,3,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,1,7,2,5,3,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,1,7,2,4,3,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,1,6,2,4,3,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[7,1,5,2,4,3,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,6,2,4,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,6,2,5,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,6,2,8,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,8,2,6,3,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,8,2,7,5,4,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,7,4,3,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,4,7,2,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,2,6,3,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,8,1,5,2,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,1,7,2,6,3,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[5,1,7,4,3,6,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[7,5,8,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,8,5,4,3,6,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,4,3,7,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,4,7,2,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,2,5,3,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,4,2,6,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,8,2,1,3,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,1,7,3,2,5,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[7,5,4,8,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,1,7,2,6,8,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[5,1,7,4,2,6,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[4,1,6,3,2,5,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[4,3,1,6,2,5,7,8]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[6,5,4,3,7,1,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,5,1,7,3,8,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,3,2,8,5,7,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,4,3,8,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,4,3,8,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,5,4,8,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,3,8,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,3,8,1,7,5,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,3,1,7,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,4,8,2,1,7,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,4,2,8,5,1,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,6,4,8,5,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,8,6,3,1,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,6,1,5,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,1,7,8,3,6,4,5]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[6,4,1,7,8,2,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[4,2,1,6,7,3,5,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[4,3,1,5,2,7,6,8]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[5,4,2,7,3,8,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[4,1,5,3,2,8,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[3,1,6,2,8,7,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[6,3,1,7,8,5,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,5,4,1,7,8,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,4,3,1,6,7,2,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[6,5,4,2,7,8,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,4,2,6,3,8,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[4,3,1,5,2,6,8,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[5,4,2,1,6,7,8,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[5,4,3,1,6,7,8,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[6,3,8,1,2,5,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,6,7,1,2,5,8,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[7,8,3,1,2,5,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,3,2,4,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,1,3,5,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,2,3,7,1,8,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[2,5,3,6,1,8,7,4]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[2,6,7,3,1,8,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[2,6,7,1,3,5,4,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[6,2,8,3,1,7,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,2,5,7,1,8,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[4,3,1,2,7,8,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[5,1,2,7,3,6,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,1,4,7,8,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,3,4,7,8,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[3,5,4,6,8,7,1,2]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[1,5,4,6,8,2,3,7]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,6,7,3,2,4,8,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,5,3,6,2,7,8,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[5,1,3,7,2,6,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[5,2,4,7,8,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[4,2,5,7,6,1,8,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[4,5,2,8,6,1,7,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[5,3,1,8,2,6,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,1,8,3,2,4,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,3,5,7,6,8,1,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[4,1,5,7,6,2,3,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[4,5,1,8,6,2,3,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[5,2,1,8,3,6,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,4,2,1,8,7,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[7,6,5,4,2,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,5,4,8,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,5,8,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,1,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,5,2,8,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,5,8,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,8,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,8,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,5,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,6,7,2,5,1,3,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[7,8,1,3,2,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,1,5,2,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,6,7,2,1,4,5,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[5,2,3,6,1,4,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[2,5,3,6,1,4,7,8]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[2,6,7,3,1,4,5,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[4,6,7,1,5,2,3,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[4,6,7,3,5,8,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[6,4,7,1,5,2,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,2,7,3,1,4,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[3,2,5,6,1,4,7,8]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[3,5,2,6,1,4,7,8]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[5,1,4,6,7,2,3,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[3,5,4,6,7,8,1,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[1,5,4,6,7,2,3,8]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,6,7,3,2,4,5,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,5,3,6,2,4,7,8]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[5,1,3,6,2,4,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[5,2,4,6,7,1,3,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[2,5,4,6,7,1,3,8]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[2,6,7,4,5,1,3,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[6,2,7,4,5,1,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[4,2,5,6,7,1,3,8]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[4,5,2,6,7,1,3,8]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[5,3,1,6,2,4,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[6,1,7,3,2,4,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,1,7,4,5,2,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,3,7,4,5,8,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[5,4,1,6,7,2,3,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[5,2,1,6,3,4,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[7,3,2,5,4,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,5,4,2,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,5,2,4,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,5,2,1,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,3,6,7,5,2,8,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[7,3,4,1,6,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,4,1,6,5,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,4,1,5,6,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,2,5,1,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,5,4,1,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,4,1,5,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,3,6,7,2,5,8,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,7,4,6,2,8,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[4,3,1,7,2,6,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[5,6,1,4,7,3,8,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[5,3,2,1,7,4,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[1,3,4,5,8,7,2,6]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[6,3,4,5,8,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,4,5,1,6,8,7,3]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[3,1,2,5,6,8,7,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[4,3,2,5,6,8,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[3,7,5,4,6,8,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,1,4,6,5,8,2,7]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[2,3,4,5,8,6,1,7]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,5,8,1,7,6]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[3,1,4,6,5,8,7,2]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[3,7,5,4,6,8,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[5,6,1,4,7,2,8,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[4,3,1,7,5,6,8,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[4,3,1,7,6,5,8,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[3,1,4,6,7,8,5,2]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[1,4,5,2,6,8,7,3]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[3,7,5,2,6,8,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,5,2,6,8,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[5,6,1,2,7,4,8,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[6,3,5,2,4,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,3,2,1,4,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[5,3,1,4,2,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[5,3,1,2,4,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[7,1,5,2,6,8,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,5,2,6,8,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,7,4,6,5,8,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,4,6,1,8,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,4,6,1,8,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,3,6,7,1,5,8,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[2,3,6,7,5,1,8,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[4,3,2,6,7,1,8,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[7,3,2,5,6,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,5,4,6,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,4,6,5,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,3,4,5,8,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,4,5,8,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,4,5,8,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,3,4,5,8,6,2,7]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,3,4,5,8,2,7,6]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[6,3,4,5,8,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,3,4,5,8,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,3,4,5,8,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,7,4,6,5,8,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,1,5,4,6,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,2,5,6,8,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,7,4,6,1,8,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,3,4,5,8,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,3,4,5,8,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,4,5,8,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,7,6,1,8,2,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,8,6,1,7,5,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,8,2,6,1,5,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[7,6,4,2,8,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,6,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,7,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,8,3,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,4,8,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,8,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,2,1,7,3,5,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[2,1,8,6,3,5,4,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,7,3,5,8,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,7,3,1,5,4,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,6,3,1,4,8,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[4,2,1,8,3,6,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[2,1,8,6,3,5,7,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,1,7,3,5,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[2,7,3,1,4,8,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,2,1,6,4,5,7,8]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[3,2,1,5,7,8,4,6]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[2,1,7,3,6,8,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,7,3,1,5,6,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,4,7,5,1,6,8,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[4,3,7,5,6,1,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,3,6,8,5,1,7,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[2,6,1,8,3,5,7,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,1,6,8,3,7,4,5]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,8,3,5,7,4,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,5,6,8,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[3,2,1,5,7,4,6,8]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[2,1,7,3,6,4,5,8]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,1,6,3,5,8,4,7]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[8,2,4,1,7,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,7,5,1,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,3,6,1,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,3,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,3,5,4,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,7,3,1,5,6,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,4,7,5,1,6,3,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[8,2,4,1,7,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,3,1,7,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,8,5,3,6]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[2,4,8,5,1,6,3,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,2,1,7,3,4,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,2,1,7,8,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[2,7,1,8,3,5,6,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,1,8,3,6,4,5,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,6,7,4,5,8]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[3,2,1,7,4,5,6,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[3,2,1,6,8,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[2,1,8,3,7,4,5,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,3,6,7,4,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,4,8,5,1,6,7,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,5,6,1,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,2,1,8,4,5,6,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,6,8,3,7,2,4,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,8,1,5,7,2,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,8,4,7,3,5]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[6,1,5,8,2,4,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,2,4,8,3,6,7,5]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[4,1,2,7,8,3,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[3,5,7,4,8,6,1,2]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[5,3,8,4,7,6,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,7,1,2,5,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,3,7,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,2,8,4,3,5,7,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,3,7,6,4,8]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[6,1,2,8,7,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,1,6,2,8,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,2,6,3,8,5,4,7]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,2,8,5,3,6,4,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,7,3,8,5,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[4,1,2,7,8,6,3,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[1,6,2,8,4,3,5,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,4,2,7,3,5,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,8,6,3,2,4,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,2,8,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,1,7,8,6,2,4,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,8,7,2,4,5,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,3,5,6,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,8,7,4,5,6]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,8,3,2,6,4,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,2,4,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,2,8,4,3,7,5,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,5,1,7,2,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,4,6,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,8,6,4,7,5,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,8,2,7,4,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,2,5,3,8,6,4,7]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,2,7,5,3,6,4,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,2,6,3,7,5,4,8]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,2,3,7,5,4,8,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[3,7,4,8,6,5,1,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,8,2,7,6,4,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,6,5,1,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,2,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,7,6,3,1,5,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,4,3,6,5,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,6,5,3,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,1,6,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,1,4,3,5,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,1,3,5,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,1,2,4,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,8,6,3,4,5,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,7,4,2,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,1,4,8,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[3,1,7,2,4,6,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[3,4,7,1,5,2,8,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,7,4,1,5,8,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[4,3,2,7,1,5,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[3,1,2,8,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,4,8,6,1,2,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,6,8,7,4,3,1,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,8,2,7,4,3,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,8,2,3,7,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,5,3,1,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,7,8,6,1,3,2,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[2,4,8,1,6,3,7,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,1,2,8,6,4,7,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,3,2,6,4,8,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[4,1,6,3,5,8,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[2,4,5,3,8,6,1,7]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,8,5,3,2,7,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,5,2,6,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,7,6,5,8,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[2,4,1,6,7,8,5,3]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,8,4,3,6,2,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,3,2,8,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[2,5,7,3,6,8,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[5,3,2,1,4,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,3,1,4,2,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[7,6,1,3,8,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,4,7,8,1,2,6,5]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,7,8,1,4,5,2]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[3,6,2,8,1,5,4,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,3,6,8,5,1,4,7]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[3,1,6,4,8,2,5,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[7,3,2,6,8,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,5,8,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,2,8,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,5,8,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,8,5,2,4,6,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,2,3,5,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,8,3,5,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,4,8,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,5,4,8,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,7,4,8,5,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,1,5,4,8,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,2,5,8,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,4,6,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,8,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,5,6,8,3,4,1,7]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[8,4,6,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,8,4,3,1,7]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[2,5,7,8,4,1,3,6]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[6,5,7,8,4,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,5,6,8,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,6,2,8,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,3,2,6,8,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[3,5,6,8,2,4,1,7]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[3,5,6,8,4,2,1,7]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[2,6,7,8,1,4,5,3]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[3,6,7,8,1,4,2,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[3,5,7,8,2,1,4,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[2,6,7,8,1,4,3,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[6,5,7,8,3,1,4,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[2,5,7,8,3,1,4,6]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[2,4,7,3,8,1,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[6,4,7,3,8,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,4,7,3,8,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,4,6,3,8,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,2,5,4,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,4,5,2,3,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,4,5,3,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,4,6,3,8,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,4,7,3,8,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[2,5,7,8,3,1,6,4]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[4,5,7,8,3,1,2,6]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[4,5,6,8,2,3,1,7]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[5,4,6,2,8,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,3,2,6,8,4,1,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,4,7,2,8,1,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[4,5,7,8,2,1,3,6]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,8,1,3,2,5]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[4,6,7,8,1,3,5,2]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[2,6,7,8,1,3,5,4]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[2,6,7,8,1,5,3,4]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[4,6,7,8,1,5,2,3]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[4,6,7,8,1,2,5,3]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[4,5,7,8,2,1,6,3]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[5,4,7,2,8,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,3,2,7,8,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[4,3,2,7,8,1,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[3,5,7,8,2,1,6,4]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[3,6,7,8,1,2,5,4]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[3,6,7,8,1,5,2,4]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[3,6,7,8,1,5,4,2]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[2,6,7,8,1,5,4,3]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[4,2,7,1,5,3,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,2,8,6,1,5,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,2,6,7,5,1,4,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[2,7,1,3,5,4,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,7,2,1,5,8,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[7,2,1,3,5,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,3,6,4,7,1,5,8]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,3,4,8,2,7,5,6]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[3,1,4,8,2,6,7,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[8,3,1,6,2,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,2,1,5,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,6,5,1,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,3,5,1,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,4,7,5,1,8,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[3,6,1,7,5,8,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[7,3,5,1,6,8,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,7,3,5,6,1,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,4,6,8,5,1,7,2]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[4,6,8,2,1,5,7,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[6,8,2,1,3,5,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,2,3,5,7,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,6,1,4,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,6,1,3,5,8,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[7,3,2,5,6,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,7,5,2,6,1,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,6,2,8,1,5,3,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[8,4,1,2,7,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,7,1,3,8]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[8,5,1,2,6,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,4,8,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[6,2,1,7,8,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,7,3,8,4,1,5,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[2,7,8,4,1,5,6,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,7,1,8,5,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[8,2,5,1,6,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,1,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,5,6,1,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,8,3,6,7,1,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,3,7,6,1,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,2,8,3,7,1,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[7,2,3,4,8,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,3,4,8,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,3,4,8,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,3,5,8,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,3,8,4,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,3,8,5,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,3,8,5,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,6,4,8,1,5,7,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[7,2,3,8,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,3,5,8,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,8,2,3,6,1,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,3,6,1,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,2,6,3,7,1,5,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[7,2,3,5,8,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,3,8,4,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,6,4,8,1,3,7,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[3,6,4,8,1,7,5,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[7,6,5,1,2,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,5,1,4,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,6,4,5,1,8,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[3,5,6,4,1,2,7,8]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[7,8,5,4,1,2,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,5,6,4,1,2,8,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[7,6,5,1,4,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,5,1,2,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,5,1,2,4,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,5,1,3,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,5,1,3,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,5,1,3,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,3,4,5,1,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,6,4,3,1,5,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,6,4,3,1,8,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,6,4,3,1,8,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[3,5,8,4,1,2,7,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,8,4,1,2,6,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,8,4,1,6,2,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[4,2,8,3,6,1,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,5,8,4,1,6,7,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,5,8,4,1,7,3,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,6,4,2,1,7,8,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[3,6,4,2,1,7,5,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[3,5,6,4,1,8,7,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[2,6,4,5,1,3,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[7,6,5,1,4,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,5,1,2,8,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,5,1,2,8,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,5,1,8,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,5,1,8,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,5,1,8,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,5,1,4,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,6,4,5,1,7,2,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[2,5,6,4,1,7,8,3]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[7,8,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,5,6,4,1,7,3,8]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[3,6,4,5,1,7,8,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[7,6,5,1,4,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,5,1,8,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,5,1,8,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,1,7,6,2,8,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[7,8,6,2,1,3,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,7,6,1,2,8,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[2,6,5,3,1,4,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[4,6,1,5,3,2,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[3,6,1,4,2,5,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[2,6,4,5,7,8,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[8,7,1,6,5,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,6,8,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,1,3,4,2,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[2,4,5,6,1,8,7,3]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[8,4,1,6,5,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,7,5,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,2,7,4,3,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,7,8,5,1,6,3,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[8,2,6,4,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,7,3,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,7,3,2,1,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,1,7,2,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,7,1,3,2,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,5,1,8,7,4,6,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[3,7,1,8,4,5,6,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,3,8,4,7,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,6,4,3,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,6,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,6,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,3,5,8,6,7,4,1]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[7,4,2,1,8,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,6,7,2,5,8,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[7,6,2,5,3,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,2,1,3,4,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,5,4,2,8,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,4,3,1,8,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,1,4,3,8,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,7,6,2,8,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[6,4,5,1,7,8,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[4,2,3,1,7,8,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[3,4,2,1,8,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[2,7,6,8,1,5,3,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,5,8,3,1,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,1,3,2,5,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,1,5,2,4,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,2,8,7,4,5,1,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[6,3,8,5,7,4,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,4,6,8,5,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,1,4,8,7,5,3,6]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,6,8,3,7,5,4]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[3,6,8,2,4,1,5,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[6,2,8,1,7,5,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,6,5,4,8,1,3,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[6,5,3,4,8,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,4,3,2,5,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,5,3,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,1,8,2,6,4,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,4,8,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,6,2,8,3,7,5,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[2,1,5,8,3,6,4,7]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,8,5,3,6,7,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,5,6,4,1,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,8,4,1,6,3,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,1,3,5,7,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,4,5,6,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,8,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,8,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,3,8,7,6,1,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,5,8,4,7,1,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,7,4,2,5,3,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,6,4,8,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,8,5,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,2,5,6,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,2,7,5,6,3,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[3,4,7,5,6,2,1,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[4,7,3,5,6,2,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[3,7,2,5,6,4,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[7,8,3,5,6,1,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,6,8,5,2,7,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,2,8,5,1,7,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,7,4,8,2,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[3,2,7,8,6,1,5,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[6,8,4,1,2,3,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,1,8,5,6,3,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,8,2,5,6,4,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,8,5,3,7,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,8,1,5,2,7,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,1,5,3,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,6,7,8,3]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[4,1,5,3,6,7,8,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[8,1,6,5,3,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,6,3,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,2,6,4,1,7,8,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[7,6,4,3,1,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,6,3,5,1,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,6,7,8,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[3,5,2,1,6,7,8,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[5,2,3,1,6,7,8,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,5,3,2,6,7,8,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[8,4,6,5,1,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,6,1,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,2,5,6,1,7,8,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[3,2,8,7,6,1,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[6,8,4,7,2,1,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,7,5,6,1,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,7,5,6,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,5,1,7,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,2,3,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[7,6,4,2,1,5,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,7,4,6,1,3,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[8,6,4,7,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,7,1,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[3,5,4,2,7,1,8,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[8,6,4,1,3,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,1,5,3,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,5,4,1,2,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,7,4,2,3,6,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,2,5,3,7,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,1,5,4,7,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,2,1,5,6,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,6,4,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,4,1,2,5,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,2,8,1,6,5,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,1,5,7,8,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[7,6,4,1,5,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,6,1,5,4,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,6,7,8,2]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[5,2,1,4,6,7,8,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[5,4,1,3,6,7,8,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[8,4,1,5,3,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,3,2,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,2,5,1,4,7,8,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[7,1,4,3,5,2,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,3,5,4,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,4,6,7,8,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[3,1,8,2,5,7,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,3,2,6,1,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,6,4,3,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,3,8,7,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,5,7,1,3,8,6,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[2,6,8,1,5,7,4,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,7,1,5,8,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,1,6,4,8,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,1,6,5,3,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,1,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,2,7,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,3,2,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,7,2,8,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[3,7,1,8,6,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,6,1,4,2,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,5,1,4,6,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[3,6,8,5,1,4,7,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[7,3,5,8,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,6,2,1,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,6,2,1,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,2,8,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,3,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,6,2,1,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,8,4,5,2,1,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,6,8,5,1,7,3,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,7,5,1,3,8,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,7,6,1,5,3,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[5,1,7,6,3,8,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,1,7,6,4,2,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,1,8,7,6,4,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,5,2,1,7,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,6,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,6,3,2,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,6,1,7,4,8,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[4,1,8,6,3,7,2,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,4,2,5,7,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,8,5,7,1,2]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[5,4,8,2,7,3,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,7,3,6,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,5,4,7,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,8,7,1,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,7,2,4,8,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[5,6,8,4,2,7,3,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,7,4,2,8,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,5,2,7,1,3,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,3,1,8,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[5,7,4,3,8,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[7,5,8,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,4,8,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,5,3,8,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,6,3,7,4,2,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[7,6,3,8,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,4,8,1,3,2,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,4,8,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,7,6,5,3,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[3,7,2,4,6,5,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[8,1,3,4,5,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,4,2,5,3,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,2,8,4,1,5,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,7,4,8,5,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[3,2,7,8,5,1,6,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[3,2,8,1,5,4,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,8,5,3,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,4,8,5,2,6,7,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,1,8,4,3,7,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,7,1,4,2,5,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[7,2,1,4,3,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,1,5,3,6,8,2,7]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[6,1,8,5,3,2,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,1,4,6,3,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,2,6,4,1,8,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[7,6,4,3,1,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,5,2,1,8,7,6,4]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[1,5,3,2,8,6,4,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[5,4,2,1,7,8,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[8,2,7,6,5,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,1,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,6,2,8,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,6,3,2,1,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,6,3,7,4,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,7,1,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[8,6,3,1,4,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,1,5,4,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[5,8,3,1,2,4,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,1,3,2,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,2,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,5,4,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,6,4,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,4,1,2,5,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,2,8,1,6,5,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,6,4,1,5,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,6,1,5,4,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,6,7,2,8]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[5,2,1,4,7,6,3,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[4,5,8,2,1,3,7,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,8,2,3,1,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,2,1,3,5,8,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[5,4,1,3,6,2,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[8,5,4,1,3,6,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,4,6,8,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[8,1,4,3,5,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,4,6,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,1,3,4,6,2,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[4,1,3,2,5,7,6,8]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[6,8,2,4,5,1,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,6,7,2,5,1,4,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[4,6,7,3,1,5,2,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[5,8,1,2,4,7,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,1,3,5,2,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,3,1,4,5,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,5,1,8,2,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,1,8,2,3,4,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,3,8,4,2,6,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,8,4,6,3,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,1,8,3,5,7,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,4,7,2,6,1,8,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[4,5,7,3,2,6,8,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[4,5,7,2,3,6,8,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[2,6,3,4,7,5,8,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[3,6,4,2,7,5,8,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[4,5,2,7,1,6,8,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[3,4,1,6,5,8,2,7]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[4,1,2,8,5,7,3,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[5,1,4,8,6,2,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[7,3,1,4,8,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,6,3,1,7,4,2,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[7,3,4,1,8,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,4,2,8,7,1,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,2,4,8,1,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,6,3,7,5,1,4,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[7,1,3,8,5,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,5,3,7,8,2,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[3,2,6,7,1,8,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[4,6,3,1,7,8,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[5,3,1,6,7,8,4,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[4,1,6,2,7,8,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[2,1,3,4,8,7,5,6]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[4,8,3,7,6,5,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,3,8,7,5,4,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,3,8,7,6,4,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,8,7,6,1,5,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,8,7,6,1,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,2,8,7,5,1,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,2,6,5,1,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,1,8,7,5,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,1,8,7,6,5,4,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,8,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,2,8,7,1,5,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,2,8,1,7,6,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,2,7,6,1,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,2,1,6,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,8,7,1,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,8,1,7,6,5,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,8,7,6,3,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,4,8,1,7,5,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,4,1,6,5,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,3,8,1,7,5,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,3,1,8,7,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[7,8,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,5,3,1,8,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,4,3,1,8,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,4,3,1,8,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[7,5,2,1,8,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,4,2,1,8,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[7,3,2,1,8,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,2,1,8,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,1,4,2,3,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,6,1,4,2,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,2,3,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,1,4,2,3,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,2,3,6,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,2,3,6,1,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,8,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,6,2,3,8,1,5,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,8,2,3,6,1,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,2,3,6,4,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,6,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,8,4,1,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,4,2,3,6,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,3,8,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,6,4,3,8,1,5,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,8,4,3,6,1,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,8,4,1,5,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,3,8,4,2,1,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,6,3,8,1,4,5,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,8,3,6,1,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,6,4,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,4,1,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,6,2,4,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,1,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,3,8,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,2,1,3,6,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,2,4,1,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,4,3,8,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,6,4,7,8,5,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[1,6,4,2,7,5,8,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[3,6,4,2,7,1,5,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[1,4,7,2,5,6,8,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[6,4,8,5,3,7,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,6,5,4,2,7,8,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[4,2,5,3,6,1,7,8]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[7,1,5,3,6,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,6,5,2,4,8,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,4,6,2,8,5,7,3]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[7,8,1,4,2,5,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,4,8,5,2,1,6,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[4,8,5,3,1,6,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,5,8,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,1,8,7,4,2,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,2,8,5,7,3,6,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,6,8,7,5,2,4]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,8,2,5,4,7,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,4,5,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,2,7,3,5,8,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[6,1,3,2,5,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,6,2,1,7,5,3,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[1,6,3,7,8,5,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[4,6,2,3,7,8,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[4,6,3,7,1,2,8,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[4,2,1,3,5,7,8,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[7,3,2,4,5,1,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,8,2,5,4,1,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,2,6,3,8,7,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[5,8,2,7,4,3,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,3,8,5,1,7,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,6,8,1,2,7,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[6,4,3,5,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,5,3,8,4,2,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,8,1,7,5,6,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,5,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,5,3,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,6,7,5,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,2,6,4,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[6,4,1,8,2,5,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,1,3,6,5,8,7,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[2,1,6,3,5,8,7,4]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[2,4,1,3,8,5,7,6]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,4,1,3,5,8,7,6]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[2,6,1,3,5,8,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[4,6,1,3,5,8,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[6,1,4,3,5,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,4,1,3,5,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,2,1,3,5,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,2,1,3,6,5,7,8]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[4,2,1,6,3,5,7,8]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[6,2,1,8,3,5,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,1,3,8,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,1,4,3,8,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,6,4,3,8,5,7,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[8,1,4,3,6,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,6,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,6,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,3,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,3,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,4,3,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[8,2,4,1,3,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,3,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,3,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,3,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,3,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,3,5,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,8,3,5,7,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,4,1,8,3,5,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,8,1,3,5,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,8,1,3,5,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,2,8,1,3,5,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,6,8,1,3,5,7,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,6,8,1,3,5,7,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,1,8,3,5,7,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,1,6,8,3,5,7,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[1,4,6,3,8,5,7,2]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[4,6,1,3,8,5,7,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[2,4,1,8,3,5,7,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,1,6,8,3,5,7,4]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[4,1,3,6,8,5,7,2]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[1,4,3,6,8,5,7,2]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[4,1,3,8,6,5,7,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[2,1,8,3,6,5,7,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,4,3,5,7,8]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[2,6,1,4,3,5,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[2,8,1,4,3,5,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,6,3,5,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,3,6,5,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,4,8,3,6,5,7,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,4,8,6,3,5,7,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,1,8,6,3,5,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,1,6,3,5,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,1,3,5,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,1,3,5,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,1,3,5,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,4,1,3,5,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[4,6,2,1,3,5,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[6,8,1,4,3,5,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,1,8,4,3,5,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,6,8,4,3,5,7,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,8,6,4,3,5,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,4,3,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,3,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,3,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,3,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,1,3,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,7,4,1,8,6,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,6,4,2,8,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,6,4,2,7,3,1,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[5,7,1,4,6,3,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,8,1,4,6,3,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,6,7,4,5,8,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[3,5,7,4,6,8,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[6,8,4,1,7,2,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,4,6,1,7,8,3,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[5,6,4,1,8,7,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[3,5,8,4,6,7,2,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,6,8,4,5,7,2,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,7,8,4,5,6,2,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[6,8,1,4,5,3,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,1,4,5,3,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[3,7,1,5,4,6,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,8,1,5,4,6,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,5,4,6,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[6,7,1,4,5,3,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[5,7,1,4,6,3,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,6,4,2,7,3,8,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[5,4,7,2,8,3,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,4,7,2,8,3,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,6,4,2,8,3,1,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,8,1,4,6,3,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,1,5,4,6,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,4,2,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[3,6,1,5,4,8,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[6,8,3,1,4,2,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,3,8,1,4,2,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,3,1,4,2,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[3,6,1,5,4,7,8,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[3,4,1,2,7,6,5,8]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[3,4,1,2,6,8,7,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[6,8,3,1,4,7,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,4,7,2,8,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,8,1,4,7,3,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,8,1,4,5,3,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,8,1,5,4,7,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,4,8,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[3,6,1,5,4,7,2,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[6,7,3,1,4,2,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,8,3,1,4,2,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,3,1,4,6,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,5,8,7,3,4,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,3,1,4,6,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,7,3,1,4,5,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[3,7,1,5,4,2,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,8,1,5,4,2,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,4,7,3,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,4,2,7,5,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,4,7,2,8,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,3,7,1,4,8,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,8,3,1,4,7,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,7,1,5,4,8,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,4,1,2,8,5,7,6]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[3,4,1,2,5,8,7,6]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[3,7,1,5,4,2,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[6,7,3,1,4,5,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,3,8,1,4,5,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,1,4,5,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,3,1,4,5,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,1,5,4,2,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,7,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,4,3,2,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,4,7,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,3,2,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,5,2,7,3,1,8,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[4,8,2,6,3,5,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,8,6,5,1,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[4,1,7,2,5,8,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[7,8,2,1,5,6,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,6,2,5,8,4,3,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,1,8,7,4,5,3,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[7,3,1,6,8,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,5,8,6,2,3,7,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,4,8,3,1,6,5,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[5,2,7,1,8,6,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[2,6,1,3,8,7,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[6,5,2,8,1,7,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,8,3,5,1,7,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,8,7,1,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,5,4,3,7,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,2,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,5,1,7,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,2,8,4,1,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,8,3,4,1,7,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,8,3,1,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[2,8,4,3,1,7,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,3,1,7,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,4,1,7,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,5,1,6,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,7,5,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,1,5,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,4,8,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,5,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,4,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,4,3,8,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,7,8,4,1,2,6,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,8,5,1,2,6,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,7,8,6,1,2,5,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[8,7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,1,2,4,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[6,4,7,8,3,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,3,4,8,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,4,8,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,8,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,5,8,7,3,1,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,4,8,3,1,5,7,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,3,2,4,8,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,3,8,4,1,6,7,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,5,1,6,7,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[6,4,8,7,3,1,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,6,4,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,2,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,1,5,6,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,6,1,5,7,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,5,8,6,1,4,7,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[8,3,5,7,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,7,2,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,7,1,3,5,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[2,6,8,5,1,3,7,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,6,8,4,1,3,7,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,5,8,3,1,4,7,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,6,8,7,1,3,4,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[7,4,6,8,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,3,5,4,1,8,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[2,3,6,4,8,1,5,7]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,8,4,6,3,5,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,8,6,2,1,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,3,6,8,1,5,4,7]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,5,6,1,4,7,8,3]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[2,5,6,1,4,7,3,8]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[7,3,5,1,6,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,6,1,8,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,6,8,1,4,5,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,8,7,6,3,2,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,6,3,2,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,8,6,2,3,4,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[2,7,6,1,8,5,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,5,1,7,2,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[2,3,4,7,6,1,5,8]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[7,3,5,8,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,8,4,5,2,7,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,5,2,7,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,8,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,7,6,4,8,5,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,3,5,4,6,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,3,5,4,7,1,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,3,5,4,7,1,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[3,4,1,5,6,8,7,2]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[3,7,1,6,8,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[2,3,1,8,6,4,7,5]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,8,4,3,6,2,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,8,6,4,5,7]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[3,7,1,6,8,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,5,4,7,2,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[7,3,5,4,6,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,6,4,8,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,8,4,5,2,6,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,8,5,3,1,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,3,5,8,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,3,4,6,5,8,1,7]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[2,3,4,7,5,1,8,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,4,7,5,1,6,8]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[2,3,4,7,1,6,5,8]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[2,3,4,7,1,6,8,5]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,4,6,1,8,7,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[6,3,5,8,4,2,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,4,8,5,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,8,4,5,2,3,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,8,5,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,3,5,8,4,2,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,2,4,6,8,3,7,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,5,7,4,6,3,2,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[5,2,8,4,6,3,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,8,5,4,6,7,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,3,4,5,7,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,5,7,4,6,3,8,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[5,4,1,7,8,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,4,2,7,8,3,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,1,4,6,8,3,2,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,1,8,4,6,3,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,1,6,4,5,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,4,6,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,4,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,4,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,4,3,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,4,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,3,4,5,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,2,5,4,3,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,7,2,4,5,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,4,7,3,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,3,2,4,7,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,7,1,3,4,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,4,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,4,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,5,2,6,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,2,8,6,1,5,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,6,1,2,4,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,4,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,2,5,4,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,2,4,5,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,2,4,8,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[3,5,2,8,6,1,4,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,7,2,5,1,4,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[5,1,8,6,2,3,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,5,4,1,8,6,3,7]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[3,7,6,1,8,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[7,6,3,1,8,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,2,3,6,1,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,6,3,4,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,3,6,4,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,4,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,2,1,3,5,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,1,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,3,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,5,8,3,4,1,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,3,8,5,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,3,6,1,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,3,7,2,5,8,4,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,7,2,3,5,8,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,4,8,1,3,6,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,1,2,3,5,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,5,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,6,1,4,7,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,7,1,4,8,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[2,6,3,8,1,4,7,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[7,5,4,8,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,5,4,7,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,5,4,6,7]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[8,6,5,1,3,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,6,3,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,6,1,8,5,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[3,5,2,6,7,1,8,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[3,2,8,4,7,5,1,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,4,7,5,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,6,5,2,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,8,3,4,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,8,3,1,7,2,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,7,2,5,6,1,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[6,8,4,2,5,1,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,7,5,3,8,4,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[8,3,1,4,7,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,5,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,4,7,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,4,8,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,3,6,4,7,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,5,7,4,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,8,3,2,5,7,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,4,2,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,3,6,4,8,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,6,1,7,3,5,2,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[5,6,1,7,3,4,2,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[6,1,7,3,4,2,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[7,3,8,1,6,5,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,3,7,1,6,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,4,2,8,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[2,8,1,7,6,5,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,8,6,5,1,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,4,2,8,5,1,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,6,4,7,1,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,8,1,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,1,6,4,2,3,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[4,2,3,8,7,5,1,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,8,7,1,6,5,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,8,1,6,7,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,4,3,7,1,6,8,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[4,2,3,7,8,5,1,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[5,1,6,4,2,3,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[6,4,7,8,1,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[8,7,4,6,1,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,1,4,2,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[4,7,8,6,1,5,2,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,2,4,7,8,1,5,6]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[3,2,4,8,7,1,5,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[4,8,7,6,1,5,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,1,4,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,6,5,7,1,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,7,4,2,3,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[6,7,4,8,1,5,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[8,4,7,6,1,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,7,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,4,8,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,5,3,7,1,6,4,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[8,4,6,7,1,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,8,1,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,1,6,8,4,2,3,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,2,3,7,5,1,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[3,7,5,8,1,6,2,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,4,3,7,1,6,5,8]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[2,4,7,1,5,8,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,2,4,7,6,1,5,8]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[4,7,6,8,1,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[8,5,6,7,1,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,1,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,1,4,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,7,5,1,4,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,6,8,7,1,4,2,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,6,8,7,1,5,2,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[2,4,6,7,1,5,8,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[3,2,4,6,1,5,7,8]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[6,7,8,5,1,4,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[7,8,6,5,1,4,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,1,7,5,4,2,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[2,1,8,5,4,6,3,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,8,5,2,3,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,4,1,3,6,7,2,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[8,4,1,2,6,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,5,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,1,5,8,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[6,3,7,1,5,4,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,3,8,1,5,4,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,5,3,8,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,5,1,3,6,8,2,7]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[3,6,8,1,5,4,2,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[6,8,3,1,5,4,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,6,3,1,5,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,6,2,1,5,8,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[8,6,2,1,5,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,1,7,5,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,3,8,1,5,7,4,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[7,1,3,2,8,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,6,2,8,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,7,1,2,6,3,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[2,7,8,1,5,3,4,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,2,1,5,3,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[4,7,2,1,8,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[8,7,2,1,4,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,6,1,4,3,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[2,7,4,1,6,5,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,1,4,5,6,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[7,1,6,4,5,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,5,1,4,7,6,8,2]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[2,6,4,1,7,5,3,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,6,8,7,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,8,5,7,1,4,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,6,5,7,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,8,1,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,2,3,1,5,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,2,8,1,6,5,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,2,4,1,8,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,3,1,4,5,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,8,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[7,5,1,6,3,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,5,8,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,8,1,6,4,3,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,3,1,8,4,6,7,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,3,1,5,4,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,4,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,4,5,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,6,1,5,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,8,6,1,5,3,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,6,3,8,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[7,1,2,5,8,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,4,5,6,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,5,6,7,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,7,5,1,4,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,6,7,1,4,5,3,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[3,5,1,7,4,6,8,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[7,1,5,6,4,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,6,5,4,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,6,1,4,5,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[5,7,6,8,1,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[7,8,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,3,1,6,5,8,7,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[5,3,1,2,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,3,6,2,1,8,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[5,3,7,2,1,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,3,7,2,8,4,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[7,2,4,5,8,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,4,5,1,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,2,4,5,1,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[3,1,4,5,2,8,7,6]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[1,6,4,5,2,8,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[3,7,4,5,1,2,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,4,5,8,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,4,2,6,3,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,7,4,5,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,1,8,4,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,7,4,1,6,3,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,7,4,8,6,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,7,4,8,6,3,1,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,8,3,5,6,7,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,5,6,7,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,5,6,7,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,6,7,2,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[5,8,4,3,6,1,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,3,8,4,1,7,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,5,8,4,6,7,3,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,8,3,6,7,5,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,2,1,7,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,8,4,2,6,1,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,5,6,7,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,5,6,7,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,5,6,7,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,1,5,6,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,6,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,3,6,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,8,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,3,1,8,5,7,6,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,1,6,8,7,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[6,3,1,8,2,7,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,5,8,2,7,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,5,4,8,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,4,8,6,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,4,1,6,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,4,5,8,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,6,4,5,8,2,3,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[7,3,6,1,8,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,7,6,5,8,3,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,8,5,3,6,7,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,5,2,1,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,6,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,6,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,6,7,3,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,2,8,5,6,7,3,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,5,6,7,3,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[1,5,3,8,6,7,4,2]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,4,5,8,6,7,3,2]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[4,3,5,8,1,7,2,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[3,5,4,8,6,1,2,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[1,4,8,5,6,7,2,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,5,6,7,1,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[2,7,1,5,6,3,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7,1,4,3,6,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[4,3,7,2,5,6,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[2,6,3,1,4,5,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[3,7,1,4,2,6,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[3,7,1,5,6,2,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[4,7,1,5,6,8,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[8,5,2,6,7,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,5,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,2,5,6,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[5,3,4,6,2,8,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[5,3,7,4,2,8,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,4,7,2,3,8,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,5,7,2,8,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,3,7,2,4,8,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[2,6,5,1,8,3,4,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[8,7,6,1,4,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,3,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,3,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,1,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,4,1,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,3,4,2,1,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[6,7,4,2,3,1,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,7,5,3,1,2,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,7,5,4,1,8,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,2,4,3,8,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,3,5,4,1,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,2,7,1,3,4,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[2,6,5,7,3,1,4,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[2,6,5,7,3,1,8,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[6,3,1,4,7,8,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,8,2,1,3,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,7,1,8,4,5,2,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,2,4,7,5,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,3,2,4,7,5,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[4,2,1,6,3,7,5,8]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[4,2,1,6,3,7,8,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[7,4,3,5,8,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,7,6,8,3,1,4,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,4,3,5,8,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,2,1,7,3,8,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[4,2,1,3,7,8,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[5,8,1,7,4,3,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,1,7,4,3,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,7,8,6,2,1,4,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,2,1,8,3,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,2,1,3,6,7,5,8]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[4,2,1,3,7,5,6,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[4,2,1,3,6,8,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[7,3,2,4,8,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,2,1,6,3,8,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[4,2,1,7,3,5,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[3,6,7,5,2,1,4,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[3,6,7,5,2,1,8,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[7,3,4,2,6,8,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,8,6,2,7,3,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,3,4,2,6,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,6,7,5,2,4,8,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[3,6,7,5,2,4,1,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[4,2,1,7,3,6,5,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[4,2,1,7,3,6,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[3,7,6,8,4,2,5,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[5,8,1,7,4,2,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,7,8,6,2,4,5,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,2,1,3,8,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,2,1,3,7,6,5,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[4,2,1,3,5,7,6,8]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[4,2,1,3,5,8,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[4,8,1,7,3,6,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,8,6,3,5,2,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,2,1,8,3,7,6,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,2,1,3,5,6,8,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[2,6,1,5,4,7,8,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[4,6,3,5,8,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[3,5,6,1,4,8,7,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[2,7,5,1,8,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[4,7,5,2,1,3,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[3,5,6,2,4,1,7,8]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[2,5,6,1,4,8,3,7]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[6,7,8,4,1,5,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[7,1,6,8,4,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,6,5,2,8,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,5,6,4,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,7,4,6,8,1,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,8,1,4,6,3,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[8,1,5,7,4,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,7,5,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,8,4,7,5,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,5,8,6,1,7,3,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,8,5,1,6,7,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,1,4,5,6,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,7,1,4,2,3,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[8,4,2,6,1,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,1,6,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,1,8,4,2,6,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,8,4,6,2,5,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,2,3,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[8,3,1,4,6,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,5,6,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,5,1,8,2,6,4,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,5,1,2,8,4,7,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[2,3,5,8,6,1,7,4]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[8,2,4,3,6,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,5,7,1,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,8,5,1,7,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[6,2,1,8,4,7,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,8,7,1,4,6,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,7,1,5,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,3,6,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,1,5,6,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,7,5,1,6,2,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7,3,6,5,8,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,7,2,4,1,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,3,6,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,8,2,6,4,3,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,3,8,2,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,2,7,3,6,4,5,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[7,1,5,8,3,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,6,2,8,4,3,7,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,3,8,7,2,4,6,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,8,3,7,2,5,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,4,7,3,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,1,3,2,5,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[7,1,4,2,3,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,1,4,7,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,4,6,7,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,4,8,5,7,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,4,7,5,6,8,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[2,4,8,7,5,6,3,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,5,3,8,4,7,6,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,8,5,7,3,6,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,8,5,2,7,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,3,5,7,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,4,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,3,4,5,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,8,3,4,5,7,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,5,7,3,4,8,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[2,7,8,5,3,6,4,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,7,6,3,4,8,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,1,8,7,2,6,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,3,7,6,1,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,2,3,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,3,6,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[3,7,1,8,2,6,4,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,1,7,8,2,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[3,1,6,5,8,2,7,4]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[6,3,5,8,7,1,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,3,8,5,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,6,1,4,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,8,3,6,1,4,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,4,8,1,2,3,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,4,6,1,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,2,3,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,6,1,2,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,1,2,8,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,7,1,2,3,6,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[3,6,8,1,2,7,4,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[4,8,6,1,2,3,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,4,6,1,2,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,2,7,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,5,3,8,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[3,1,4,8,7,5,2,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[4,3,6,8,7,5,1,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[5,4,1,8,2,7,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,4,1,8,2,7,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,6,7,4,1,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,2,5,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,7,3,1,4,8,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,6,3,8,7,1,4,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,4,1,6,8,2,7,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,4,7,1,2,8,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,7,4,1,2,8,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,5,1,2,3,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,5,1,2,3,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,6,5,1,2,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,3,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,7,4,1,2,5,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,8,6,4,1,2,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,4,6,3,5,7,1,8]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,4,6,3,7,2,5,8]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[8,6,2,5,3,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,5,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,4,2,7,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,4,1,6,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,2,3,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,6,1,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,2,4,3,1,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,5,8,2,3,1,7,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,1,4,3,7,2,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[6,1,3,5,7,2,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[2,1,4,7,5,3,6,8]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[7,1,3,6,2,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,1,3,6,2,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,7,5,4,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[7,1,8,2,5,6,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,5,8,2,7,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,5,2,8,1,6,7,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[6,2,5,8,1,4,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,2,8,5,1,6,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,2,7,1,4,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,5,7,4,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,8,7,1,6,4,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,1,5,6,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,5,6,1,7,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[8,3,7,4,1,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,2,7,3,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[8,4,5,7,1,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,8,4,1,7,2]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[6,2,3,1,5,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[7,2,3,1,4,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,3,1,4,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,2,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,2,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,6,1,4,5,3,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[3,6,4,1,5,2,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[4,5,6,1,3,2,7,8]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[4,5,7,1,2,6,3,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[3,7,4,1,2,6,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[6,7,1,4,2,5,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[2,7,1,3,5,6,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,6,1,2,4,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,4,6,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,1,2,5,3,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,8,4,1,2,5,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,7,5,3,8,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,7,5,3,2,8,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,6,7,5,3,8,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,6,5,7,2,3,8,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,3,8,2,6,5,7,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,5,7,6,3,4,8]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,3,4,8,2,5,7,6]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,5,7,6,2,3,4,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,5,3,8,2,6,4,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,4,8,3,2,5,7,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,4,8,3,5,7,6,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,2,4,8,3,5,7,6]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,8,4,2,6,7,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,4,8,2,3,5,7,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,5,7,3,8,2,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[4,2,6,7,5,8,3,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[6,7,5,2,1,8,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[3,4,8,7,5,2,1,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,7,5,2,8,4,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,6,8,3,1,7,2,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,1,4,8,3,2,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,4,7,1,8,6,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[3,4,6,8,2,1,5,7]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[3,8,2,5,6,1,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,8,6,4,1,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,5,7,3,8,6,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[7,4,2,5,3,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,1,2,8,5,6,4,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,2,1,6,8,3,4,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,2,6,8,4,1,3,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,5,6,8,3,4,2,7]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,8,1,6,3,2,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,1,6,8,3,2,7]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[4,5,7,3,8,2,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[6,4,3,7,8,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,4,3,1,7,8,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[4,5,3,1,7,8,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[7,1,3,5,4,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,2,8,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,7,3,8,4,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[1,4,5,7,3,8,6,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[4,6,3,7,8,5,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[5,3,6,7,8,4,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,5,3,6,7,8,4,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[4,6,1,7,3,8,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[6,3,7,1,8,4,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,7,2,4,8,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[2,6,1,4,7,3,8,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[3,2,5,6,7,8,1,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[5,2,3,6,7,8,4,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[6,7,1,3,2,8,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,2,7,1,3,4,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,2,1,7,3,8,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[6,4,2,7,1,8,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[4,2,6,3,7,8,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[4,2,6,3,7,8,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[6,7,3,8,2,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[3,6,2,7,4,1,8,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[6,7,3,2,1,4,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,1,8,3,4,2,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,4,1,8,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,4,8,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,4,8,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,5,7,2,1,8,6,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[6,7,8,3,2,5,1,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,3,7,8,2,5,4,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[2,6,7,4,8,5,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[6,2,4,7,1,8,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[4,6,2,7,1,8,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[1,7,4,8,5,2,6,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,3,7,8,5,2,6,4]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,5,7,8,1,6,3,4]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[6,3,7,1,8,2,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,6,4,7,8,2,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[2,5,6,1,7,8,4,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[5,6,1,2,7,8,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[6,7,2,1,8,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,2,8,5,4,1,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,6,7,4,8,5,3,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,8,2,4,6,3,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,8,3,5,1,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,3,7,4,6,2,5,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,5,7,4,3,6,2,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,8,4,5,3,6,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,3,4,7,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,4,6,3,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,5,4,6,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,7,1,4,5,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[6,3,8,1,2,4,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,3,7,4,6,2,8,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,4,7,5,2,6,8,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[4,5,2,7,1,3,8,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[4,5,2,3,6,1,8,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[4,6,5,3,7,1,8,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[2,5,4,7,1,6,8,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,2,3,8,6,7,1,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[6,2,4,8,5,1,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,2,4,8,1,3,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,2,5,4,8,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,4,3,5,8,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,2,3,4,8,1,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[3,5,2,4,7,1,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[5,3,4,8,1,6,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,5,3,7,1,6,2,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[6,2,4,8,5,1,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,6,3,8,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,4,3,7,8,2,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[4,2,6,7,3,8,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[1,5,7,4,2,8,6,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,3,7,2,8,6,4,5]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,4,3,7,8,6,2,5]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,5,3,6,8,2,7,4]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,5,2,7,1,8,6,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[4,3,6,5,7,8,1,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[4,2,3,5,6,8,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[5,2,6,4,7,8,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[4,2,6,7,3,8,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[3,2,5,6,8,1,7,4]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[6,4,5,2,3,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,4,6,7,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,2,3,1,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[6,4,2,5,3,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,4,2,5,3,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,6,4,7,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,4,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,5,8,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,6,2,5,3,8,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[4,6,5,2,3,8,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[6,8,7,4,5,2,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,6,7,5,2,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,8,4,7,5,2,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,7,4,5,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,6,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,7,5,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,2,6,7,5,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,6,7,5,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,7,4,5,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,7,2,4,5,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,6,4,5,8,7,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,4,8,7,5,3,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[4,6,2,8,7,5,3,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[8,2,4,6,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,2,6,8,7,5,3,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,2,6,5,8,7,3,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[6,2,4,5,8,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,2,6,7,4,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,4,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,2,8,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,2,3,6,8,7,5,1]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[6,4,5,8,7,2,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,6,7,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,2,5,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,8,7,4,5,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,7,5,2,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,6,8,7,5,2,3,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,5,8,7,2,3,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[2,1,6,8,7,4,5,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,6,8,7,4,5,3,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,4,8,6,7,5,3,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,2,8,6,7,5,3,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,2,8,4,7,5,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,2,6,4,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,7,5,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,6,8,2,7,5,3,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[2,6,8,4,7,5,3,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,6,8,7,2,5,3,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,5,8,2,7,3,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[2,1,6,8,4,7,5,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,8,6,4,7,5,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,8,7,4,2,5,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,6,4,7,5,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,2,7,5,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,6,3,8,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[6,2,5,7,4,8,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[8,5,2,1,4,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,2,5,8,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[3,2,6,4,8,1,5,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[2,3,6,4,7,8,5,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[7,5,1,8,3,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,7,8,2,6,3,4,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[7,1,6,3,5,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,3,1,7,8,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,3,6,7,4,1,8,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[7,3,1,2,5,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,6,3,5,2,4,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[3,4,8,2,7,5,1,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[6,3,2,8,5,7,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,8,4,7,2,5,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,8,1,5,3,7,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,1,6,2,7,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,8,4,6,7,3,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,3,4,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,1,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,7,6,8,3,4,2,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[2,8,1,6,5,7,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,8,2,5,3,7,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[5,2,3,7,6,1,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[8,1,2,4,6,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,7,4,8,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,2,6,8,4,3,1,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[7,8,1,5,4,3,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,2,4,8,5,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,7,5,1,8,4,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,8,5,4,6,1,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[5,7,4,3,8,6,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[4,8,1,6,3,5,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,3,1,7,4,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,4,5,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,1,3,7,6,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,7,1,4,5]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[4,3,2,8,5,7,1,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,6,4,2,8,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[4,7,3,2,5,1,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,2,4,7,5,8,6,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[4,2,3,8,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[2,4,3,5,1,8,6,7]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[3,2,8,1,4,6,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,7,8,5,6,1,2,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,6,1,8,4,7,2,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,1,6,8,4,7,2,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[4,1,6,8,3,2,7,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,6,1,8,3,2,7,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,7,8,1,3,2,6,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,7,8,3,1,2,6,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[2,7,8,3,4,6,5,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[4,7,8,2,1,3,6,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,6,1,8,2,3,7,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,1,6,8,2,3,7,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,5,1,2,8,3,7,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[4,5,2,1,8,3,7,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[4,6,2,8,1,3,7,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[3,6,2,8,4,7,1,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,3,6,8,4,7,5,1]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[3,2,6,8,4,7,1,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[4,2,6,8,3,1,7,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,2,5,1,8,3,7,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[4,1,2,5,8,3,7,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[5,1,2,4,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,2,4,1,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[4,2,5,3,8,1,7,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[3,2,5,4,8,7,1,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[3,5,2,4,8,7,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[5,4,2,1,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,1,4,2,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,4,1,3,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,4,3,1,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[4,5,3,1,8,2,7,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[4,5,1,3,8,2,7,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[3,1,5,4,8,7,2,6]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[3,5,1,4,8,7,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[3,5,4,1,8,7,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[3,6,5,8,7,1,2,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,5,6,8,7,3,4,1]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[3,4,5,1,8,7,2,6]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[3,4,1,5,8,7,2,6]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[4,1,3,5,8,2,7,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[4,3,6,8,2,1,7,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,3,7,5,1]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,4,5,2,8,7,1,6]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[5,3,1,4,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,1,3,4,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,1,3,2,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,3,2,1,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[4,3,2,5,8,1,7,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[3,4,2,5,8,7,1,6]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[3,2,4,5,8,7,1,6]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[4,2,3,5,8,1,7,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[5,2,3,1,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,2,1,3,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,1,2,3,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[8,6,2,5,4,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,4,2,8,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,7,5,3,8,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[8,2,1,6,3,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,6,2,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,3,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,7,8,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[7,5,8,2,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,1,6,5,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,5,6,7,3,4,8,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[6,7,8,2,1,4,5,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[8,4,7,6,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,4,7,2,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,1,3,7,6,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,7,8,6,2,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[3,5,8,2,7,1,6,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[6,2,8,5,3,1,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,2,6,4,7,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,2,8,5,1,7,6]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,8,6,5,2,1,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,7,4,2,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,2,1,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,4,1,8,2,6,7,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[8,4,6,3,7,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,1,5,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,1,7,6,2,8,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,8,2,5,7,4,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,5,6,7,1,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,6,3,1,8,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,2,8,3,1,5,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,5,7,3,8,4,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,2,7,1,8,5,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,2,1,8,7,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[8,3,6,7,1,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,5,8,6,4,2]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[5,7,8,4,3,1,6,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[2,7,4,5,8,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,5,7,1,4,8,6,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[7,2,8,5,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,6,5,3,8,4,2,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,7,4,8,3,6,2,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,8,6,1,3,5,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,2,4,7,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,3,2,5,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,2,5,7,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,3,7,2,5,8,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[3,2,4,7,8,5,6,1]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[2,6,4,3,8,5,1,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[3,8,2,1,6,4,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,1,3,4,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,2,1,5,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[3,2,6,8,5,4,1,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[7,3,8,2,5,4,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,5,3,8,7,6,1]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[4,8,2,6,5,3,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,6,8,5,4,1,3,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,1,8,6,5,4,2,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[5,4,8,7,3,2,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,4,8,3,7,2,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,7,3,6,2,1,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[5,4,3,7,1,8,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[7,3,8,5,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,4,8,7,6,2,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,8,1,5,7,4,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,7,3,1,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,8,3,7,6,2]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,8,3,6,7,1,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,8,3,1,6,5,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[8,7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,8,7,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[6,8,2,1,7,4,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,7,1,6,4,2,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[3,1,2,7,5,6,8,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[3,6,1,2,7,5,8,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[3,7,6,2,5,8,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,6,2,5,8,7,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[8,5,2,3,6,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,6,3,8,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[6,3,2,4,8,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,7,2,4,6,1,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[5,3,7,2,8,1,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[6,3,2,8,7,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,3,8,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,4,8,7,2,5,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,5,4,8,1,7,6,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,2,8,1,7,6,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,2,1,3,8,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,6,1,8,7,5,2,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[5,6,1,2,8,7,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[7,5,2,8,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,7,6,8,1,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,8,5,1,6,2,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,4,8,6,1,2,5,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,1,8,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,8,7,1,6,4,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,5,4,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,8,3,2,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,6,4,3,2,8,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,1,4,8,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,1,2,5,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,7,4,2,5,1,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[5,7,2,4,6,8,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[4,7,5,1,6,2,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[5,7,4,6,3,1,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[7,5,1,4,3,2,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,6,4,2,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,3,8,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[5,4,2,7,3,1,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,5,1,2,7,6,8,3]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[5,4,6,8,3,1,2,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,4,8,1,3,7,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,6,1,3,8,5,2,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[1,3,8,4,5,7,2,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,6,7,4,5,3,1,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[2,6,8,4,3,5,1,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,3,7,4,2,8,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[4,6,1,3,7,2,5,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[7,5,8,6,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,8,1,3,6,5,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,3,5,4,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,6,8,7,1,5]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[7,4,2,3,6,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,2,3,6,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,4,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,3,2,7,1,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,5,6,3,7,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,5,8,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,7,8,3,4,5,1,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,1,2,4,6,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[7,5,6,8,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,1,6,5,2,7,4,8]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[2,8,6,5,3,4,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,3,5,6,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,7,4,2,1,5,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,4,6,2,8,5,7,1]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[4,2,1,7,5,8,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[4,7,2,6,5,1,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[3,7,4,1,2,5,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[4,7,1,6,5,2,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[4,7,3,6,5,1,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[4,3,7,1,6,8,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,2,1,7,5,6,8,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[3,2,4,8,6,7,1,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[4,2,6,8,7,3,1,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[3,4,6,1,8,5,2,7]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[4,1,6,7,5,8,2,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[4,3,6,7,5,1,2,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[4,3,7,1,6,8,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,3,7,5,6,8,2,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,1,7,3,6,5,2,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[2,8,7,4,5,3,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,4,3,5,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,4,2,6,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,6,2,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[5,8,7,6,1,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,2,1,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,1,7,2,6,8,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,2,7,3,6,1,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,2,7,3,6,5,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[3,8,2,4,5,6,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,4,1,6,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,6,2,4,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,5,3,7,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,5,1,4,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,1,4,6,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,5,4,6,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,6,3,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,2,7,5,6,1,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,2,6,7,5,3,1,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[3,2,6,1,4,5,8,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[2,8,7,3,4,5,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,2,4,6,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,1,3,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,2,3,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,6,2,3,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[3,8,1,5,2,6,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,5,3,4,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,5,4,3,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,6,3,2,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[5,8,7,6,1,3,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,6,4,1,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,4,2,3,7,6,8,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[7,4,3,5,2,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,4,3,7,5,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,5,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,3,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,1,7,2,4,6,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[4,5,7,1,2,6,8,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[5,4,1,7,3,6,8,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[3,6,4,7,5,2,8,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[3,4,7,6,2,5,8,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[4,7,5,6,1,3,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[5,7,6,4,3,1,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,7,6,3,1,4,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[7,5,2,3,4,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,8,4,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,6,1,3,4,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,6,5,2,7,8,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[3,2,8,6,7,1,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,8,3,6,5,2,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,5,4,2,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,2,3,5,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,2,5,3,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,8,5,1,2,4,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,7,5,1,8,2,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[7,1,2,8,3,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,1,7,8,2,5,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,7,5,2,8,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,1,4,5,8,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,7,6,4,2,8,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[7,5,6,1,2,8,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,1,3,7,8,6,2,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[5,1,4,3,6,8,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[4,5,7,6,8,2,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[5,7,6,8,4,2,1,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,1,6,8,4,2,7,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[7,4,8,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,6,8,4,7,3,2,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,4,7,8,5,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[3,6,4,8,5,1,2,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,7,4,8,1,2,5,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[7,4,3,8,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,8,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,1,3,5,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,4,2,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,8,3,1,4,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,1,4,8,2,5,7,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[4,8,5,2,1,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,6,3,1,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,2,3,7,4,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,1,7,2,4,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,2,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,6,3,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,7,1,6,3,5,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7,1,5,4,3,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[7,2,1,5,4,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,1,3,5,4,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,4,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,2,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,3,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,5,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,4,5,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,7,1,4,5,3,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,6,3,1,5,4,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[6,3,2,1,5,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[7,3,1,4,5,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,1,5,4,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,1,6,2,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,7,1,6,2,5,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,1,4,5,2,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,6,2,1,5,4,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[2,3,6,1,5,4,7,8]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[3,5,2,4,1,6,7,8]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[6,3,4,1,5,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,2,4,1,5,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[2,6,4,1,5,3,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[2,6,5,1,3,7,4,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[6,2,5,1,3,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,5,2,1,3,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[7,6,1,2,4,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,1,2,8,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,1,2,5,4,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[5,6,2,1,3,7,4,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[5,2,6,1,3,7,4,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[2,4,6,1,5,3,7,8]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[4,7,1,3,5,2,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,7,1,5,3,2,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[5,7,1,4,2,6,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,7,1,6,2,3,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,6,3,1,2,7,4,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[4,2,5,3,1,6,7,8]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[5,3,6,1,2,7,4,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[3,4,6,1,5,2,7,8]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[6,5,1,8,7,3,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,2,7,5,4,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,3,4,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,6,8,7,1,5,3,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[8,5,6,2,7,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,2,7,8,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[4,7,6,1,5,3,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[5,7,6,4,1,3,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[7,6,2,4,5,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,7,5,3,8,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[8,6,7,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,5,3,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,6,2,4,7,8,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[3,4,6,1,7,8,5,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[3,4,8,6,7,1,5,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[4,8,5,6,7,2,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,4,1,2,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,1,7,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,3,2,6,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,1,7,2,6,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,1,5,7,2,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,5,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,2,5,1,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,7,2,1,6,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,1,5,2,6,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,7,8,5,1,6,2,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[6,5,2,7,8,1,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[7,1,2,8,5,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,7,2,1,5,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,5,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,5,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,5,6,2,1,8,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,5,8,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,1,3,4,6,8,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[4,5,3,6,8,2,7,1]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[5,6,3,4,8,1,7,2]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[4,6,7,8,5,1,3,2]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[8,4,3,1,2,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,3,4,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,6,3,4,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,6,8,1,5,3,7,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[6,4,5,8,3,2,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,6,4,8,7,1,5,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[6,5,8,1,3,4,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,6,8,3,1,2,7,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,1,8,3,5,2,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,6,8,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,6,1,3,5,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,5,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,3,5,1,2,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[3,4,8,1,2,6,7,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[5,8,2,4,3,6,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,2,3,1,6,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,2,3,5,1,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,2,3,5,6,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,5,1,4,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,1,3,7,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,7,1,8,4,3,5,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[2,7,8,6,1,4,3,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,7,3,8,1,6,4,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,5,1,8,2,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,7,8,4,1,6,3,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,6,5,4,1,3,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[4,1,7,6,3,8,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,8,2,5,7,6,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,4,6,5,1,8,2,7]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[2,6,5,3,4,1,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[4,6,1,5,2,3,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[6,2,3,5,1,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,6,7,5,1,8,4,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[8,6,1,2,5,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,1,8,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,6,5,2,8,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,6,3,5,1,8,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,4,7,6,5,8,1,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[2,1,4,8,7,6,3,5]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[7,4,6,8,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,1,3,5,7,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,5,1,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,8,5,1,6,7,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,1,6,7,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,6,1,3,5,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,6,7,2,8,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[2,5,1,8,6,7,4,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[3,5,1,8,6,7,4,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[5,2,3,8,6,7,4,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,3,5,4,6,7,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,8,6,7,4,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,2,5,8,6,7,4,1]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[6,2,1,5,3,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,6,3,2,8,1,4,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[8,1,6,3,5,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,5,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,8,3,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[2,7,5,8,1,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,6,2,8,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,1,3,7,5,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,7,5,1,6,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[6,3,8,1,4,2,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,8,5,7,4,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,4,6,8,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,1,4,8,7,5,6,3]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[7,1,5,8,2,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,6,8,2,4,1,7,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[4,5,8,2,6,7,3,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,2,8,1,6,7,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,5,8,4,6,7,3,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,8,3,4,6,7,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,4,3,2,6,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,6,7,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,1,6,7,3,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[5,1,8,2,6,7,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,4,8,7,2,1,5,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[7,8,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,8,5,7,4,1,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,1,6,7,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,1,4,6,7,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,3,4,6,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,3,8,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,4,3,2,8,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,3,2,8,4,6,1,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,4,2,6,5,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,5,3,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,3,6,2,5,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,2,6,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,5,8,2,4,6,1,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[6,4,7,8,2,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,8,3,6,4,2,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,6,2,5,3,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,2,8,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,5,3,2,8,4,7,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[5,7,4,3,1,2,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[2,8,7,3,5,1,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,8,6,4,1,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,2,7,3,8,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[2,1,7,4,3,8,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[6,1,4,3,8,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,1,3,2,8,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,8,4,2,7,6,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,7,2,6,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,8,3,7,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[2,1,6,8,5,4,7,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[6,1,5,7,8,2,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[8,3,1,6,7,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,6,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,7,6,1,2,5,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[3,7,6,1,5,2,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,5,4,8,3,2,7,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[7,3,6,1,2,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,4,7,1,3,2,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,7,4,8,2,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,6,8,2,5,1,3,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[7,4,6,2,1,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,2,6,3,8,5,7,4]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,2,6,8,4,7,3]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[5,7,2,3,8,1,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,4,7,5,8,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,4,8,5,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,8,3,6,1,7,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,1,5,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,4,1,8,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,6,4,8,7,5,3,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,3,1,2,8,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,5,1,3,2,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,7,1,2,5,8,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[6,8,4,1,2,7,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,5,8,1,2,6,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,1,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,8,2,1,7,3,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,6,1,8,2,4,7,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,3,8,7,6,2,5,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[5,4,1,8,7,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,5,1,8,7,2,4,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[4,6,1,8,3,7,2,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,7,1,2,8,6,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,8,4,1,7,6,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,6,8,1,5,4,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,6,1,7,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,6,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,1,8,7,3,6,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,1,8,7,6,2,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,1,8,7,6,5,2,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,6,4,5,2,3,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,7,4,5,2,3,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,3,5,2,4,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,6,3,5,2,4,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,6,3,4,2,5,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,7,3,4,2,5,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,6,7,3,4,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,7,3,4,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,2,6,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,5,2,8,4,7,3,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,4,2,8,5,7,3,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,7,3,5,2,6,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,4,7,3,5,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,6,2,5,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,3,6,2,4,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,4,6,2,3,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,5,6,2,3,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,6,2,4,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,8,5,6,4,7]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,4,2,8,5,6,3,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,5,2,8,4,6,3,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,6,2,8,4,5,3,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[8,1,2,4,5,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,7,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,2,8,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,4,7,3,5,8,2,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[8,4,6,2,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,2,3,6,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,4,8,5,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,8,6,2,4,5,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,2,3,5,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,4,8,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,6,4,8,2,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,8,7,4,1,2,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,5,3,4,1,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,3,7,2,1,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,5,1,6,3,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,7,4,8,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[4,1,7,3,5,8,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[7,1,6,4,8,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,8,5,7,2,3,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,5,8,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,1,7,3,8,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[6,1,5,7,8,2,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[7,4,8,6,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,8,7,5,1,2,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,2,4,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[4,7,6,1,2,3,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[1,6,5,8,2,3,4,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,5,8,4,1,2,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,5,7,4,1,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,4,8,2,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[7,6,4,8,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,2,3,8,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,8,5,1,6,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,6,2,3,1,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,2,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,6,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,6,1,3,8,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,8,1,3,6,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,4,1,8,2,3,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,4,8,7,2,3,5,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,5,8,7,2,3,4,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[6,5,1,8,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,7,1,3,8,2,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[7,6,8,1,5,2,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,5,8,6,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,1,8,2,7,3,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,1,8,7,2,3,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,1,8,7,2,3,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,8,7,6,4,5,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,3,6,5,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,8,3,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,4,3,2,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,4,2,3,8,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,4,2,7,5,8,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[2,4,1,7,5,8,3,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[7,1,4,6,5,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,4,6,5,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,4,6,3,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,4,3,2,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,4,6,5,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,4,6,5,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,4,6,5,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,4,2,7,5,3,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[3,4,7,2,6,8,5,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[3,4,7,1,6,8,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[3,4,7,1,6,8,5,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[2,4,1,7,5,3,6,8]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[3,4,1,7,8,6,2,5]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[6,4,2,3,8,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,4,2,7,5,8,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,4,2,7,5,3,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[3,4,7,2,6,8,1,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[5,4,7,3,6,8,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[3,4,7,2,6,5,1,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[4,8,3,2,5,6,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,3,5,1,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,1,3,5,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,1,2,6,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,1,6,2,5,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[3,4,7,1,6,2,8,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[3,4,7,2,6,5,8,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[4,8,3,1,2,6,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,6,3,4,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,5,1,3,7,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,1,3,4,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,3,4,2,6,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,6,2,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,4,7,2,6,1,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[6,4,3,7,5,1,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,4,3,7,5,1,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,2,4,3,1,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[3,8,7,4,1,5,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,3,6,1,5,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[5,8,3,2,1,6,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,4,3,1,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,4,7,3,6,2,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[7,3,8,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,3,8,5,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,2,8,4,3,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,3,2,8,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,8,7,5,1,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,2,5,8,6,1,4,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[8,4,3,7,5,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,8,5,1,2,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[5,3,7,8,4,1,2,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[6,2,5,8,3,1,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,4,8,3,1,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,2,3,8,4,1,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,3,8,7,4,1,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,3,2,8,6,4,1,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[7,5,3,8,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,7,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,8,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,4,5,3,8,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,4,6,3,8,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,6,3,8,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,5,6,3,7,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,5,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,6,3,5,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,5,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,5,8,4,3,2,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,3,4,2,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,5,8,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,3,5,2,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,4,8,3,5,2,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,7,3,5,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,4,8,3,7,2,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,5,8,3,7,2,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,4,7,2,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,4,7,3,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,7,3,8,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,4,7,3,8,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,4,6,3,8,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,3,6,2,4,7,8,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[5,3,6,1,4,8,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[5,3,7,2,4,6,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[4,3,1,5,6,8,7,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[4,2,1,5,8,6,3,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[4,2,1,5,8,6,7,3]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[4,2,1,5,8,7,6,3]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[4,3,1,5,7,8,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[4,3,1,7,5,8,6,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[6,7,3,1,4,8,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,3,7,1,4,8,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[4,3,1,5,7,8,2,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[3,2,1,8,5,4,6,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,8,5,7,4,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,8,7,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,2,7,1,8,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[6,7,2,1,8,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,2,1,8,4,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[3,2,1,8,5,6,4,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,8,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[4,3,1,6,7,8,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[4,2,1,6,8,7,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[4,2,1,6,8,5,7,3]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[4,2,1,6,8,5,3,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[5,2,6,1,8,4,3,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,2,6,1,8,7,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,2,6,1,8,7,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,2,6,1,8,3,4,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[4,2,1,6,8,3,7,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[4,3,1,6,7,8,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[6,7,3,1,5,8,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[4,2,1,7,8,6,3,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[3,2,1,8,7,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,8,6,4,7,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,8,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,8,4,6,5,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,8,4,6,7,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,8,4,7,6,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,8,7,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[4,2,1,7,8,3,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[5,2,7,1,8,3,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[6,7,2,1,8,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[5,2,7,1,8,3,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[4,2,1,7,8,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[3,2,1,8,4,5,7,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[7,5,2,8,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,8,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,6,2,4,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,3,1,8,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,2,8,5,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,8,5,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,4,5,6,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,3,8,2,4,5,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,8,2,5,7,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,3,8,1,5,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,7,8,2,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,6,7,3,8,2,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[5,4,7,2,6,8,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,3,8,2,4,6,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,3,8,2,4,7,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,7,4,2,6,8,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,4,8,2,7,5,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,3,1,4,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,7,4,2,6,1,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,6,4,2,3,8,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[5,6,3,7,8,2,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[5,6,3,8,2,4,7,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[6,3,7,2,4,5,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,3,7,2,5,8,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[5,3,6,8,2,4,7,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[5,4,6,2,3,8,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[5,3,6,7,8,2,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[3,6,4,2,1,5,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[3,5,8,6,4,2,1,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[5,8,6,3,4,2,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,6,3,4,2,1,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[6,3,4,2,1,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,6,4,2,1,3,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[2,5,4,1,7,8,6,3]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[2,7,8,5,4,1,6,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,8,5,4,1,6,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,8,5,4,1,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,8,6,3,5,4,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,4,2,1,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,2,1,5,7,8,6,3]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[2,7,8,6,3,5,4,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[4,3,8,5,7,6,2,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[7,6,2,1,8,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,1,8,5,6,4,3,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,8,5,6,3,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[8,4,2,1,5,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,3,8,4,1,7]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[6,3,4,2,1,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[3,7,8,5,6,4,2,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,8,5,6,4,2,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,4,2,1,8,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[3,8,6,4,2,1,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,8,6,4,2,1,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[8,5,3,7,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,4,1,8,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,5,4,1,7,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,8,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,1,7,8,6,4,3,5]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[2,1,6,4,3,7,8,5]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[6,4,2,1,3,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,3,7,8,4,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,8,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,7,6,2,3,8,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[2,6,1,8,4,3,7,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,1,7,5,8,4,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[8,4,2,3,7,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,7,6,2,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,2,1,3,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[7,5,6,1,8,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,7,5,8,4,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,8,4,3,6,1,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,8,3,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,4,3,7,5,2,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,5,3,2,8,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,2,7,8,4,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,4,3,2,5,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,3,7,2,5,4,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,3,2,7,5,4,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[8,4,2,6,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,7,4,2,8,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,6,7,3,4,2,8,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[8,6,5,2,3,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,3,4,2,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,6,3,2,5,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,5,2,3,1,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,6,2,3,1,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,2,6,3,1,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,6,4,1,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,7,5,4,8,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[4,1,3,7,5,2,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[5,1,7,3,4,2,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[7,1,6,3,2,5,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,2,7,4,3,6,8,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[6,1,8,2,4,5,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,1,8,3,2,6,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,2,8,7,1,5,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,8,2,7,1,5,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,2,1,4,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,7,1,3,4,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,6,1,3,4,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,7,8,2,4,5,6,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,6,7,1,3,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,1,3,4,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,5,8,2,3,1,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,6,8,3,2,5,7,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,5,3,8,2,6,7,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[8,4,2,7,1,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,8,1,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,4,2,8,3,1,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,4,2,3,8,1,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[4,5,2,3,1,6,8,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[7,4,2,1,3,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,2,1,3,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,2,4,7,8,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[8,5,1,3,2,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,1,3,4,2,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[4,6,2,1,5,3,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[4,7,2,1,3,6,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[5,7,1,3,2,6,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[6,7,1,2,4,5,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[8,6,1,2,4,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,5,6,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,2,4,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,2,4,5,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,8,1,3,2,6,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,2,1,3,6,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,2,5,7,8,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[5,1,2,4,3,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[5,4,8,1,2,3,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,4,7,6,3,2,5,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[4,8,3,2,7,6,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,8,2,7,1,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,4,7,3,6,2,5,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[4,3,2,8,1,7,6,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,1,8,3,7,2,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,8,7,3,2,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,7,8,1,2,5,3,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,4,7,6,2,1,8,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[3,4,2,7,1,6,8,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[2,3,6,7,4,1,8,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[2,6,3,4,7,8,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[2,6,7,8,3,4,1,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[3,1,7,8,4,2,5,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[4,1,3,2,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[3,7,8,2,6,4,1,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,2,3,8,1,6,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,1,8,2,5,7,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,3,6,7,4,2,5,8]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[3,2,7,8,4,1,6,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[4,2,8,6,3,1,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,7,2,4,8,6,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,2,7,4,8,1,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[1,3,6,4,7,2,5,8]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[3,2,4,7,1,8,6,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[3,7,4,2,6,8,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,4,6,2,8,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[4,7,1,5,8,2,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[3,7,6,4,8,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,1,7,4,8,2,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,7,3,8,4,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[2,3,6,4,7,1,8,5]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[8,7,5,2,6,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,7,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,4,6,7,8,5,1,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[1,2,6,4,7,5,8,3]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[3,1,7,5,4,2,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[6,3,8,5,4,7,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,6,2,5,4,7,8,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,8,2,5,6,3,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,4,8,5,7,3]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[7,8,3,1,4,2,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,8,1,5,2,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,2,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,6,1,8,4,3,2,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,1,8,6,4,3,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,6,3,8,7,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[6,1,2,5,8,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,1,8,7,4,3,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,1,2,5,4,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,2,7,5,8,3,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[4,1,6,3,7,5,2,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[1,3,6,7,8,5,2,4]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,2,6,4,7,8,5,3]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[4,1,6,3,7,8,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[3,1,6,4,8,2,7,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[7,8,4,1,6,3,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,1,6,3,8,7,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[7,5,1,8,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,1,7,4,3,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[4,1,8,5,2,3,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,6,8,3,7,2,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[5,4,6,1,3,8,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[6,5,8,1,4,3,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,3,5,7,6,8,2,4]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,3,5,7,6,2,8,4]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,3,5,7,2,6,8,4]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,3,5,2,7,6,4,8]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,3,5,7,6,2,4,8]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,3,5,7,4,6,8,2]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,3,5,7,4,6,2,8]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,3,5,7,4,2,6,8]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,3,5,4,7,2,6,8]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,3,5,4,7,8,2,6]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,3,5,4,7,2,8,6]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,3,5,7,4,2,8,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,3,5,7,4,8,2,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,3,5,7,4,8,6,2]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,3,5,7,8,4,6,2]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,3,5,7,8,4,2,6]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,3,5,2,7,8,6,4]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,3,5,7,2,8,6,4]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,3,5,7,8,2,6,4]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,6,3,2,7,4,8,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[3,5,1,6,2,8,7,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[1,3,7,2,5,4,8,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,1,7,4,3,8,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,4,7,3,5,2,8,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,3,7,5,2,4,8,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,5,7,4,3,8,1,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[2,5,3,7,4,8,1,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,4,7,2,3,8,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[2,4,7,3,1,8,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,4,6,3,8,2,7,5]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,3,5,2,8,7,6,4]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,4,7,3,8,2,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[2,5,1,7,8,4,6,3]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[3,2,6,7,8,1,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[4,3,6,7,8,2,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[3,5,2,7,8,4,1,6]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[1,5,7,4,8,3,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[2,5,1,6,8,4,7,3]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,6,2,1,7,8,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[5,3,6,4,7,8,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[3,5,2,6,8,4,7,1]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[2,5,4,6,8,7,1,3]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,3,6,2,8,7,5,4]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,4,6,3,8,7,2,5]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,5,7,4,3,8,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,5,7,2,4,8,6,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,6,3,7,2,8,5,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[4,3,6,7,8,2,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[1,4,7,3,8,6,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[2,5,4,7,8,6,1,3]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[3,2,6,7,8,5,1,4]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[1,3,7,2,8,6,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[5,1,6,8,2,4,3,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[5,3,7,8,2,4,1,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[8,5,3,7,2,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,3,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,8,3,1,5,6]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[6,3,1,5,8,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,3,4,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,2,4,3,8,1,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[3,2,4,8,1,5,6,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,2,4,6,8,1,5,7]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[8,1,5,7,3,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,7,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,2,3,1,5]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[7,4,6,8,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,4,8,3,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,3,8,7,2,4,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,4,8,7,3,1,5,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,6,8,7,2,3,1,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[8,7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,7,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,4,8,7,2,3,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,1,7,4,2,8,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[3,2,8,4,1,7,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,6,4,8,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,7,6,8,2,3,1,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,7,6,8,2,3,1,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[8,6,4,7,2,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,7,4,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,8,4,1,6,5]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[3,7,4,8,2,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,3,7,4,1,6,8,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[8,1,6,4,2,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,6,2,3,1,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[2,4,7,3,1,5,8,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[6,3,1,7,4,2,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[8,5,7,6,2,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,6,2,3,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,6,4,2,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,1,7,6,4,2,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[4,8,7,6,2,3,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,8,7,5,2,3,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,3,6,1,5,8,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[4,3,6,5,1,8,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[4,6,3,5,1,8,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[4,6,3,1,5,8,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[4,1,6,5,3,8,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[4,6,1,5,3,8,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[2,6,5,3,1,8,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,6,5,1,8,7,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,5,8,1,7,3,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,5,8,1,3,7,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,5,8,3,1,7,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,5,3,8,1,7,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[4,6,1,5,8,3,7,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,1,6,5,8,3,7,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[1,4,6,5,8,3,7,2]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[4,1,6,5,8,7,3,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[2,6,5,3,8,7,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[6,4,3,8,7,1,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,8,3,7,1,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,6,8,5,3,7,1,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,6,8,1,5,7,3,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,1,8,5,7,3,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,1,6,8,5,7,3,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[1,4,6,8,5,7,3,2]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,4,6,8,5,3,7,2]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[4,6,1,8,5,3,7,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[2,6,8,5,3,1,7,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,6,8,5,1,7,3,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,6,8,3,5,1,7,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,8,3,1,5,7,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,3,1,8,5,7,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,6,3,8,1,5,7,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,6,3,8,5,7,1,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,3,6,8,1,5,7,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,3,6,1,8,5,7,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,3,1,6,8,5,7,2]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[4,1,3,6,8,7,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[4,3,6,1,8,7,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,3,6,8,1,7,5,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[6,5,2,8,7,3,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,2,8,7,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,5,8,7,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,5,8,7,3,1,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,6,3,8,1,7,5,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,6,3,1,8,7,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,1,6,3,8,7,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[1,4,6,3,8,7,5,2]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[4,1,6,8,3,7,5,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,6,1,8,3,7,5,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,6,8,1,3,7,5,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[6,2,8,5,7,3,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,8,5,7,1,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,4,8,7,1,5,3,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,2,8,7,5,3,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,4,1,8,7,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,1,4,8,7,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,6,4,8,7,3,5,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,4,1,8,7,3,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,2,8,7,5,1,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,7,3,5,1,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,3,4,7,8,5,6,1]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[2,3,7,1,4,8,6,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,1,3,7,8,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[2,6,7,3,4,8,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,5,3,2,6,4,7,8]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,5,3,2,6,7,4,8]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,7,3,2,8,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,3,2,5,8,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,3,2,7,5,4,8,6]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[6,5,2,4,3,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,4,2,5,3,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[5,4,7,6,2,3,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[3,6,4,8,2,1,5,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,2,8,5,3,4,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[4,6,2,3,7,5,1,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[4,7,2,3,6,5,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,7,2,3,5,6,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[5,3,2,7,4,6,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,3,2,6,4,7,1,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[4,6,2,3,5,7,1,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[3,5,2,1,6,8,4,7]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[1,5,2,6,8,4,3,7]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,5,7,2,8,4,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[3,5,2,1,8,6,4,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[3,6,8,4,2,1,5,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[4,3,2,6,1,8,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,5,8,2,7,4,3,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,7,2,3,4,8,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,8,2,3,4,1,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,1,8,2,3,5,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,3,1,8,4,5,7,6]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[7,3,2,1,4,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,8,1,4,3,5,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,2,3,4,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,2,3,4,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,8,2,3,4,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,2,3,4,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,5,4,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,4,3,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,4,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,5,6,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,1,6,5,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,8,3,5,4,2,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,4,1,8,3,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,4,1,7,3,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,6,2,1,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,2,5,3,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,3,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,4,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,5,1,8,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[3,5,2,4,1,8,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[2,4,7,8,1,5,3,6]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,8,7,3,5,4,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,8,2,7,4,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,7,2,8,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[6,1,2,8,5,3,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,2,1,8,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,3,2,8,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,7,8,4,3,5,1,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,1,8,3,5,4,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,8,2,3,4,6,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,7,1,3,4,8,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,8,1,3,4,7,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,7,2,3,4,6,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,6,2,3,4,8,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[7,6,2,3,4,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,6,2,3,4,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,5,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,4,5,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,3,4,1,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,6,2,3,4,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,6,2,3,4,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,8,7,5,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,8,7,3,5,6,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,5,3,6,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,3,4,6,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,2,1,6,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,1,2,6,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,3,7,2,6,1,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,2,8,1,6,3,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,2,1,4,7,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,2,5,1,7,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,8,4,1,2,6,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,8,1,5,2,7,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,2,4,7,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,2,8,3,6,7,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,8,7,6,2,4,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,6,4,1,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,2,6,5,1,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,8,7,6,4,2,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,6,3,1,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,6,2,4,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,6,3,4,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,4,5,6,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,3,6,5,8,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[3,1,7,2,6,5,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[3,2,7,1,6,5,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[6,1,2,8,5,7,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,1,8,5,7,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,1,8,5,7,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,2,1,7,5,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,1,3,8,5,2,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,3,7,1,6,8,5,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,3,7,2,6,8,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[7,8,2,6,5,3,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,2,6,7,5,8,1,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[1,2,7,5,6,3,8,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[2,8,7,6,4,3,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,6,1,2,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,6,2,1,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,6,2,1,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,6,1,3,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,6,4,1,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,3,6,5,1,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,3,7,5,6,8,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[3,8,7,6,4,2,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,6,8,2,3,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,7,6,3,5,4,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,3,7,2,6,5,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[3,4,6,1,5,7,2,8]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[1,6,8,5,7,3,4,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,4,1,5,8,6,3,7]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[4,6,1,2,5,8,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[5,6,7,2,1,4,8,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[7,8,6,5,1,2,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,3,6,5,7,8,2,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[7,4,8,5,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,5,2,4,1,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,3,1,6,8,5,7,4]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[7,3,2,5,1,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,4,2,3,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,5,8,3,4,6,7,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[8,3,1,2,4,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,1,6,5,4,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[8,1,4,7,2,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,2,4,1,7,8,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[3,4,7,8,6,2,1,5]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[3,4,8,6,2,7,1,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[5,8,2,1,6,7,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,7,2,8,6,4,3,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[6,1,2,7,5,3,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,3,2,8,6,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,7,8,4,6,3,1,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,4,5,7,2,6,8,3]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[7,3,5,2,6,1,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,5,2,3,6,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,5,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,3,7,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,2,6,4,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,7,6,5,1,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,7,3,6,5,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,8,7,3,6,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,5,8,7,1,2,6,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,5,8,7,3,2,6,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,7,3,2,1,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[2,6,8,1,7,5,4,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,6,8,4,7,2,1,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[2,5,8,3,7,6,1,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,2,8,4,7,6,1,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,5,8,3,7,2,6,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,8,4,7,2,1,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[5,6,8,2,3,7,1,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,6,8,4,2,7,5,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,5,8,4,2,7,6,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,5,8,2,3,7,6,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,1,8,4,3,7,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,5,8,4,3,7,1,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,6,8,4,1,2,7,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,6,8,1,3,2,7,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,6,8,4,3,2,7,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,6,8,4,3,2,1,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[7,1,2,8,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,4,8,6,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,1,8,6,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,4,8,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,4,8,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,5,8,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,6,2,8,7,5,4,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,4,8,7,2,5,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[3,6,4,8,7,2,1,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,2,5,8,7,6,1,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[3,2,4,8,7,6,1,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,1,5,8,7,2,6,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[3,1,4,8,7,2,6,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[1,6,4,8,2,7,5,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,4,5,8,2,7,6,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[2,4,5,8,3,7,1,6]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[4,6,5,8,1,2,7,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[1,6,4,8,3,2,7,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,4,5,8,3,2,7,6]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[7,6,1,4,8,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,1,3,8,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,3,4,8,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,5,1,8,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,5,3,8,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,1,4,8,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,1,3,8,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,3,4,8,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,5,4,8,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,6,5,1,8,7,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,3,5,4,8,7,1,6]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,6,5,4,8,2,7,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,6,5,3,8,2,7,4]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,6,3,4,8,2,7,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,3,5,4,8,2,7,6]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[3,6,5,4,8,2,1,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[7,6,5,2,3,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,1,4,2,8,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,1,2,3,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,2,4,3,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,5,4,2,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,5,2,3,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,2,4,3,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,6,5,4,3,8,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[7,6,1,4,3,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,5,4,3,2,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,4,2,6,7,8,1,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[3,1,4,2,6,8,7,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[8,3,4,2,6,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,5,4,1,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[2,7,8,3,5,4,1,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,6,8,3,5,4,1,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,7,1,2,8,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,8,1,2,7,5,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,3,7,5,4,8]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[2,7,1,3,6,8,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,7,3,2,8,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,3,4,2,6,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,1,2,8,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,7,4,2,1,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,6,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,3,1,5,6,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,4,1,5,8,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[4,7,5,1,6,8,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,5,3,1,7,6,8,2]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[4,6,1,2,7,5,3,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[2,7,1,3,6,5,4,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[4,1,8,2,6,5,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,6,1,2,8,5,3,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[8,4,3,1,5,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,8,6,7,2]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[4,8,5,6,3,1,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,8,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,4,3,8,1,6,7,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,5,3,4,1,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,2,1,5,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,7,3,2,5,1,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,8,3,2,5,1,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,7,1,4,6,8,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,1,3,4,7,6,8,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[6,1,4,2,7,5,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[5,4,3,7,1,6,8,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[6,7,5,4,1,8,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[7,6,4,2,1,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,7,6,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,2,6,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,7,6,5,1,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,8,7,6,5,3,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,8,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,3,8,6,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,8,5,7,6,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,5,6,1,3,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,3,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,3,2,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,1,7,5,3,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,5,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,5,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,1,5,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,1,5,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,7,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,1,5,4,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,1,5,2,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,2,7,5,1,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,5,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,5,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,7,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,3,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,3,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,3,2,6,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[8,2,6,1,5,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,6,7,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,8,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,7,2,5,1,8,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[7,5,1,6,8,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,7,1,8,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,7,3,8,1,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,5,4,1,8,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,1,4,8,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,1,6,4,7,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,3,2,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,8,4,1,3,2,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,3,7,4,1,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,3,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,7,3,2,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,1,8,4,3,6,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,1,8,6,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,3,1,7,4,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,7,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,7,2,3,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,5,8,1,2,7,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,3,1,8,5,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,2,7,8,3,1,5,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,8,1,7,3,2,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,4,1,7,3,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,1,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,3,8,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,2,3,6,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,7,1,5,4,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[7,8,5,2,3,6,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,2,3,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,2,3,4,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,5,2,6,8,1,4,7]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[3,5,2,4,6,8,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[2,4,5,7,3,6,8,1]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[2,4,5,3,6,8,1,7]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[5,2,4,6,8,1,3,7]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,1,3,4,6,8,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[4,3,5,2,6,8,1,7]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[4,3,5,7,2,8,1,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[4,3,5,7,2,6,8,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[4,6,3,7,2,5,8,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[4,6,3,1,7,8,2,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[4,3,5,1,7,8,2,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[5,7,1,3,4,8,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,1,3,4,6,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[4,5,7,1,3,6,8,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[4,3,6,7,1,5,8,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[4,6,3,5,1,7,8,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[4,6,3,5,7,2,8,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[3,5,6,4,1,7,8,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[3,1,5,6,7,4,8,2]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[5,1,6,7,3,4,8,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[6,4,7,1,3,5,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,6,7,3,4,5,8,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[2,6,7,4,5,8,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[2,6,7,4,8,1,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,3,6,1,2,7,8,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[3,5,2,6,1,7,8,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[3,5,2,6,7,4,8,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[5,2,3,6,7,4,8,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[5,2,3,6,1,7,8,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[5,2,6,1,3,7,8,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[4,2,6,7,3,5,8,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[6,3,7,2,4,5,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[3,5,7,2,8,1,4,6]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[3,7,2,4,8,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[7,2,4,6,8,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,3,4,6,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,7,2,4,6,8,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,5,7,2,6,8,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[6,3,7,2,5,8,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,3,5,7,2,8,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,3,5,7,2,4,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,2,4,5,7,3,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,2,4,5,1,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,7,1,2,5,6,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[2,6,7,5,8,1,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[4,6,7,1,2,5,8,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[5,6,2,4,7,3,8,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[5,4,2,6,7,3,8,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[5,4,2,6,1,7,8,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[1,5,4,6,2,7,8,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[5,6,4,1,2,7,8,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[6,4,5,1,2,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,3,5,1,7,8,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,5,7,2,8,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,5,7,1,3,4,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,6,4,7,1,3,8,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[5,4,6,3,1,7,8,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[7,5,3,2,4,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,4,5,2,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,1,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,4,1,6,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,1,6,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,1,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,4,2,1,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,5,3,1,6,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,3,5,6,1,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,6,3,7,4,1,8,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[5,6,7,3,1,4,8,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[6,7,3,4,1,5,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,7,4,2,1,5,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[5,6,7,3,1,8,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[5,6,3,7,8,1,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[5,6,3,7,2,4,8,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[5,6,7,2,3,8,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[7,4,5,2,8,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,3,2,4,8,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[7,6,4,2,1,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,3,4,1,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,3,2,4,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,3,2,5,1,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,5,3,2,7,8,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,5,3,2,7,4,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,4,5,2,7,3,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,4,5,2,7,8,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[7,4,5,2,6,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,5,6,1,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,6,2,1,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,3,5,1,2,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[5,6,7,4,1,2,8,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[5,6,7,2,4,1,8,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[5,6,4,2,7,8,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[6,5,7,2,1,8,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,5,7,2,1,4,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,4,6,7,3,1,8,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[5,7,8,3,6,4,1,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[3,7,8,5,6,4,1,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,8,5,6,1,4,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,8,5,6,3,4,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,5,8,6,3,4,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,5,8,6,1,4,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,5,8,6,4,1,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[5,7,3,8,6,4,1,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[7,3,8,5,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,5,8,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,5,7,8,6,4,1,2]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[1,5,7,8,6,3,4,2]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,5,7,8,3,6,4,2]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[3,5,7,8,1,6,4,2]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[5,3,7,8,1,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[7,3,5,8,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,8,5,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,8,1,5,6,3,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,8,5,6,3,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,5,8,6,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,1,7,8,3,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[3,1,7,8,5,6,4,2]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,3,7,8,5,6,4,2]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[3,1,7,5,8,6,4,2]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[5,1,7,3,8,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[7,1,5,3,8,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,5,8,3,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,8,1,5,3,6,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,5,1,6,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,3,5,8,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,3,7,1,8,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[3,5,7,1,8,6,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[1,7,5,3,8,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,7,3,1,8,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,3,8,6,1,4,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,7,5,8,1,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,5,8,3,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,8,5,3,6,4,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,8,5,1,6,4,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[5,7,8,3,6,1,4,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,6,3,1,4,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[7,5,8,6,1,3,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,7,8,1,6,3,4,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,1,3,6,4,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[3,7,8,1,5,6,4,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,8,3,5,6,4,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,3,8,5,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,1,8,5,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[5,7,1,8,3,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,7,1,8,6,3,4,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[7,5,1,8,6,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,8,1,6,3,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,8,5,1,6,3,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,1,3,6,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,5,8,1,3,6,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,1,8,3,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,1,3,8,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,7,1,3,8,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[3,7,1,5,8,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,3,5,8,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,5,3,7,8,6,4,2]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[3,5,1,7,8,6,4,2]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[5,3,1,7,8,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[7,3,1,5,8,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,1,8,5,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,8,1,5,6,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,8,3,1,5,6,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,3,5,6,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,8,3,5,6,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,3,8,5,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,3,5,8,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,1,5,7,8,6,4,2]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[5,7,3,4,6,8,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,3,4,8,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,3,4,8,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,3,4,1,8,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,3,4,1,6,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,7,3,4,6,1,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[7,3,5,6,1,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,7,3,1,4,6,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,7,3,1,4,6,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,7,3,1,4,8,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,3,1,4,8,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,3,7,4,1,2,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,3,7,4,1,2,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,3,7,1,4,2,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,3,7,1,4,2,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[3,7,5,1,2,8,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[7,8,3,5,1,2,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,3,8,5,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,5,8,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,7,5,1,2,6,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,5,1,2,6,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1,4,3,5,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,5,7,3,8,4,1,6]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[5,4,7,8,6,1,3,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[7,5,6,2,8,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,7,2,5,8,3,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[6,2,4,5,1,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,1,4,6,3,2,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[3,5,6,2,4,1,8,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[3,8,6,7,5,4,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,8,3,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[2,5,3,4,8,1,7,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[8,7,1,2,5,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,2,3,4,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,7,6,2,8,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[3,7,8,1,5,4,6,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[7,1,3,4,6,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,3,6,5,7,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,1,4,6,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,8,3,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,7,2,6,3,8,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[2,1,8,4,6,7,3,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,7,8,6,3,1,2,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,8,1,5,6,7,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,4,8,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[2,8,3,6,7,5,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,1,7,6,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,5,8,1,7,6]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[7,4,6,3,2,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,7,3,2,1,8,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[6,4,7,5,2,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,4,8,1,7,3,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,8,7,2,3,1,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,1,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[7,6,8,1,3,5,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,5,2,3,1,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[4,7,2,6,5,1,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[6,4,2,1,8,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,2,1,5,6,8,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,7,2,6,4,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,8,2,5,3,1,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[2,1,7,3,6,8,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,1,5,7,8,4,6,3]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,5,7,8,3,6,1,4]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[6,4,1,5,7,2,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[7,4,8,1,2,5,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,7,8,6,3,5,1]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[6,1,7,4,3,2,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,8,3,4,2,1,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,2,6,1,5,7,8,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[2,4,6,7,3,5,8,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[6,5,8,3,7,4,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,1,4,8,3,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,8,7,5,3,4,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,6,3,1,5,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,2,5,7,6,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,5,7,2,8,6,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[2,5,7,4,8,6,1,3]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[2,6,3,7,5,1,8,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[2,6,4,8,7,5,1,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,3,7,2,8,5,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[3,6,2,5,8,7,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[5,2,8,4,7,6,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,2,4,8,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,2,4,8,7,5,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,4,5,8,7,6,1,3]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[4,2,7,3,8,1,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[2,5,1,4,7,3,8,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[6,1,3,8,7,2,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,1,5,6,2,8,7,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[1,2,4,6,3,8,7,5]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[4,1,5,2,8,7,6,3]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[7,1,4,2,8,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,1,5,3,2,8,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[7,2,3,5,1,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,4,5,1,8,7,6,2]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[1,4,5,2,8,7,6,3]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,6,4,2,8,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,6,3,1,8,7,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[7,4,2,5,1,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,3,6,2,8,1,7,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[4,6,2,7,5,1,8,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[1,5,3,6,2,8,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,5,8,3,2,7,6,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,2,1,7,6,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,6,2,5,1,4,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[5,2,8,4,1,3,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,4,8,7,1,3,6,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,3,8,2,4,7,6,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,5,2,1,7,4,8,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[6,3,1,7,2,8,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[7,5,1,2,8,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,5,2,3,8,7,6,4]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,5,1,2,8,7,6,3]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[6,4,1,2,8,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,3,1,7,2,8,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,2,8,1,3,7,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,7,5,6,8,3,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[8,6,4,7,5,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,4,1,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,6,3,7,5,8,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,3,7,4,5,8,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[7,2,6,3,4,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,3,7,4,6,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,7,5,3,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,7,5,6,3,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,6,4,5,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,8,3,7,4]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[8,6,5,2,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,3,1,4,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,8,5,3,2,1,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,7,6,4,5,1,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[5,7,2,6,4,1,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,1,3,7,5,8,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[4,1,7,3,6,8,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[8,1,6,4,3,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,8,6,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,8,6,3,7,5,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,7,3,6,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,8,4,7,5,6]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[8,1,2,7,4,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,8,4,7,2]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[6,2,8,7,1,4,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,7,2,1,5,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,4,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,3,1,5,6,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,2,7,1,5,6,8]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[4,7,3,8,2,1,5,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[5,2,7,3,1,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[8,3,7,2,1,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,2,8,4,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,4,2,5,8,6,7,3]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[6,5,3,8,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,6,4,5,7,1,3,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,4,6,2,7,1,3,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[7,6,3,1,8,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,2,1,8,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,7,5,8,6,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,1,2,8,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,6,1,4,3,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,3,7,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,5,7,1,3,8,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[5,8,3,1,7,4,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,3,1,7,5,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,7,4,6,5,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,7,6,3,5,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,2,1,7,6,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,7,4,5,6]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,4,1,8,5,7,3,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[5,8,2,1,7,6,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,8,5,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[8,7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,1,8,7,5,6,3,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,1,7,8,4,6,3,5]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[3,5,8,7,2,6,4,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[5,8,2,7,1,6,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,1,6,4,5,8,3,7]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[8,6,3,7,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,5,2,1,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,6,3,7,5,2,8,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[3,5,7,8,2,6,1,4]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[5,6,2,4,1,3,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[7,6,3,8,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,2,3,4,6,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,6,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,3,4,7,5,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,6,8,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,8,3,6,5,1,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,2,3,6,1,5,8,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[4,8,3,7,5,1,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,2,3,4,7,8,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[8,2,3,4,7,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,8,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,2,3,4,6,8,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[4,2,8,5,7,6,1,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,7,6,4,5,1,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[3,8,6,4,5,1,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,5,8,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,8,3,7,5,2,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,7,3,6,5,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,1,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,5,8,6,3,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[5,8,1,7,3,6,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,2,7,8,4,6,3,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,2,8,3,7,6,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,2,7,3,1,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,2,5,7,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,3,8,5,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,2,3,4,7,5,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,2,3,4,8,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,2,3,4,1,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,1,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,2,3,4,8,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,8,3,1,5,7,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,2,3,4,1,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,2,3,4,1,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,2,3,4,8,7,5,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,8,5,3,4,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,8,4,2,3,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,7,4,1,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,7,5,1,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,1,8,4,6,5,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,1,5,4,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,4,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,5,1,7,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,8,5,7,1,6,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,4,7,1,5,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,5,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,6,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,4,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,2,5,1,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,8,5,2,7,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[8,7,1,4,2,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,2,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,5,6,2,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,8,7,1,2,5,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,8,7,1,2,6,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,3,8,5,7,1,6,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,8,7,1,5,6,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,8,7,1,6,2,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,3,8,6,7,5,1,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,8,6,7,5,1,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,1,8,6,2,7,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,7,4,1,2,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,7,5,2,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[5,7,1,8,2,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[2,8,7,1,5,6,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,5,2,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,2,4,6,5,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,6,2,8,4,7,5,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,3,8,5,7,2,6,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,8,3,7,2,5,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,1,3,5,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,8,2,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[7,1,8,2,3,5,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,6,3,7,4,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,6,7,5,1,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,4,2,7,5,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,6,1,7,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,3,4,7,5,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,4,5,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,5,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,6,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,4,1,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,7,2,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,8,2,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,2,8,6,7,1,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,7,4,1,2,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,6,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,3,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,7,1,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,2,1,3,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,3,6,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,2,6,3,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,7,3,6,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,6,2,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,7,6,3,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,7,4,1,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,5,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,5,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,5,6,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,1,6,7,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,6,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,8,6,7,4,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,2,8,6,7,5,3,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,8,3,6,7,5,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,3,6,7,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,5,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,5,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,7,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,6,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,6,7,3,5,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,1,2,7,3,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,6,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,6,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,3,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,2,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,6,7,2,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,8,2,3,6,5,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,3,7,1,2,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,3,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,4,6,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,8,5,7,4,2,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,3,5,7,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,4,5,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,3,5,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,8,3,5,4,7,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,7,5,8,4,6,3,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[8,4,2,7,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,6,3,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,6,2,3,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[3,7,1,8,6,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,1,7,6,4,5,2,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,1,7,5,8,4,2,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[3,1,6,8,7,5,2,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[6,3,8,7,5,2,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,3,5,8,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,6,4,2,8,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,8,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,4,8,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,5,2,3,1,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,6,2,3,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,2,5,8,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,6,5,8,1,3,2,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,7,1,5,3,8,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,7,8,1,3,6,2,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[5,7,1,3,4,6,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,7,1,4,2,3,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,8,1,3,2,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,6,1,3,2,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,4,6,2,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,2,3,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,7,3,1,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,8,3,7,2,5,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,4,6,8,2,3,7,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[5,7,4,2,8,3,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,4,7,2,1,8,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,5,3,4,1,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,8,5,4,1,3,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,4,3,7,1,5,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[7,4,2,6,1,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,2,5,6,1,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,4,2,8,1,5,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,7,8,2,5,1,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,3,5,6,4,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,3,1,5,6,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,2,6,1,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,3,7,2,8,6,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,3,8,2,6,7,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,3,8,2,5,4,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,2,1,5,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,3,1,8,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,3,7,8,2,6,4,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,7,8,5,6,3,2,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[5,3,7,6,8,2,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,7,8,4,6,2,1,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,8,4,3,6,7,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,4,7,2,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,3,8,6,2,7,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,7,5,8,6,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,8,6,7,5,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,3,8,7,2,4,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,3,8,7,2,6,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,3,8,6,7,2,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,3,7,8,6,2,4,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,7,6,4,8,2,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,8,4,6,7,2,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,2,8,1,7,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,2,4,3,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,4,6,2,8,7,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,6,3,8,7,2,4,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[6,7,4,3,1,8,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,7,4,3,6,8,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,3,8,6,2,4,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,5,8,6,7,3,2,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,6,8,5,7,3,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[5,6,8,3,7,2,4,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,4,6,8,2,7,1,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[5,7,8,2,6,4,1,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[3,6,8,5,7,1,4,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,7,4,8,6,2,3,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,6,2,5,7,8,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[5,2,7,4,6,8,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,3,6,7,1,8,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[4,2,5,6,7,1,8,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[8,1,3,6,7,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,5,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,7,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,8,2,7,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,4,1,8,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,3,4,1,5,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,7,5,2,8,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,4,1,8,5,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[5,6,3,1,7,8,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[3,6,4,8,1,5,7,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,5,8,4,2,6,3,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,7,4,1,6,8,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,5,7,1,2,6,4,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[4,5,1,8,2,3,7,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,7,1,8,2,6,3,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[7,5,1,2,3,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,2,6,1,3,4,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[7,8,4,5,1,3,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,7,1,3,2,5,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,7,1,4,3,5,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,8,2,3,1,5,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,4,3,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,4,1,5,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,4,2,6,5,7,3,8]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[5,6,1,4,2,7,3,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[6,7,2,4,1,5,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,7,2,4,3,5,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,7,2,3,1,5,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,7,3,5,4,8,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[2,4,1,6,5,7,3,8]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,5,2,6,4,7,3,8]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[2,5,1,6,4,7,3,8]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[3,6,5,7,4,8,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[5,6,2,4,3,7,1,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[4,5,2,6,1,7,3,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[4,5,1,6,3,7,2,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[4,5,3,6,1,7,2,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[5,6,3,4,1,7,2,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[5,6,1,4,3,7,2,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[5,6,1,3,2,7,4,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[5,6,4,7,1,3,2,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[6,7,4,5,1,3,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,7,5,8,1,3,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[4,5,1,3,2,7,6,8]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[4,6,5,7,1,3,2,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[4,6,1,3,2,7,5,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[1,4,3,6,2,7,5,8]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[3,4,1,6,5,7,2,8]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[4,5,2,3,1,7,6,8]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[4,5,3,7,6,8,1,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[4,6,5,7,3,8,1,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[4,6,5,7,2,3,1,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[3,5,4,6,1,7,2,8]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[3,5,1,6,4,7,2,8]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[1,5,3,6,4,7,2,8]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,5,3,6,2,7,4,8]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[3,5,2,6,1,7,4,8]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[3,5,2,6,4,7,1,8]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[3,4,2,6,1,7,5,8]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[4,6,2,3,1,7,5,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[2,4,3,6,1,7,5,8]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[2,5,3,6,4,7,1,8]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[2,5,3,6,1,7,4,8]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[4,6,2,7,3,5,8,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[3,6,2,7,5,4,8,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[4,6,1,7,3,8,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[2,4,7,1,3,8,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[5,2,6,7,4,3,8,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[3,5,2,7,6,4,8,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[1,5,7,4,3,8,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[2,5,7,3,1,8,6,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,5,7,2,8,3,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[2,5,7,3,1,8,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,5,7,3,4,8,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[5,2,6,7,1,8,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[1,3,7,2,8,5,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,3,1,5,8,4,7,6]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[2,1,5,6,8,4,3,7]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[2,3,1,5,8,6,4,7]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[2,4,7,3,1,8,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,3,7,2,8,5,4,6]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,3,1,6,8,5,4,7]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[4,6,2,7,1,8,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[1,5,4,3,6,8,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,6,4,5,7,8,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[2,5,1,7,8,6,3,4]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,3,6,2,8,7,4,5]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,1,5,6,8,4,7,3]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[2,4,1,7,8,5,6,3]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,3,6,2,8,4,7,5]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,1,5,6,8,7,3,4]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[3,6,5,2,7,8,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[6,2,4,7,5,8,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,5,7,8,4,2,6,3]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[3,7,4,1,8,6,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,4,6,8,5,7,2,1]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[4,2,5,7,3,1,8,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[4,5,6,2,8,7,3,1]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[2,5,6,8,1,7,4,3]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,5,6,1,8,7,3,2]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[4,5,6,3,1,8,7,2]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[4,3,6,2,1,7,5,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[4,6,3,2,1,7,5,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[4,6,3,1,7,5,2,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[4,5,3,7,6,1,8,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[4,5,1,7,3,8,6,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[2,5,7,1,4,3,8,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,3,5,7,6,1,8,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[4,3,6,1,7,5,2,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[4,3,2,6,1,7,5,8]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[5,3,2,1,6,4,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[5,3,1,6,2,7,4,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[5,1,6,3,2,7,4,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[2,6,1,4,7,5,3,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[3,6,1,7,4,2,5,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[4,6,1,7,5,3,2,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[5,1,6,3,7,4,2,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[5,3,6,4,2,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[5,3,2,6,4,1,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[5,2,1,6,3,7,4,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[5,2,6,3,1,7,4,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[4,2,6,3,1,7,8,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[3,6,2,1,7,4,5,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[3,6,2,7,4,1,5,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[3,5,7,2,8,6,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[2,4,7,1,3,6,5,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[2,6,1,3,7,5,4,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[3,6,1,7,5,2,4,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[5,1,6,2,7,4,3,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[5,2,6,4,3,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[5,2,1,6,4,3,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[5,4,2,1,6,3,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[5,4,2,6,3,1,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[5,4,1,6,2,7,3,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[5,1,6,4,2,7,3,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[3,6,1,7,5,4,8,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[2,6,1,5,4,3,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[3,1,6,2,5,4,7,8]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[5,1,6,4,3,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[5,4,1,6,3,2,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[5,4,3,1,6,2,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[7,3,1,6,5,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,2,8,1,5,4,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,7,6,5,8,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[3,8,2,6,5,4,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,5,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,8,6,1,4,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,2,7,6,8,4,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[3,8,7,2,5,4,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,1,6,8,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,2,1,5,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,8,6,5,1,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,3,2,6,7,4,1,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[4,3,7,2,5,6,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[6,7,1,4,3,2,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[3,4,2,6,7,1,5,8]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[3,7,1,6,5,2,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,5,6,2,4,7,1,8]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[3,5,8,7,2,4,6,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,7,8,2,5,4,3,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,7,1,3,8]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[4,7,1,6,3,5,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,5,3,8,7,2,6,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[1,4,5,3,7,8,2,6]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,4,8,2,7,6,3,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,7,3,5,1,8,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[8,7,3,6,1,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,4,6,1,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,4,2,1,7,8,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[4,7,8,3,5,2,1,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,7,6,2,1,8,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,4,6,7,3,5,8,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[8,3,6,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,4,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,4,7,6,5]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,7,4,8,6,5,1,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[8,6,5,1,4,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,7,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,2,8,5,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,6,3,8,2,7,5,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,7,5,3,8,2,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,7,4,1,8,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[8,6,3,2,7,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,1,3,8,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,6,4,3,8,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,2,4,8,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,4,2,8,7,6,1,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[5,1,4,3,2,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[3,7,8,5,2,4,1,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,6,2,4,1,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,6,8,2,5,7,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,7,2,5,8,4,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[5,2,7,8,4,3,1,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,3,1,7,8,4,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[2,7,6,4,1,3,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,1,7,6,3,2,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[8,4,2,7,6,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,7,5,2,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,2,7,5,3,1,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,5,8,2,7,4,6,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,7,2,8,4,6,3,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,7,3,1,8,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[8,4,7,3,1,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,5,7,4,1,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,5,2,1,7,4,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[5,7,4,6,2,1,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,6,4,8,3,7,2,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[6,7,1,8,3,4,2,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,8,3,5,1,4,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,6,2,7,1,8,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[6,7,2,4,3,8,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[2,4,3,8,6,7,1,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,8,2,7,4,5,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,8,3,6,1,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,3,1,8,5,6,4,7]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[3,8,5,6,4,7,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,4,8,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,2,3,1,6,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,7,2,4,3,6,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[4,6,2,7,1,5,3,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[4,7,1,6,2,5,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,7,1,5,3,6,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,6,3,5,1,7,2,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[6,7,3,5,1,4,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[5,6,3,7,1,4,2,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[5,7,1,6,3,4,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,8,5,6,3,4,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,6,4,7,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,6,4,8,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[4,6,5,8,1,7,2,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[3,7,1,4,2,8,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,5,1,4,2,8,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[4,6,5,8,3,7,1,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,6,5,8,2,3,1,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[3,4,2,6,5,8,1,7]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[3,5,4,6,2,8,1,7]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[1,8,3,5,4,7,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,2,7,1,8,5,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[4,7,2,3,1,8,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[2,4,3,8,1,7,5,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,5,3,8,4,7,1,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,6,3,8,1,7,4,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,7,1,8,3,6,4,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,2,8,7,4,6,3,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,7,4,8,6,1,5,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[4,5,1,8,7,6,2,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[1,5,2,8,7,6,3,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,1,2,8,7,6,3,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,1,5,8,7,6,2,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[2,3,6,8,7,4,5,1]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,3,7,8,6,4,5,1]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[4,5,7,8,2,6,3,1]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[4,5,6,8,2,7,3,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[5,2,6,8,3,7,4,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[3,1,6,8,7,4,5,2]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[6,1,4,8,7,2,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,1,8,4,7,3,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,8,3,4,7,1,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,3,5,7,1,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,1,7,8,6,4,5,2]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[5,2,7,8,3,6,4,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,6,7,8,2,5,3,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[7,4,5,2,8,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,8,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,4,5,2,7,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,5,3,7,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,3,8,4,2,7,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,5,3,8,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,4,7,5,8,6,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[3,6,7,4,8,5,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[6,7,4,2,8,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[4,7,5,2,8,6,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[2,7,5,3,8,6,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,6,2,8,3,7,4,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,7,8,3,2,6,4,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,6,8,3,2,7,4,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[3,6,8,4,2,7,5,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,5,8,2,7,3,6,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,8,4,7,2,3,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,6,8,1,3,7,4,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,7,4,8,1,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,7,2,8,3,6,4,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[1,7,4,8,6,2,5,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,4,2,8,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,8,5,3,7,2,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,2,3,7,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,5,3,8,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,2,3,8,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,7,4,5,8,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[6,7,3,4,8,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[3,6,4,7,8,5,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[6,4,2,7,8,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[7,4,2,5,8,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,1,8,3,4,7,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,4,2,5,7,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,5,8,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,5,8,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,3,4,7,8,5,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,1,2,7,4,5,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[2,5,8,3,4,1,6,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,6,2,7,4,3,8,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[4,6,7,3,2,5,8,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[2,6,7,3,8,5,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[2,6,1,8,4,5,3,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,5,7,8,4,3,6,1]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[3,6,8,4,5,7,1,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,6,8,4,7,2,3,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,4,5,7,8,2,6,3]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,5,7,8,6,1,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,5,7,6,8,1,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[3,6,7,4,8,5,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[3,4,5,6,8,7,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,4,5,8,7,2,3,6]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,2,5,8,3,6,4,7]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,4,5,8,6,2,3,7]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[7,8,1,4,6,2,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,6,7,4,8,2,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,4,5,6,8,2,7,3]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,4,5,8,6,2,7,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,2,5,8,3,4,7,6]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,6,7,2,3,5,8,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[7,8,1,2,3,5,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,6,7,2,3,5,4,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,4,5,7,6,2,3,8]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,2,5,7,3,6,4,8]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,2,5,7,3,6,8,4]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,6,8,2,3,5,7,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,6,8,4,5,2,3,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,6,8,4,5,2,7,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,6,8,2,3,4,7,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,6,8,2,3,7,4,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,4,5,7,6,2,8,3]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[7,8,1,4,5,2,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,2,3,4,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,2,3,6,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,6,7,2,3,8,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,2,5,6,3,8,7,4]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[4,2,1,6,5,3,8,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[8,2,4,3,1,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,3,1,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,2,6,3,5,1,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[4,6,2,1,5,8,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[4,6,5,2,1,8,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[2,1,6,4,3,8,7,5]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[4,8,2,1,6,7,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,8,2,1,4,3,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,6,2,4,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,3,1,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,7,2,4,3,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,1,8,4,6,5,3,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,4,8,5,7,3]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[4,6,5,2,8,3,7,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[2,6,4,5,8,3,7,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[6,4,2,8,3,5,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,4,2,6,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,4,8,5,3,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,2,6,3,5,8,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[4,2,6,3,8,7,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[6,2,4,3,8,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,2,4,3,6,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,6,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,4,8,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,2,1,8,7,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,1,8,4,3,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,4,6,5,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,5,2,1,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,5,7,2,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,6,8,7,5,2,1,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[2,1,4,8,6,7,3,5]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,6,8,7,4,5,1,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,4,8,6,7,5,1,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,2,8,6,5,7,1,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,2,6,4,5,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,7,2,1,5,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,5,8,2,1,7,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[2,1,6,8,4,3,7,5]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[6,8,7,4,2,1,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,6,4,7,1,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,2,1,7,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,3,1,4,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,8,3,5,1,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,4,8,3,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,2,8,4,3,5,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,4,2,1,5,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,2,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,3,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,3,8,4,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,3,8,4,2,1,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,1,8,4,3,5,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,7,8,4,3,5,2,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,1,4,8,3,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,8,1,5,6,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,8,4,3,5,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,7,3,1,8,4,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,3,8,4,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,1,4,8,3,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,4,1,3,8,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,6,7,8,4,3,2,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[7,2,1,8,4,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,2,7,1,8,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,2,7,8,4,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,2,7,8,4,3,5,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[2,6,7,4,8,3,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[2,6,7,4,8,3,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[7,8,1,3,6,2,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,2,7,8,6,3,4,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[2,6,7,1,8,5,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[2,6,7,8,5,3,1,4]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[2,6,7,8,5,3,4,1]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[6,2,7,8,4,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,2,1,8,4,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,7,2,8,4,5,6,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,8,1,5,6,2,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[6,3,7,8,1,5,2,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,7,1,2,8,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,6,7,8,4,2,5,3]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[3,1,2,7,6,5,8,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[6,1,2,4,7,3,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,7,5,3,6,4,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,1,2,6,7,4,8,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[4,1,5,7,3,2,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[4,6,1,7,3,2,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[4,6,1,8,3,2,5,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,7,1,8,3,5,2,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,1,7,8,6,2,3,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[1,6,5,7,8,3,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,6,5,8,7,3,4,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[4,1,8,7,6,2,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,1,7,3,5,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,6,3,2,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,3,2,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[6,1,2,3,7,5,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,8,1,5,3,7,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,4,8,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,5,8,3,4,7,6,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[7,8,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,2,3,5,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,1,2,3,5,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,5,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,6,3,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,2,4,3,1,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,2,4,3,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[3,8,1,2,4,5,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,8,6,4,2,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,6,4,3,7,5,8,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[3,1,2,6,7,5,8,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[3,8,1,7,6,4,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,2,4,3,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,7,2,4,3,5,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,6,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,5,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,4,6,8,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[8,7,2,5,3,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,5,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,2,3,5,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,1,2,3,5,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[5,1,2,3,7,6,4,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[5,1,2,3,8,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,5,6,3,4,7,8,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[8,6,5,2,4,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,5,3,1,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,5,2,3,8,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,2,3,7,4,5,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,2,5,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,6,3,1,2,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[4,6,2,3,1,5,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[7,2,3,4,5,8,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,2,3,4,5,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,6,8,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,7,3,2,8,6,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[3,7,4,5,1,8,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,8,2,6,7,4,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,5,6,7,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,4,6,7,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,1,3,4,2,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,2,4,3,1,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,1,7,6,8,5,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[3,7,6,1,8,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,7,2,3,8,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[7,1,3,6,4,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,1,4,8,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,2,3,7,8,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,2,3,8,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,2,3,6,8,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,2,3,5,7,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,3,5,1,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,4,8,3,6,7,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,5,1,8,4,6,7,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,6,1,8,4,5,2,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,6,8,3,5,2,7,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[5,7,8,3,2,4,1,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,8,2,3,5,6,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,8,2,3,1,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,2,7,4,8,3,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[3,7,8,2,1,4,6,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,5,2,8,4,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,2,4,1,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,2,3,4,8,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,7,3,1,4,2,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[3,7,4,1,8,2,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,7,4,8,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[8,3,7,4,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,5,6,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,3,2,4,5,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,1,6,3,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,7,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,8,7,6,4,2]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[7,2,4,8,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,2,8,7,5,6,3,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,8,6,7,5,2,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,4,8,6,5,7,2,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,6,5,4,8,2,3,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,1,6,8,3,4,2,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,2,5,1,7,4,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[5,2,1,8,7,4,3,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,2,6,3,8,1,4,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,2,8,3,4,6,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,2,8,4,3,1,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,8,1,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,1,4,6,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,7,8,5,4,6,3,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,5,8,4,6,3,7,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,3,8,4,1,2,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,4,3,6,2,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,8,3,6,5,2,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,4,7,6,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,4,6,7,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,5,1,7,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,8,2,5,1,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,2,4,3,5,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,6,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,5,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,5,2,4,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,1,8,5,2,7,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,5,1,3,6,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,6,1,5,7,2,8,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[6,3,1,2,8,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,1,8,2,3,7,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,3,8,7,2,1,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,7,3,5,1,4,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,4,7,5,8,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,7,8,4,2,6,3,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,4,7,6,2,8,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,7,4,1,6,8,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,8,4,5,7,1,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,4,6,1,7,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,7,8,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[5,6,7,2,4,8,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[5,6,3,7,4,8,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[5,3,6,7,4,8,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[5,3,2,8,6,7,4,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,4,8,2,6,7,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,6,2,7,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,4,8,5,7,2,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,4,8,5,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,6,8,5,7,2,3,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[5,6,8,2,4,7,3,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,6,3,8,4,7,2,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,6,3,5,8,7,2,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,6,3,2,8,7,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[5,6,3,8,2,7,4,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[3,6,5,8,7,2,4,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,6,8,2,7,4,1]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,3,7,2,8,6,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[5,4,7,2,6,8,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,3,2,7,6,8,4,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[6,7,3,8,5,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,3,2,7,5,4,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,4,7,2,5,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,2,7,5,1,4,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[2,7,8,5,3,6,1,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,3,7,8,4,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[3,5,7,8,4,6,2,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[5,3,7,8,4,6,2,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,7,8,2,4,6,3,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[2,5,8,4,3,7,6,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,6,8,4,7,3,5,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,7,4,8,6,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,6,4,8,7,2,5,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,5,4,8,2,7,6,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,7,5,8,6,2,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,5,7,3,8,6,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[3,5,6,8,4,7,2,1]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[6,3,1,8,7,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,4,8,1,7,6,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,4,1,7,6,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,5,4,1,8,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,5,4,1,7,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,6,3,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,8,4,5,1,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,3,7,5,6,2,4,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,6,7,4,3,5,2,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,8,5,2,3,7,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,5,3,6,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,8,4,3,5,7,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[7,5,8,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,4,1,5,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,1,2,6,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,6,7,4,3,2,8,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,5,2,6,4,7,8,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,5,4,6,2,3,7,8]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[6,2,5,7,1,4,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,5,4,3,8,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,3,6,8,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,7,8,3,6,5,1,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,7,8,5,4,6,3,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,6,5,8,3,4,1,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,5,7,3,4,1,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[6,2,5,7,4,1,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,2,5,8,4,1,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,7,8,4,6,1,3,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,1,2,8,3,7,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,1,2,8,5,4,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,5,7,8,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,5,4,2,6,7,3,8]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[2,6,5,7,3,8,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,6,2,7,5,8,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,3,2,7,8,5,6,4]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,6,2,4,8,7,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[6,5,2,1,8,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,6,5,3,7,8,4,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[6,2,5,3,8,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,2,3,8,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,4,1,2,3,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,1,4,2,3,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[1,5,4,2,6,3,8,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,8,7,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,1,6,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[4,7,3,1,5,6,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[5,8,3,4,1,6,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,7,8,4,5,6,2,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,5,8,4,2,6,7,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,6,3,8,5,2,7,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,3,7,1,6,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[6,2,3,7,5,1,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,7,3,4,8,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,3,4,8,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,2,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,3,7,1,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,1,8,5,3,7,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,4,8,6,3,1,7,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,6,8,2,1,7,5]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[3,4,1,5,8,2,7,6]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[8,1,4,5,3,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,5,2,8,7,6]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[3,4,6,2,1,8,7,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,6,2,1,7,8,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[3,4,6,2,7,8,1,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[8,1,4,6,3,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,3,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,6,2,1,7,4,8]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[8,1,5,6,7,3,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,7,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,8,7,2,5]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[3,5,6,1,8,7,2,4]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[2,1,3,8,6,7,4,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[8,1,3,2,6,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,6,7,1,5,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,4,1,8,6,7,5,3]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,5,8,6,1,7,4,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,6,1,8,7,4,2]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[3,4,1,6,8,7,5,2]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[3,4,6,8,7,1,5,2]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[8,1,4,6,2,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,7,8,4,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[4,5,6,1,7,8,3,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[4,5,6,1,7,3,8,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[3,5,1,6,7,4,8,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[8,1,5,6,7,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,7,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,7,4,2,8]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[4,5,6,1,7,3,2,8]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[6,5,8,7,4,3,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,2,7,8,5,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,1,4,8,7,5,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,6,4,8,7,5,2,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,8,6,2,4,7,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,2,4,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,1,4,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,1,7,8,5,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[7,6,1,2,4,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,1,3,4,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,1,6,3,4,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,4,7,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,4,8,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,1,2,5,4,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,1,5,4,8,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,8,6,3,4,7,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,1,4,7,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,5,4,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,2,7,5,4,8,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[3,2,7,5,4,8,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[2,5,8,4,7,3,1,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,3,7,5,4,8,1,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[6,8,3,2,4,7,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,7,2,5,4,8,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,1,7,5,4,8,2,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[1,3,7,5,4,8,2,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,5,8,4,7,3,2,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,1,8,4,7,3,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,2,4,7,3,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,4,3,7,5,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,7,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,7,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,4,7,3,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,5,4,8,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,6,3,1,4,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,7,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,4,6,8,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[4,1,3,2,7,8,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[1,4,3,2,7,8,5,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[2,4,3,1,7,8,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[2,7,3,5,4,8,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,8,5,4,7,3,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,6,8,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[8,2,5,4,7,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,5,4,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,2,1,4,7,8,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[8,1,7,6,4,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,5,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,4,3,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,2,5,1,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,6,5,2,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,3,6,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,2,1,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,8,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,4,2,8,1,3,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,8,2,6,4,1,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,2,5,1,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,3,5,2,1,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[2,5,8,6,3,1,4,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,3,5,8,1,4,7,6]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,3,6,8,1,5,7,4]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[6,3,8,5,2,7,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,7,5,2,1,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[2,5,7,6,3,1,4,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[2,8,7,6,3,1,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,8,7,6,3,1,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,4,8,1,6,5,7,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,8,7,3,6,1,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,2,1,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,4,2,5,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,6,8,1,4,7,5]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,7,8,6,3,1,4,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,3,8,5,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,3,6,1,8,4,7,5]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,8,6,3,1,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,5,2,1,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,1,3,7,5,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,5,8,1,7,3,6,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,8,1,5,7,3,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,6,1,4,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,4,7,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,8,1,5,7,3,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,7,1,5,8,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,1,6,3,8,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[4,7,6,1,8,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[3,7,5,8,1,2,6,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[7,3,6,1,2,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,4,8,1,6,5,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,6,1,8,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,5,8,6,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,8,4,5,1,7,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,6,8,5,1,7,2,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[5,1,7,6,2,3,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,1,7,6,2,8,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,1,8,7,6,2,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,5,1,7,6,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,2,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,8,4,7,5,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,6,1,8,7,5,2,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[8,4,6,1,7,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,7,2,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,5,1,8,7,2,3,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,4,8,7,1,2,5,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[5,8,4,1,7,2,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,6,4,7,1,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,1,2,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,6,8,3,7,1,4,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,4,7,1,2,8,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,5,1,2,7,3,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,5,1,8,2,7,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,6,5,1,2,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,7,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,7,2,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,5,1,7,2,8,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,5,1,7,2,3,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,7,4,1,8,2,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,6,8,7,4,1,2,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,8,5,7,4,1,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,3,8,1,5,2,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,1,7,5,3,6,2,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[1,8,4,2,3,6,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,8,3,4,6,7,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,1,7,2,3,6,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,6,2,1,5,7,8,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[4,5,2,3,1,7,8,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[3,2,6,7,4,1,8,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[5,6,2,7,1,4,8,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[6,2,3,8,1,7,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,6,8,3,4,7,1,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,6,2,7,5,1,3,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[2,6,3,1,8,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,4,3,7,8,1,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[5,3,2,7,4,8,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,1,2,7,6,8,4,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[2,6,3,1,8,7,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[3,5,6,4,7,8,1,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[5,3,6,4,2,8,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[5,4,2,3,7,8,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[4,1,8,2,5,7,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,1,8,4,7,2,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[6,2,3,8,4,1,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,6,4,1,5,3,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[3,2,7,6,4,1,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[2,5,4,1,7,6,8,3]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[6,2,1,4,7,8,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[2,6,5,1,7,8,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[4,7,5,2,1,6,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,2,3,7,8,1,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[5,8,3,1,7,2,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,3,1,5,2,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,2,7,1,6,3,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[5,1,7,4,2,6,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[6,8,4,2,1,5,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,2,1,7,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,2,1,4,7,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,3,2,5,1,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,3,1,5,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,2,1,5,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,3,2,1,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,1,7,3,2,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,2,1,8,3,6,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,3,8,1,6,2,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,4,7,2,1,6,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,2,1,7,3,4,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[6,4,3,1,7,5,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[5,3,1,7,2,6,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[3,2,1,7,6,4,8,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[4,2,1,6,5,8,3,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[4,2,1,8,5,7,3,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[7,4,3,1,8,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,2,1,8,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,2,1,7,4,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,4,2,1,7,5,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[7,5,2,1,8,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,1,8,4,2,7,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,1,8,3,7,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,2,1,7,3,6,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,3,2,7,6,1,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,3,2,8,6,1,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,3,2,8,7,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,2,8,1,7,3,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,7,2,1,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,1,5,8,4,7,3,6]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[4,3,2,5,8,1,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[4,3,2,5,7,1,6,8]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[4,3,1,6,2,7,5,8]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[4,3,1,7,2,8,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[5,4,1,7,2,8,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[6,5,3,1,7,8,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,4,2,1,7,8,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,4,2,1,6,7,3,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[5,3,2,1,6,7,4,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[6,4,2,1,7,8,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,3,2,6,8,1,7,4]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[3,2,1,4,8,7,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[3,2,1,4,6,8,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[4,3,2,6,1,7,8,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[5,3,2,1,6,7,8,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[8,6,1,4,5,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,5,7,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,8,3,7,4,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,2,8,5,4,7,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,8,6,3,7,4,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,5,7,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,8,4,3,6,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,2,7,3,6,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,4,2,8,3,6,1,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,5,3,8,4,7,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,2,8,4,3,7,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,2,8,3,7,4,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,4,2,7,3,1,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[6,4,3,7,1,2,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,4,3,8,1,2,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,6,3,8,4,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,8,5,1,6,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,4,3,1,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,3,8,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,4,2,7,3,1,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[7,6,4,8,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,8,1,2,5,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,3,1,7,8,4,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,3,2,7,8,4,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,4,1,6,3,8,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[6,5,1,7,8,2,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,3,1,7,8,4,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,4,1,7,3,8,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[6,3,2,7,8,4,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,1,5,4,3,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,7,6,1,3,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,5,7,3,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,7,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,5,3,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,1,3,5,2,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,1,3,7,4,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,7,5,2,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,7,1,8,5,3,4,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[2,7,6,4,8,3,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,5,2,7,1,4,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,4,6,1,3,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,2,1,3,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,4,7,6,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,6,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,4,7,5,6,1,8,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[2,4,7,5,6,3,8,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[5,4,1,7,6,2,8,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[3,5,6,7,1,4,8,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[2,7,6,1,3,4,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,7,2,1,6,3,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[4,7,2,5,6,3,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[8,6,2,5,7,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,3,8,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,8,7,1,3,2,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,6,5,7,1,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,3,2,6,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,8,5,6,2,4,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,5,6,2,4,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,3,2,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,4,5,2,8,6,7,3]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[2,3,1,7,8,6,4,5]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[3,5,7,6,2,8,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[4,5,6,1,2,8,7,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[5,4,1,2,8,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[8,4,5,2,1,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,6,8,4,7,5]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[5,1,3,2,7,8,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[1,5,4,2,7,8,3,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,6,7,8,3,1,5,2]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[7,6,2,8,4,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,2,8,6,3,4,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,6,8,4,3,2,7,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,3,8,1,7,2,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,6,7,8,4,2,1,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[6,5,1,8,4,3,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,8,4,2,1,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,5,8,3,1,6,7,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,8,1,2,6,7,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,2,8,1,5,6,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,5,8,3,2,6,7,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,3,8,6,2,4,7,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,7,8,4,6,1,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[5,1,8,3,4,6,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,8,7,2,1,6,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,6,3,4,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,4,2,1,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,5,8,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[8,4,5,2,6,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,3,6,1,7]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,5,8,1,2,6,4,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[8,6,1,3,5,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,6,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,1,3,4,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,6,1,3,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,3,4,5,2,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,7,4,3,6,1,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[2,6,4,3,7,8,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[7,4,1,8,3,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,2,1,7,8,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[7,6,3,1,5,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,4,6,5,1,7,8,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,4,7,5,6,8,2,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,4,7,6,5,8,2,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,7,5,2,4,6,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[5,6,1,7,4,2,8,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[3,7,4,8,1,2,6,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,5,7,8,1,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[3,6,5,7,1,8,4,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[6,4,7,8,2,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,7,3,8,4,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[2,7,8,3,4,6,1,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,5,8,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,7,5,8,3,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[3,6,7,4,8,1,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[5,7,3,1,6,8,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[2,7,3,1,8,6,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,8,4,3,1,5,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,2,3,5,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,6,8,1,2,4,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,8,5,1,3,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,8,5,4,6,1,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,5,2,7,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,1,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,3,5,2,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[5,7,2,3,6,8,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[8,5,3,2,7,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,5,8,1,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[3,4,5,7,6,1,8,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[2,6,4,5,7,8,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[3,8,5,1,6,2,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,3,6,8,7,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[5,4,6,1,3,7,8,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[6,3,5,7,1,4,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,3,4,6,8,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,2,8,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,7,6,4,1,8,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,8,4,1,5,6,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,6,7,4,2,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[5,8,1,6,7,3,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,7,2,5,1,8,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,8,2,1,6,7,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,5,2,8,6,3,7,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,6,1,2,5,8,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,4,5,8,2,3,7,6]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,2,6,4,5,8,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,5,2,4,6,8,3,7]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[3,6,1,5,8,2,4,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,5,1,4,8,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,2,6,1,4,8,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[2,5,1,8,4,7,3,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,7,1,4,3,6,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,3,7,5,8,2,4,6]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[8,2,1,5,7,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,8,1,3,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,4,1,3,8,6,7,5]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[8,4,3,7,1,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,3,5,8,2,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,8,4,2,6,7,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,8,7,2,4,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[7,2,1,6,8,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,1,7,6,8,2,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[4,1,7,2,6,8,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[5,1,7,2,3,6,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[7,2,1,6,3,5,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,6,1,7,3,5,8,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[7,1,2,5,3,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,4,1,2,7,8,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[8,1,3,2,4,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,4,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,8,3,4,7,2,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,8,1,2,7,4,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,6,8,1,2,4,7,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[4,1,3,8,7,2,6,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,3,7,4,8,2,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,4,6,8,2,3,7,5]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,8,1,7,2,4,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,6,8,1,7,3,4,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,1,5,8,2,3,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,8,3,2,7,5,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,7,2,8,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,7,3,8,1,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[8,4,1,7,3,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,6,1,5,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[6,2,3,8,7,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,8,2,4,3,7,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,7,3,5,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,7,2,4,1,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,8,2,4,1,5,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[6,5,1,4,2,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,6,1,7,2,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,2,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,1,6,2,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[8,3,4,7,1,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,1,8,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,8,5,2,7,1,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,7,5,3,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,8,7,3,6,4,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,6,5,8,2,4,7,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,1,8,7,3,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,5,2,7,4,3,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[4,6,5,2,7,3,8,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[6,2,7,1,8,3,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[2,7,5,4,8,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[8,7,5,1,2,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,7,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,2,3,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,8,1,3,2,7,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,4,7,5,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,8,7,4,5,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,1,4,8,5,2,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,5,7,4,6,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,8,2,3,5,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[8,7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,3,5,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,8,3,2,4,6,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,2,6,5,3,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,6,5,2,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,1,8,6,4,3,7,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,7,6,5,3,8,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[2,7,6,1,3,5,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[7,2,5,4,6,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,7,6,1,2,5,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[2,4,1,7,6,8,5,3]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,4,1,7,8,5,6,2]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[7,5,4,3,1,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,5,6,2,7,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,6,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,4,1,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,1,3,6,7,5,8,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[1,7,5,3,8,2,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,2,4,5,8,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,2,5,3,1,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,8,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,6,4,7,8,3,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[2,6,4,7,8,3,1,5]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,2,6,4,7,8,3,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[2,7,4,5,8,1,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,5,3,1,8,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,4,7,8,3,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[3,6,4,7,8,1,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[4,3,6,7,1,8,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[4,3,6,7,1,8,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[3,6,4,7,8,1,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[2,3,6,4,1,7,8,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[4,7,2,1,5,3,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,7,4,5,2,1,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,3,6,4,7,2,8,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[3,6,4,7,2,8,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[5,1,3,4,2,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[5,4,2,1,3,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[6,1,7,3,8,2,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,6,7,3,8,2,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[6,1,4,7,8,5,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,3,2,1,7,8,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,2,7,3,1,8,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,2,4,7,8,1,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[2,6,7,3,1,8,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[8,6,5,1,3,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,8,3,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[3,8,4,7,1,2,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,1,2,5,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,6,1,5,3,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,4,1,3,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,3,6,4,5,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,7,4,2,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,3,8,7,1,6,4,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,3,7,8,1,6,2,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[3,5,8,7,4,1,2,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[7,3,8,4,1,2,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,8,1,2,7,3,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,8,1,2,7,4,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,6,8,4,1,3,7,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[8,5,4,7,1,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,3,6,4,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,4,8,7,5,6,1,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,4,8,5,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,8,7,5,1,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,8,5,2,4,6,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,8,4,6,2,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[6,3,8,7,2,1,4,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,3,7,8,5,6,1,4]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[3,7,6,8,5,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,6,7,8,5,1,3,4]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[2,4,7,8,1,6,3,5]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[5,4,7,8,2,6,3,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[2,8,3,4,1,5,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,3,4,1,2,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,7,1,5,2,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,3,2,7,6,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,5,3,1,8,6,7,4]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,5,3,2,8,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[3,5,8,6,1,4,7,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,8,5,6,1,4,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,1,5,2,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,3,7,6,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,6,8,5,3,2,7,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[2,6,4,8,5,1,7,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[7,6,4,8,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,4,8,6,5,2,7,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,7,5,6,2,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[7,5,3,2,8,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,5,1,3,8,6,7,4]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,5,1,2,8,6,7,3]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[5,4,8,1,3,6,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,3,5,4,1,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,5,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,1,5,7,2,4,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,4,5,1,2,3,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,3,1,2,8,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,4,7,6,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,5,7,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,4,5,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,4,1,6,3,5,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,5,7,6,4,1,8,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[4,7,5,2,1,3,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[5,7,2,3,6,4,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[8,6,2,3,7,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,4,8,3,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[1,7,2,4,8,6,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,6,1,5,4,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,7,3,2,1,8,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,1,7,2,5,8,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[4,8,7,6,1,2,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,8,6,1,3,2,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,8,6,7,4,1,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,4,2,3,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,8,3,1,6,5,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,2,5,7,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,5,4,2,7,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,3,1,2,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,6,8,7,3,1,5,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[6,5,3,7,8,4,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[4,1,3,8,7,5,6,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[6,2,7,4,8,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[8,4,5,2,1,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,6,8,1,7,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[7,1,5,6,3,8,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,1,2,4,7,8,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[3,5,4,2,8,1,6,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[5,1,3,8,4,2,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,2,8,7,3,5,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,1,8,4,3,6,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,6,8,7,4,1,2,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,6,8,1,7,3,2,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[3,1,6,8,7,4,2,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[7,4,6,8,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,8,4,3,1,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,5,8,3,6,7,4,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[8,5,1,3,7,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,3,7,4,2,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,8,2,7,1,5,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,3,6,4,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,2,3,4,7,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,5,8,7,4,2,6,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[7,5,1,8,4,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,6,8,5,2,7,4,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[2,1,6,5,4,8,3,7]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[2,1,7,8,4,6,5,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[2,1,7,4,3,5,8,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[3,5,7,8,4,6,1,2]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[7,5,2,8,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,6,2,3,5,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,2,4,3,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,6,3,8,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,2,7,1,3,5,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,1,8,2,3,5,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,4,1,6,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,3,1,7,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,6,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,8,5,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,3,8,7,1,6,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,7,1,8,5,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[5,3,2,4,7,8,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[5,3,4,2,8,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,2,4,3,6,8,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[3,8,6,5,4,1,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,6,3,8,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,8,5,7,2,3,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,5,8,3,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[3,8,5,7,1,4,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,7,3,4,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,2,5,4,3,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,2,4,5,3,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[5,7,2,8,3,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,1,3,6,4,2,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[5,1,8,7,4,6,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,8,3,7,5,4,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,1,3,4,7,5,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,3,2,1,4,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,2,3,1,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,2,1,4,8,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,2,8,3,5,7,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,2,1,3,6,4,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[7,1,8,3,5,4,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,2,4,8,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,3,2,4,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,2,1,3,4,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,7,3,5,4,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,5,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,6,4,3,2,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[8,3,7,1,4,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,4,7,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,5,8,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,3,8,7,5,2,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,7,2,1,5,8,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[7,6,8,1,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,4,8,7,6,1,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,6,1,8,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,8,1,7,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,7,4,1,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,6,4,8,3,2,5,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,8,3,5,6,2,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,8,5,6,2,3,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,2,8,5,3,7,4,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,4,8,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,7,2,5,6,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,4,7,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,1,2,3,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[1,7,4,2,5,3,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,7,4,2,1,3,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,4,3,8,5,7,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,4,3,6,2,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,5,3,4,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,3,7,4,5,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,3,1,5,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,8,4,2,3,1,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,7,5,2,4,1,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[7,1,3,2,8,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,1,7,4,8,3,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[5,2,8,6,1,3,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,8,3,1,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,8,2,3,1,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,7,3,1,5,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[8,3,7,2,1,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,4,7,1,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,5,7,4,1,8,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[7,6,4,5,1,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,6,4,1,3,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,1,8,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,4,1,2,8,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,8,1,3,5,7,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,8,4,1,3,6,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,5,8,1,3,7,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,3,6,1,8,2,4,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[4,7,3,1,8,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[8,3,1,7,2,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,4,7,3,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,8,5,4,7,6,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,1,5,8,3,7,6,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,1,5,3,8,7,6,2]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[4,5,1,8,2,7,6,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,8,5,3,1,7,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,8,1,7,6,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,5,2,1,8,7,6,3]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[5,6,2,7,8,1,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[4,6,2,8,7,1,5,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,8,6,3,7,1,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,3,7,5,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,6,8,2,7,5,1,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,2,8,7,5,1,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[5,6,2,7,4,1,8,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[5,6,7,2,3,1,8,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[5,6,7,2,8,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[5,6,7,2,1,8,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[5,6,7,2,1,3,8,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[5,6,1,7,8,2,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[5,6,1,7,2,4,8,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[5,1,6,7,8,3,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[4,1,6,8,7,3,5,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[3,1,8,6,7,5,4,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,1,6,8,7,5,3,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[5,1,6,7,4,8,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[5,6,1,7,8,4,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[4,6,8,1,7,5,2,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,8,6,1,7,5,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,8,3,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[5,6,7,1,3,8,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[5,6,7,1,3,2,8,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[5,6,7,3,1,2,8,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[5,6,7,3,8,1,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[5,6,8,7,4,2,1,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,6,7,3,8,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[7,4,6,2,3,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,4,8,6,3,2,5,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[7,4,1,6,3,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,3,1,5,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,2,5,7,3,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[4,2,5,7,6,3,1,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[7,4,5,6,1,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,1,5,8,6,3,2,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[3,2,7,6,1,8,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[4,7,5,1,6,8,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[8,6,5,1,2,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,1,4,8,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[8,5,4,1,3,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,6,8,7,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[5,4,8,3,7,1,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,7,1,8,2,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[6,4,1,8,5,3,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,4,6,1,3,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,4,7,8,1,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[5,2,4,3,7,8,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[8,1,6,7,2,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,6,5,8,2,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[1,2,7,5,6,8,3,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[6,1,4,7,2,8,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[3,2,1,7,6,8,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[3,2,8,6,4,7,1,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,8,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,8,6,5,3,7,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,5,3,6,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,2,7,6,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,1,8,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,5,3,6,8,1,7,2]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[3,5,2,6,1,8,7,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[1,6,3,5,7,2,8,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,5,4,6,7,8,2,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[8,4,6,5,7,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,2,6,8,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,4,2,6,8,7,1,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[6,5,1,4,3,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[3,6,4,5,2,1,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[7,5,4,2,3,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,8,1,3,5,6,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,1,5,6,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,7,8,3,5,6,2,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,5,7,8,3,4,6,2]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,3,7,8,2,5,6,4]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[3,1,7,8,5,2,6,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,3,7,5,8,2,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[3,1,7,5,8,2,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[3,5,7,1,8,4,6,2]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[3,5,7,8,1,4,6,2]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[5,3,7,8,4,6,1,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,3,7,1,8,4,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[1,5,3,7,8,4,2,6]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[5,1,3,7,8,4,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[3,6,2,1,4,5,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[4,6,2,5,1,3,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[6,4,2,5,1,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,6,1,7,3,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,7,3,4,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[6,8,2,7,3,1,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,3,7,1,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,6,2,7,4,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,1,7,3,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,2,3,8,1,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[5,2,8,3,7,1,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,8,4,6,1,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,1,5,8,4,3,6,7]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[5,8,3,2,7,1,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,1,3,8,2,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,5,8,2,7,1,4,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,2,6,1,3,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[2,6,8,3,7,1,4,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,1,8,3,7,2,4,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,8,4,6,2,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,4,1,6,2,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,5,8,1,6,2,3,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,4,8,1,6,2,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,8,5,1,6,2,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,4,8,3,6,7]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[2,4,3,8,1,5,6,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,8,4,2,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,8,4,2,1,5,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,8,4,1,5,6,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,4,2,8,1,5,6,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,8,5,2,7,1,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,2,6,1,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,8,5,3,6,7]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[3,2,8,4,1,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,8,4,3,1,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,6,2,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[5,7,4,3,8,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,4,3,8,2,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[3,8,4,2,6,7,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,1,6,7,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,5,2,8,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[5,6,4,3,2,8,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[2,6,7,5,3,8,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[6,7,4,8,2,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[2,1,6,7,5,3,8,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[3,8,4,2,1,6,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,4,3,8,2,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,7,4,8,1,2,5,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,5,8,1,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,4,8,3,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[3,4,8,1,2,5,7,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[6,1,3,4,8,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,2,3,4,8,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,4,8,2,1,5,7,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[6,7,5,8,2,4,3,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,5,8,3,1,4,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[3,4,8,1,5,7,6,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[2,5,7,6,1,4,8,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[6,7,4,8,2,3,5,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,4,8,1,3,5,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[2,6,7,5,1,3,8,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[6,3,1,4,8,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,7,4,8,1,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,5,8,4,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,4,8,2,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,4,8,1,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,5,6,3,4,8,2,7]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,4,3,6,5,8,2,7]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[8,1,3,4,7,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,3,4,8,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,7,8,2,3,5,4,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[5,8,6,2,3,7,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,8,3,4,7,5,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,4,7,6,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,7,5,2,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,6,7,2,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,8,4,6,5,7]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[8,2,1,7,4,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,5,4,6,7]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[8,3,1,5,7,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,7,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,8,7,4,2,3]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[8,4,5,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,7,6,2,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,5,7,3,6,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,6,5,7,2,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,7,2,8,5,3,4,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,2,7,8,6,3,4,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,2,8,6,7,3,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,2,8,7,5,4,6,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,8,7,5,6,2,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,1,8,6,7,5,2,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,1,7,8,6,4,2,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[6,7,1,8,5,4,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,8,3,2,6,1,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,4,8,2,6,1,7,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[7,8,4,1,5,6,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,4,5,6,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,2,6,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,1,4,6,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,5,1,6,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,3,8,4,1,6,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,2,4,8,1,5,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,4,8,5,1,6,7,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,5,8,1,4,6,7,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,8,2,6,3,7,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[5,3,8,1,4,6,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,2,6,8,1,5,3,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[7,4,2,8,1,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,1,7,5,8,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,2,1,8,4,5,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,2,7,8,5,3,4,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[6,3,7,8,5,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,1,5,7,8,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,7,5,6,8,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,1,8,4,5,6,7,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,8,6,5,3,7]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,4,1,8,6,5,3,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[4,2,1,8,6,5,3,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,2,7,8,5,1,4,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[2,3,7,8,5,1,4,6]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,7,3,8,5,1,4,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,6,2,8,5,1,4,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,1,2,8,7,5,3,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,4,2,8,7,5,3,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[7,3,6,8,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,1,8,5,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,2,6,8,4,5,3,7]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[7,1,6,5,8,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,7,1,8,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,7,6,1,8,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,7,1,5,8,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,3,8,5,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,1,2,8,4,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,1,5,8,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,6,1,8,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,6,5,3,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,8,7,5,3,2,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,4,2,5,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,4,2,5,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,4,2,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,6,5,4,7,1,3,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[7,1,5,3,6,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,3,7,1,6,4,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,3,6,4,2,7,1,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[1,5,3,8,7,4,2,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[7,4,2,8,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,3,6,1,8,7,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[6,1,5,3,8,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,8,7,5,4,6,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,1,8,7,5,4,6]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[5,3,8,7,4,2,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,4,2,1,8,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,6,3,5,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,5,7,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,8,5,2,1,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,6,3,7,4,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,7,5,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,8,6,3,7,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,3,7,4,1,8,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[8,5,2,6,3,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,7,4,2,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,6,3,7,4,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,2,4,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,3,2,4,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,8,6,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,1,8,7,5,3,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,3,2,8,7,6,1,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[2,4,5,1,3,8,7,6]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[7,5,8,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,7,5,8,6,3,2,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,4,2,5,8,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,6,3,1,7,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,2,5,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,7,4,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,1,8,7,5,3,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,8,6,4,1,3,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,8,6,3,2,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[7,4,2,8,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,3,1,8,5,2,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,5,2,6,3,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,8,5,2,7,4,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,5,2,7,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,1,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,3,1,7,4,8,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[8,6,3,1,5,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,5,8,6,3,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[2,3,1,7,5,8,6,4]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[7,4,8,5,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,5,2,1,7,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,6,3,8,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,6,5,2,1,4,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[3,5,6,2,1,4,8,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[3,5,7,8,1,4,2,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[4,1,8,5,7,3,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,7,5,8,3,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[2,1,5,8,7,4,3,6]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,1,5,7,8,4,3,6]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[5,1,7,4,8,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[4,7,2,8,3,6,1,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,6,2,7,3,1,8,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[3,7,8,2,4,1,6,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,8,7,2,4,1,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,2,4,1,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,8,4,1,7,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,3,4,8,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,3,4,8,1,7,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,3,4,8,1,2,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,3,5,8,1,2,7,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[1,8,5,4,2,3,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,8,1,2,7,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[4,5,3,8,1,2,7,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[6,4,3,8,1,7,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,4,3,8,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,3,8,7,1,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,6,3,8,7,1,2,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,6,3,8,1,7,2,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[2,6,8,4,1,7,3,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,8,7,4,2,6,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,8,6,1,2,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,7,5,8,6,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,8,5,6,1,3,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,8,7,5,6,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,8,5,7,1,3,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,3,6,8,7,1,2,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,3,5,8,7,1,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,2,8,5,6,1,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,2,8,6,7,1,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,8,3,2,7,6,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,8,7,6,1,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,2,8,7,5,1,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,4,7,8,1,6,2,5]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,8,5,7,6,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,8,7,6,1,3,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[7,4,6,5,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,6,7,8,5,1,2,4]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[2,6,8,7,5,1,3,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,8,6,7,5,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,8,6,5,1,3,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[5,7,6,4,8,1,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,3,8,7,5,1,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,8,7,4,1,3,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,8,7,1,3,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,8,6,1,3,2,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,7,6,8,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[2,8,7,1,4,5,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,1,8,7,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[5,1,6,3,2,8,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[4,6,1,8,7,3,2,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[8,7,2,3,5,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,4,8,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[4,3,5,2,8,7,1,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[3,4,2,8,6,1,5,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,7,6,8,1,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[8,1,4,2,3,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,1,8,6,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[2,8,6,1,7,3,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,5,8,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,5,1,6,8,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,6,5,8,1,4,7,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[8,1,5,6,4,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,4,1,8,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[1,7,4,6,8,2,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,5,8,2,6,3,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,1,6,5,4,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[7,3,2,6,1,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,7,2,3,1,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,3,1,8,4,6,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,8,1,6,7,4,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,3,6,8,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,8,4,6,1,5,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,1,6,3,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,8,5,2,1,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[3,1,7,4,8,5,2,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[7,4,1,6,3,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,8,6,2,7,4,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,1,4,5,2,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,4,8,5,3,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,1,2,4,6,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,7,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,8,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,6,2,4,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,5,1,8,6,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,7,3,2,8,5,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[8,4,5,7,6,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,8,4,6,1,7,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,5,2,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[4,2,7,6,1,5,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[8,3,1,4,5,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,6,8,4,7,2]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[6,1,5,7,3,8,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,8,4,7,3,2,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,2,6,5,8,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,3,2,5,1,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,3,7,4,1,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[8,1,5,6,4,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,1,6,4,7,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[7,4,1,8,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,3,7,4,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,8,3,1,7,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[3,6,5,8,4,1,7,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[7,3,6,1,8,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,2,7,3,4,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,2,5,6,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,7,3,1,6,4,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[6,1,3,2,4,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,4,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,1,5,2,8,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[8,7,2,5,4,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,3,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,7,1,4,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,1,8,6,2,4,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,1,6,2,7,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,2,8,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,4,1,7,2,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[7,2,4,3,5,1,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,1,7,2,3,8,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[8,2,3,5,1,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,1,4,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,1,8,2,7,5,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,8,1,6,5,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,6,4,3,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,1,7,4,3,8,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,3,1,7,4,8,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[7,4,8,2,1,5,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,2,4,1,6,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,1,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,3,2,8,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[4,7,2,1,6,3,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[6,2,1,5,3,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,3,1,6,2,8,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[6,1,5,2,8,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,4,3,8,1,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,8,1,5,3,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,5,3,2,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,3,2,8,4,1,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,3,4,2,8,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,6,3,4,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,5,1,3,7,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,5,2,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,1,3,7,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,6,1,7,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,3,8,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[3,6,7,1,5,2,8,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[7,1,3,8,4,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,6,2,7,1,3,8,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[5,6,2,8,1,3,7,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[6,1,8,3,7,5,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,4,2,1,5,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,4,1,5,8,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,2,6,4,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,2,7,3,8,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,1,8,3,7,4,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,4,8,3,1,5,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,2,1,7,4,8,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[6,1,8,4,5,2,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,1,6,4,5,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,5,2,7,1,6,8,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[4,5,7,3,1,6,8,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[4,5,7,2,8,6,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[3,5,1,7,2,6,8,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[4,5,7,2,8,1,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[4,6,7,2,1,5,8,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[4,6,7,1,3,8,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[3,6,1,5,7,8,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[4,6,7,1,5,8,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[6,1,3,7,4,8,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[3,2,1,7,4,8,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[4,1,5,2,7,6,3,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[2,5,1,3,7,6,4,8]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[2,5,1,4,3,8,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[3,7,2,1,5,8,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,7,1,4,8,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[3,7,4,2,1,8,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[7,2,5,3,1,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,1,4,2,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,4,1,3,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,3,2,1,7,6,4,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[6,3,2,8,1,5,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,4,3,2,8,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,2,4,8,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,6,4,8,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,7,5,3,8,1,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,8,5,3,6,4,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,2,3,7,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,2,7,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,7,1,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,1,5,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,5,7,4,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,7,1,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,6,1,4,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,8,4,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,4,8,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,8,1,4,2,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,4,1,3,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,4,8,3,2,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,3,7,2,1,6,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[2,5,8,1,4,3,7,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,6,8,2,1,5,7,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,8,1,3,6,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,7,1,4,8,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[2,7,4,1,8,3,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,5,1,8,4,2,7,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[4,1,5,7,3,6,2,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[4,2,5,8,3,1,7,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[6,1,2,7,8,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,3,1,8,6,4,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,1,8,4,7,5,2,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,2,8,7,3,5,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,1,7,6,2,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,8,1,4,7,5,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,3,8,1,6,4,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,7,8,1,5,3,2,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[7,1,8,6,2,5,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,8,7,1,3,6,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,7,2,1,6,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,1,6,3,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,5,4,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[4,8,7,6,1,3,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,2,6,1,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,1,7,5,2,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,3,8,6,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,7,8,4,3,1,2,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,8,6,4,3,2,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,7,3,6,4,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,5,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,3,7,5,4,2,8,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[6,1,3,5,4,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,1,2,5,4,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[5,1,6,3,4,7,8,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[5,2,6,3,4,7,1,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[3,4,7,5,8,6,1,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[2,4,7,1,5,3,8,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[2,3,6,7,4,8,1,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,3,6,7,4,8,5,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[2,7,6,5,3,1,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,2,6,1,4,7,8,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[4,7,6,5,2,1,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[5,3,6,2,4,1,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[5,7,4,2,1,3,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,3,1,5,4,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,3,6,1,4,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[1,7,4,2,6,3,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,7,4,1,2,3,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,4,1,2,5,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[4,7,6,3,8,5,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[3,7,6,5,2,8,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,6,5,1,2,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[4,7,2,6,1,3,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[2,7,1,6,8,3,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,6,5,8,1,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,2,8,7,6,4,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,2,7,6,1,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,6,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,3,8,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[4,5,3,2,7,8,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[6,5,7,3,8,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,8,7,2,4,3,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,2,7,4,5,8,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[6,8,1,5,2,4,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,3,4,6,1,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,5,8,1,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[6,3,4,7,8,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,3,7,4,8,6,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[8,3,6,4,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,4,8,6,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[3,7,8,5,4,1,2,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[5,4,3,1,7,8,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[5,7,6,2,8,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,1,7,5,8,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,5,6,4,1,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,5,6,8,4,7,3,2]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,1,3,7,6,5,8,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[3,4,1,7,5,8,6,2]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[8,5,7,4,3,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,7,2,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,2,4,1,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,6,2,1,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,1,7,4,2,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,3,5,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,1,6,7,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,3,1,5,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,1,2,7,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,2,3,6,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[6,3,2,1,8,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,3,7,4,1,8,5,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[6,4,1,3,2,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[2,7,8,5,1,3,6,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,2,5,6,7,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,4,7,6,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,5,8,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[4,8,7,6,2,3,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,8,1,5,3,2,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,5,7,3,8,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[8,1,4,7,2,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,6,1,5,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,3,4,5,7,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,6,8,3,1,5,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[3,7,6,2,4,5,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[2,3,6,5,8,1,4,7]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,3,5,8,6,1,4,7]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[4,2,3,8,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[6,4,1,2,8,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,2,3,7,4,6,8,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[3,2,7,1,4,5,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[2,1,5,3,8,7,4,6]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[5,8,3,2,4,1,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,2,7,1,8,3,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,1,8,2,7,3,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,2,7,5,3,8,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[3,2,7,1,4,8,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[1,2,3,7,6,8,4,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,2,3,6,8,7,4,5]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,3,7,8,4,6,5]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,3,6,8,4,7,5]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,3,7,8,6,4,5]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[6,2,8,3,7,5,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,2,8,3,7,5,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[7,3,4,8,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,3,4,8,7,2,6,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,3,5,8,7,2,6,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,6,3,8,5,7,2,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[7,5,3,8,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,6,8,3,7,4,5,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,8,4,3,7,5,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,8,3,7,4,6,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[7,4,3,8,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,5,4,8,7,2,6,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[4,5,3,8,6,7,2,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,6,7,8,4,5,2,1]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[2,6,8,5,4,7,3,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,8,5,6,4,7,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,8,6,4,7,3,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[7,4,6,5,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,7,8,4,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[4,3,7,8,5,6,2,1]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[5,2,8,6,4,7,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,2,8,6,5,7,3,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,2,8,6,7,4,5,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,7,5,4,6,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,8,2,7,4,5,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,8,6,3,4,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,8,4,5,7,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,2,8,4,6,7,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,2,8,5,6,7,3,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,6,8,5,7,2,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[3,4,6,8,7,2,5,1]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[7,3,5,8,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,8,3,5,7,4,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,8,4,5,6,3,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,5,8,4,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[5,7,4,6,8,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[3,6,5,8,4,7,2,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,8,4,5,7,3,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,2,7,1,3,8,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,2,5,1,3,8,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[5,3,6,1,7,2,4,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[3,7,1,2,5,8,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,4,1,2,8,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[7,5,1,3,4,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,1,2,4,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,2,3,7,1,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[7,6,3,8,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,2,3,8,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,7,5,2,8,1,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[8,2,6,3,7,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,7,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,2,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,2,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,3,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,1,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,6,1,2,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,5,8,1,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[7,6,4,8,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,8,1,2,4,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,6,8,1,2,5,7,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,7,2,4,8,1,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,6,3,8,1,2,5,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,6,3,7,1,2,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[4,1,7,8,2,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[5,1,2,8,6,3,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,3,8,1,6,2,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,1,8,5,2,3,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,1,7,5,2,3,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,8,1,3,7,4,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,2,8,1,6,3,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,7,8,2,5,1,3,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[6,8,2,7,1,4,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,7,1,3,5,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,1,2,4,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,1,2,3,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,1,2,4,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,1,3,4,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,1,8,6,2,3,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,8,6,4,1,2,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,8,4,1,2,5,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,2,6,5,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,4,8,2,7,5,3,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,1,3,4,7,2,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[7,8,2,1,6,3,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,1,2,7,5,4,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,2,8,7,5,4,3,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,7,3,6,4,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[6,2,1,5,7,4,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,2,3,7,4,1,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[3,4,8,7,5,6,1,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[2,3,8,7,4,1,5,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,8,6,4,1,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,8,3,7,6,4,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,4,6,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[4,6,7,5,2,1,8,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[6,3,1,4,5,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,3,1,4,6,2,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[5,1,2,4,7,6,8,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[5,7,4,1,2,6,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[4,8,1,2,6,7,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,8,2,6,3,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[1,2,8,7,6,5,3,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,4,6,8,7,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[3,1,8,4,5,7,6,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,8,5,4,7,1,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,2,8,1,5,3,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,5,7,6,1,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,2,1,6,3,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,5,2,7,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,6,1,7,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,8,1,2,6,4]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[3,7,8,5,2,1,6,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,2,8,4,1,6,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,8,1,7,4,6,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,5,1,6,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,7,5,1,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,6,7,2,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[1,3,4,8,7,5,2,6]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[8,2,4,1,7,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,2,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,4,2,8,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,6,8,4,3,7,2,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,1,4,7,8,5,2,6]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[6,1,7,4,3,8,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,8,7,4,3,6,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,8,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,8,2,3,1,5,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,2,1,3,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,1,8,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,8,4,2,3,6,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[4,7,1,3,8,2,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[8,7,1,3,4,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,6,2,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,8,6,4,5,2,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,6,5,2,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,7,5,8,1,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,4,7,3,6,2,8,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,8,3,4,2,6,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,7,2,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[8,1,4,3,6,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,8,5,7,1,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[2,8,5,7,3,4,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,6,4,3,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,2,5,8,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,2,3,5,8,7,1,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[8,2,3,5,4,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,3,4,2,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,8,6,4,2,3,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,5,6,2,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,5,7,8,1,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[3,8,6,5,4,2,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,1,4,2,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,3,8,1,2,6,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,4,5,3,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,8,4,2,6,5,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,8,6,3,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,3,1,8,4,7,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,3,8,1,5,7,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,3,1,2,5,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[7,1,4,2,6,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,8,4,1,6,5,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,6,4,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,6,4,5,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,7,2,4,5,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,8,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,7,5,4,8,6,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,1,8,7,5,3,6,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,8,3,7,4,1,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,1,7,4,2,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,1,8,4,7,2]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,7,1,4,8,6,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[3,5,7,4,8,6,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[2,6,7,4,5,8,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[6,1,7,4,5,8,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[5,3,7,4,8,6,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[8,5,3,6,1,4,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,6,8,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[6,5,3,7,4,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[7,5,8,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,8,4,5,1,6,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[5,7,3,8,4,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,6,3,8,1,4,7,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[8,4,1,2,5,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,1,6,5,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[6,8,3,1,2,5,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,5,1,7,2,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,5,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,1,5,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,1,8,2,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,7,3,1,5,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,1,5,4,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[5,4,2,6,1,3,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[3,2,6,5,1,4,8,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[2,5,8,1,7,4,3,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[6,8,2,7,4,3,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,3,7,5,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,6,2,5,4,8,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,6,5,1,8,4,3,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[4,2,7,3,1,8,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,2,3,7,1,5,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[5,2,7,3,8,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[2,1,5,8,4,3,7,6]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[5,8,4,2,6,7,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,2,4,8,1,5,7,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[2,4,8,3,1,7,5,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,8,3,2,1,7,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,2,6,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[3,4,8,2,1,6,5,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[6,8,3,7,2,1,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,5,8,1,7,2,6,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[5,1,7,4,6,8,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[7,6,4,8,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,3,7,1,8,2,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[2,7,6,3,8,1,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,1,7,6,4,8,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,1,5,4,8,7,3,6]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[5,4,8,7,2,6,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,4,3,8,7,1,5,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,4,1,8,6,2,7,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,8,5,4,2,1,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,5,2,7,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,7,5,4,1,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,8,6,5,4,3,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,3,1,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[6,5,2,1,3,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,5,2,7,3,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,5,2,8,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,2,3,4,8,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,3,8,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,2,3,5,8,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[3,7,6,4,2,8,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[2,1,7,6,4,8,5,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,1,8,7,4,3,5,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,8,3,7,2,1,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,7,4,2,1,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,2,3,5,1,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,8,6,3,1,4,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,3,2,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,4,8,3,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,1,7,5,4,8,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,3,7,5,8,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,6,1,5,8,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,6,7,5,1,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,1,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,6,8,3,7,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[6,5,2,8,1,4,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,4,2,8,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,7,8,4,5,1,3,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[5,7,3,8,4,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[2,4,8,1,5,6,3,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,1,5,2,7,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,6,8,4,1,2,7,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[4,8,1,2,5,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,1,2,4,3,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,4,6,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,7,6,3,5,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,6,5,2,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,7,6,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,5,4,7,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,7,6,2,5,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,6,3,2,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,6,5,2,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,8,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,8,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,5,2,4,7,6,1,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[3,5,4,7,2,6,1,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[3,5,4,7,6,1,2,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[3,5,4,7,6,1,8,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[3,5,7,4,6,1,8,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,5,7,4,6,1,2,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,5,7,4,6,2,1,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,2,5,7,4,6,1,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[3,5,2,7,6,4,1,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[3,5,7,2,6,4,1,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[5,3,7,6,2,4,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,3,7,6,1,2,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,3,7,6,1,4,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,3,7,6,4,1,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[3,5,7,2,6,1,4,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,5,2,7,6,1,4,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[5,3,7,6,4,1,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[3,7,5,4,1,8,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,5,4,1,8,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,5,1,4,8,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,5,1,4,8,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,5,7,1,2,6,8,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,5,7,2,1,6,8,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,5,2,7,1,6,4,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[3,5,7,2,1,6,4,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[5,3,7,1,6,2,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[3,5,7,1,4,6,8,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,5,7,1,4,6,2,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,5,7,1,4,2,6,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,5,7,2,1,4,6,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,5,2,7,1,4,6,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[3,2,5,7,4,1,6,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[3,5,2,7,4,1,6,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[3,5,7,4,2,1,6,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,5,7,4,1,2,6,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,5,4,7,1,6,8,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[3,5,4,7,1,2,6,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[3,5,4,7,2,1,6,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[3,5,4,2,7,1,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[3,2,5,4,7,1,6,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[3,5,4,7,2,1,8,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[3,5,4,7,1,2,8,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[5,7,6,3,1,8,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,6,3,1,8,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[3,5,7,4,1,2,8,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,5,7,4,2,1,8,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,2,5,7,4,1,8,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[3,2,5,7,1,4,8,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[3,5,2,7,1,4,8,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[3,5,7,2,1,4,8,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,5,7,1,4,2,8,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,7,5,2,1,8,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,2,5,1,8,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,2,7,5,1,8,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[3,2,7,5,1,8,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[3,7,2,5,1,8,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,5,2,1,8,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[2,1,7,5,8,4,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[5,8,3,4,1,7,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,2,4,1,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,6,4,1,7,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,6,8,1,7,2]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[3,7,6,4,1,8,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,4,1,8,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,8,4,1,7,6,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,1,5,4,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,2,8,7,6,1,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[5,7,8,2,4,1,6,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,2,5,8,1,6,7,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,2,5,8,1,7,3,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[5,8,2,4,1,6,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,4,2,6,5,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,1,5,4,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[8,3,2,5,6,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,6,7,1,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,6,8,7,1,5,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[3,2,6,7,1,5,4,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[8,7,3,2,5,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,1,5,3,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,4,2,7,5,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,8,5,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,4,1,8,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,2,8,5,7,1,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,7,1,8,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[2,5,1,8,7,4,3,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[8,1,4,6,3,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,1,6,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,4,1,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,8,2,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[4,1,8,2,3,7,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,1,8,5,3,4,7,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,4,6,8,7,3,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,6,8,3,4,5,7,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,4,8,6,1,3,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,4,2,6,7,8,1,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[6,4,2,7,3,5,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,4,1,8,3,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,4,8,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,3,2,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,3,1,7,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,4,3,2,6,8,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,4,3,8,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[8,3,7,2,1,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,2,4,3,1,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[8,4,7,3,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,7,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,5,7,4,8,1,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[8,2,7,3,4,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,3,5,8,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,8,5,6,7,1,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,7,8,6,4,3]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[2,6,8,5,1,4,7,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,4,2,8,6,5,7,3]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,5,1,6,8,7,2,4]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[5,7,6,2,1,3,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[2,5,8,7,4,1,6,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,1,7,5,2,6,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[7,6,2,4,5,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,3,4,2,5,8,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,7,4,2,5,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,2,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,6,7,1,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,5,6,2,1,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,1,5,6,7,8,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,4,6,5,1,7,8,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[7,3,5,2,4,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,3,7,2,4,6,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[3,7,5,2,4,6,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[5,7,3,2,4,6,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,5,3,2,4,7,6,8]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,5,3,2,7,4,6,8]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[5,7,3,2,1,4,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,7,3,2,4,1,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[3,7,2,5,4,1,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[5,1,3,2,4,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[5,1,3,2,7,4,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[7,1,3,2,5,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,7,3,2,5,4,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[7,1,3,5,2,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,1,3,7,2,4,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[3,2,7,5,1,4,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,7,5,1,2,4,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[5,7,3,1,2,4,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,5,3,7,2,4,6,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[5,3,2,7,4,1,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,3,2,4,7,1,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[5,3,2,1,4,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[5,3,2,1,7,4,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[1,3,2,7,5,4,6,8]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,3,7,2,5,4,6,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[7,3,1,2,5,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,3,1,2,7,4,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[5,3,1,2,4,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[3,2,5,1,4,7,6,8]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[7,3,1,5,2,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,3,7,5,2,4,6,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[7,5,1,3,2,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,7,1,3,2,4,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[3,7,1,5,2,4,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,1,2,5,4,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,2,1,5,4,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,2,1,7,5,4,6,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[3,1,2,7,5,4,6,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[3,1,7,2,5,4,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,1,7,5,2,4,6,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[7,1,5,3,2,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,7,5,3,2,4,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,7,4,2,6,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,1,7,6,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,5,1,2,7,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,1,4,7,6,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,4,3,2,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,4,2,7,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,4,2,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,7,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,3,6,8,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,5,6,4,8,2,7,1]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[3,5,1,4,8,2,7,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[1,7,5,4,8,2,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,5,1,6,4,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[2,7,5,4,8,1,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,5,4,8,6,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,5,4,8,6,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,5,1,4,8,7,3,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[3,6,4,2,8,7,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,5,2,4,8,1,6,7]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[3,5,6,4,8,1,2,7]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[1,5,6,4,8,7,2,3]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[3,6,4,1,8,7,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,6,4,5,8,7,2,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[1,6,4,3,8,5,2,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[7,1,3,4,5,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,1,4,5,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,1,3,5,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,3,2,5,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,6,4,2,8,5,3,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[7,6,5,8,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,5,8,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,6,4,3,8,1,7,5]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,4,3,8,5,7,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[7,2,3,1,5,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,5,6,3,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,6,5,1,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,2,6,5,3,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,2,3,1,4,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,2,3,5,4,8,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,6,4,5,8,1,7,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,5,6,4,8,3,7,2]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[2,5,6,4,8,3,1,7]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[3,5,6,1,4,7,8,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[7,6,1,3,4,5,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,3,2,4,8,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,1,5,3,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,1,5,4,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,6,4,5,8,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[7,6,5,8,1,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,4,6,8,7,2,1,5]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[3,5,6,8,2,1,7,4]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[4,2,1,5,3,7,8,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[4,2,5,6,3,1,8,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[3,5,6,8,1,7,2,4]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[4,1,5,6,3,2,8,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[4,5,3,1,7,2,8,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[4,1,3,5,2,7,8,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[2,5,4,7,3,8,6,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[3,5,7,1,8,4,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[4,1,5,3,2,7,8,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[4,5,3,7,1,2,8,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[4,3,6,1,2,7,5,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[5,1,3,2,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[3,6,1,7,4,5,2,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[5,1,3,4,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[5,3,1,4,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[4,5,2,3,7,1,8,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[4,2,6,1,3,7,5,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[4,6,2,1,3,7,5,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[3,6,2,1,7,4,8,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[3,1,4,7,6,5,2,8]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[3,6,2,7,1,5,8,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[4,6,2,7,1,3,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[3,5,7,1,8,2,6,4]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[5,1,4,2,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[3,6,1,7,2,5,8,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[2,6,5,3,4,7,8,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[3,6,1,7,5,4,2,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[5,1,4,3,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[5,4,1,3,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[6,4,2,5,3,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,6,2,3,5,1,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[6,2,4,5,1,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,2,6,7,1,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,7,4,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,3,5,8,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[2,6,4,1,5,8,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,8,1,6,7,4,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,4,5,7,2,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,6,1,4,7,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,6,4,7,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,4,8,5,3,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[6,4,5,2,8,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,2,3,6,1,8,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[4,2,3,1,6,8,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[4,2,3,8,6,1,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[6,4,5,8,2,3,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,6,7,2,4,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,5,2,3,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,2,8,3,1,6,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,1,3,6,7,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,1,8,3,6,7,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,1,4,8,6,3,7,5]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[6,4,8,2,5,3,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,6,2,4,7,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,3,5,7,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[2,6,8,4,1,5,7,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,6,8,1,4,5,7,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,1,6,8,4,5,7,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,8,1,4,6,7,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,2,3,7,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,4,2,6,7,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,5,1,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,6,7,5,3,4,8,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[7,6,2,3,8,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,6,7,5,8,2,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[6,2,5,8,3,4,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,3,8,7,4,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,4,7,3,5,8,6,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[2,5,3,7,1,8,4,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[5,2,8,3,1,4,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,8,2,3,6,5,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,3,6,4,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,1,4,3,6,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,1,3,7,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,8,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,6,5,3,7,1,2,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[4,5,1,3,6,2,8,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[4,2,6,5,1,7,3,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[4,3,5,7,2,1,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[3,4,7,6,8,1,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[3,4,6,2,5,8,7,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,2,4,6,1,8,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[4,2,5,1,6,8,3,7]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[1,8,2,3,6,5,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,8,3,5,7,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,6,5,7,1,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,3,7,2,6,5,8,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,3,6,4,2,5,8,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,5,4,7,3,6,8,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[5,2,3,8,4,1,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[7,5,3,4,8,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,8,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,3,8,5,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,6,2,7,3,1,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[7,6,3,8,2,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,8,5,1,3,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,5,3,7,6,8,4,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,6,3,7,8,2,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,4,3,7,8,5,2,6]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[4,2,6,5,7,8,3,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[4,2,6,7,5,8,1,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[3,2,4,7,8,5,1,6]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[3,2,6,7,8,1,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[5,1,8,3,6,4,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,6,8,5,7,2,1,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,1,3,8,7,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,8,5,6,1,7,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,1,7,6,2,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[4,7,6,8,5,1,3,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[6,7,4,8,5,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,3,6,8,7,1,4,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,8,4,6,7,2,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,8,3,7,1,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,4,5,8,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,3,6,8,7,1,5,2]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[6,4,8,3,1,7,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,6,5,8,7,1,4,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[5,7,4,8,2,6,3,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,6,4,8,2,7,3,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,6,8,3,1,7,4,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,6,3,8,2,7,5,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[5,3,8,1,7,2,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,5,8,1,3,7,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,3,8,2,7,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,8,1,3,7,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,8,3,4,7,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,6,3,1,4,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,5,4,3,7,8,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[7,8,4,2,5,3,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,2,7,8,5,3,1,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[4,2,5,3,1,7,8,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[4,2,8,7,6,3,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,2,7,6,3,1,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[6,3,1,7,5,2,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,3,1,8,7,5,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,6,3,1,7,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,6,3,1,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[7,6,3,1,8,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,4,2,1,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,8,2,7,6,4,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,5,7,6,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,7,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,4,8,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,4,6,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,2,8,6,3,7,4,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,4,7,5,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,4,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,5,3,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,8,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,2,6,3,1,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,2,7,4,1,8,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,2,8,7,4,1,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,7,4,1,5,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,5,2,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,3,1,4,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,2,8,6,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,7,5,2,6,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,1,3,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,7,5,2,1,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,1,3,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,3,7,6,5,8,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[8,6,4,7,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,5,2,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,7,5,2,1,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,3,1,4,7,5,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,3,1,4,8,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,6,3,1,4,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,5,7,6,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,6,4,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,2,1,6,4,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,3,8,7,4,1,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,7,4,1,5,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,4,1,6,3,5,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,1,8,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,4,6,3,1,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,5,2,1,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,6,4,7,5,3,8,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[8,6,3,5,2,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,2,8,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,3,5,2,7,4,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[4,5,7,2,6,3,1,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[3,5,8,4,6,1,7,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,7,3,5,2,6,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[5,7,4,2,6,3,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[4,2,6,3,5,7,1,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[1,4,5,8,2,7,3,6]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[2,4,5,8,1,6,7,3]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[8,3,4,7,1,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,8,1,6,3]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[8,3,4,6,5,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,7,3,5,2,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[6,1,3,7,4,2,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[3,1,6,8,2,7,4,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[6,1,3,8,2,5,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,8,2,3,1,6,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,8,1,5,7,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[8,2,6,1,5,4,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,1,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,7,4,2,8,1,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,3,7,2,8,1,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,5,2,8,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,7,3,8,1,5,6,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,6,8,5,2,4,3,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,5,7,2,8,1,6,3]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[4,5,6,8,3,1,7,2]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[8,4,6,5,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,8,3,1,7,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[3,4,7,1,2,6,5,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[4,8,1,6,2,3,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,7,2,6,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[4,7,3,1,2,6,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[5,2,7,1,3,6,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[7,8,1,2,4,3,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,4,1,6,2,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,1,2,5,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,3,6,5,7,8,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[6,1,3,4,2,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,1,4,2,5,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,5,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,1,3,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[2,6,5,3,1,7,8,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[8,3,2,1,5,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,6,8,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,6,3,1,8,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,8,4,6,3,7,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,3,6,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,7,4,2,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,5,7,1,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,2,7,1,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,3,8,2,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[1,6,5,8,3,4,2,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,1,5,3,8,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,1,5,4,7,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,5,8,3,6]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[6,3,5,8,7,4,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,7,2,8,5,6,3,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[1,4,8,7,3,5,6,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[8,1,7,6,3,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,7,4,1,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[4,7,6,8,5,3,1,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[5,7,2,8,6,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,8,7,5,6,4,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,6,4,5,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,6,5,3,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,2,5,3,1,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[3,6,7,4,8,1,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[3,8,5,7,6,1,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,8,2,6,5,3]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[2,4,7,8,1,6,5,3]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[4,2,6,8,7,1,5,3]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[3,1,7,8,2,6,5,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[6,1,3,8,2,7,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,1,8,4,2,7,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,2,6,1,7,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,7,1,5,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,7,3,8,1,6,5,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,3,8,2,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,6,8,4,1,7,5,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,5,8,6,3,1,7,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,6,7,1,2,8,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[3,6,1,8,2,7,5,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[5,7,4,1,2,8,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,3,7,1,2,8,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,2,1,8,3,7,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,1,5,6,3,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,5,2,4,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,5,3,7,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,8,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,8,5,4,3,2,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,6,8,7,4,3,5,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,2,6,7,8,4,3,5]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,7,5,8,4,1,3,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,1,7,8,4,5,3,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[3,7,8,2,1,5,4,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[8,5,1,4,7,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,7,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,6,7,4,1,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,6,8,4,7,1,5,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[4,7,1,3,6,8,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,7,6,4,8,1,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,1,7,5,6,8,2,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[2,3,6,5,7,1,8,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[3,7,5,4,2,1,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,3,6,7,4,2,8,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[3,6,4,8,2,7,5,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,4,6,3,2,7,8,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[8,7,1,5,6,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,7,5,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,5,3,2,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,7,2,4,6,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,6,4,5,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,7,2,5,4,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,5,3,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,1,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,7,3,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,5,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,1,8,4,6,5,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,8,2,1,6,5,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[8,7,6,1,4,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,3,7,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,3,6,5,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,8,4,7,2,6,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,8,5,4,6,2,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,4,6,1,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,1,6,4,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,4,6,1,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,4,6,3,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,4,6,3,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,8,4,7,3,6,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,6,4,2,7,8,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[3,5,4,1,6,2,7,8]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[4,5,8,1,7,6,2,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,5,8,4,7,1,6,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,5,8,4,7,3,6,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,6,4,1,7,8,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[3,6,4,8,7,5,2,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,4,3,7,8,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[7,1,3,4,8,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,1,3,8,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,6,4,2,7,8,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[2,6,4,3,7,1,8,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[2,6,4,1,7,8,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[7,2,3,4,8,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,3,1,8,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,3,4,1,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,2,4,3,8,5,7,6]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[7,3,8,6,1,4,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,6,3,4,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,3,1,5,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,2,3,8,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,3,8,5,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,6,4,8,7,1,5,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,5,8,4,7,6,2,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,8,1,6,7,2,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[7,6,1,3,5,8,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,3,2,5,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,3,8,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,1,8,5,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,1,6,5,8,2,7,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[3,1,6,5,8,4,7,2]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[3,2,6,5,8,4,7,1]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[4,3,7,1,6,5,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[5,2,6,4,8,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,1,6,4,8,3,7,2]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,1,6,4,8,2,7,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,2,6,4,8,1,7,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[4,3,7,5,8,1,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,3,7,5,8,2,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[5,3,7,4,8,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,3,7,4,8,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,4,8,1,6,2,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,3,7,2,6,1,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,3,7,1,5,2,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,3,7,1,6,2,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[5,4,8,2,6,3,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,1,6,3,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,1,7,5,2,3,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[4,1,7,8,6,3,2,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[4,7,2,8,3,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[1,2,6,8,3,7,4,5]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[6,8,3,2,1,4,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,2,4,1,6,5,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,8,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,2,4,1,3,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,4,7,6,3,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,2,7,5,8,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[4,2,7,3,8,5,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,5,2,6,8,3,7,1]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[4,8,3,2,5,7,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,8,5,3,4,7,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,1,5,3,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,3,5,1,4,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,4,2,3,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,2,4,3,7,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,2,1,3,5,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,5,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,3,4,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,2,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,4,2,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,5,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,5,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,3,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,8,4,2,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,4,5,1,6,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,7,3,5,6,2,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[6,7,8,4,1,3,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[3,1,6,8,4,7,5,2]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[8,3,6,1,5,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,5,8,6,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[2,5,4,7,8,1,6,3]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[2,4,6,7,8,1,5,3]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[2,4,6,8,1,7,5,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[7,4,3,8,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,2,7,6,1,8,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[4,3,6,2,1,8,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[3,6,4,2,5,8,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[4,6,2,3,7,5,8,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[5,8,4,2,3,6,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,4,5,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,4,2,1,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,4,2,3,7,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,4,8,3,2,7,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,8,3,7,2,1,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,7,1,8,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[2,5,4,8,1,6,7,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[6,4,7,3,8,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,7,4,3,2,1,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[8,4,3,7,2,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,5,8,7,3,4]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,2,8,4,6,7,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,5,2,7,4,6,8,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[5,1,2,7,3,6,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[5,1,2,8,3,6,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,6,3,4,8,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[6,5,3,4,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,1,2,8,3,6,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,1,2,7,3,6,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[7,5,3,8,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,5,3,7,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,3,4,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,1,2,8,3,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,1,8,2,3,5,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,1,7,2,3,5,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,6,8,2,4,5,7,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,3,8,7,5,6,2,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,8,2,7,4,6,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,2,3,5,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,6,2,3,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,3,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,4,6,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,7,3,4,5,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,7,2,4,5,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,2,3,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,3,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,3,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,4,5,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,7,4,6,3,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,7,5,1,4,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[4,2,5,8,7,3,6,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[1,8,3,5,7,2,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,6,8,5,7,1]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[2,3,5,7,4,8,6,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[2,4,6,3,7,8,5,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[2,5,7,1,8,6,3,4]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[8,2,4,5,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,2,4,6,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,6,7,1,8,4,5,3]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,8,3,1,4,2,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,4,2,6,7,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,1,8,5,6,3,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,6,2,7,8,5,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[3,5,2,6,7,8,4,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[4,5,1,6,7,3,8,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[2,8,4,1,7,5,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,5,3,1,7,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,1,5,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,2,6,8,1,7,4,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[5,7,3,2,6,8,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[8,4,7,3,1,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,1,2,3,5,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[3,1,6,7,8,4,2,5]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[3,1,4,8,5,6,2,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[8,3,1,4,5,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,5,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,7,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,8,7,5,4,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[8,2,3,7,5,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,5,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,2,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,5,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,5,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,5,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,7,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,5,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,1,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,8,7,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,6,1,8,7,5,4,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,8,1,5,7,6,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,8,7,6,4,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,4,8,2,7,6,5,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,7,1,6,5,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[8,1,3,5,7,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,5,7,6,3,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,2,7,1,4,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,4,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,2,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,7,6,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,7,4,6,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,3,7,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,3,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,6,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,2,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,7,4,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,5,7,6,3,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[8,2,4,3,7,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,5,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,3,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,1,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,5,7,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,8,7,5,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,1,8,2,7,5,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,1,7,3,5,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,7,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,4,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,1,7,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,3,7,6,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,2,1,7,6,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,1,8,7,2,6,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,1,3,7,6,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,2,5,4,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,4,8,7,6,3,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,1,4,3,7,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,7,6,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,8,1,7,6,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,8,6,3,2,1,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,2,4,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,5,7,2,4,3,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[5,7,1,3,2,8,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,8,1,3,2,7,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,5,1,3,2,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,3,2,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,8,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,1,2,5,7,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,1,2,3,8,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,1,6,4,2,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,2,3,7,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,7,8,2,3,5,6,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,5,8,2,3,1,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,1,2,6,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,2,8,1,5,7,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,5,4,1,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,5,4,2,1,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,3,2,8,5,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,7,4,3,6,8,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[4,7,6,5,2,3,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[4,7,6,5,1,3,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[5,4,6,8,7,2,1,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,7,4,2,1,8,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,7,3,2,1,8,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,7,6,3,2,8,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,4,2,1,7,3,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[6,5,8,1,7,3,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,3,4,1,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,1,2,8,5,3,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,7,4,1,6,5,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,5,8,2,6,1,7,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,7,6,1,5,2,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,7,6,2,5,8,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,6,5,8,4,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,6,5,8,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,6,2,8,4,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,3,6,8,5,1,2,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[2,7,1,5,8,4,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,6,1,8,4,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,1,2,6,3,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,6,3,4,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,7,8,4,2,5,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,1,2,5,7,8,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[4,1,2,7,8,5,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[4,7,3,1,2,6,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,7,6,1,5,8,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,8,5,6,4,2,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,6,4,7,8,5,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[4,2,7,5,8,3,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,2,7,1,3,8,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[5,2,1,4,7,8,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[5,6,2,7,3,4,8,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[6,1,3,8,5,4,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,7,6,8,5,1,3,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,6,8,5,3,1,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,5,8,6,4,2,3,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,5,8,6,4,1,7,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,4,6,1,5,7,3,8]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,6,2,3,5,8,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[4,7,2,3,1,6,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[6,7,3,1,5,4,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,4,6,2,8,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,5,1,4,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,4,6,5,1,2,7,8]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[7,5,4,3,8,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,3,8,2,6,7,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,2,5,7,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,6,2,5,3,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[5,1,8,6,4,7,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,1,8,5,6,3,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,2,6,1,5,3,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[6,7,2,3,1,5,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,5,2,3,8,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,2,3,8,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,5,1,7,6,3,8,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[8,1,7,5,2,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,4,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,2,8,7,3]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[4,8,3,6,1,7,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,8,3,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,2,4,6,8,5,7,3]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,7,5,8,6,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[4,7,3,8,6,5,2,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[3,8,7,4,6,5,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,8,4,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,3,6,5,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,5,8,7,2,6,1,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,8,6,7,5,1,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,7,6,5,8,3,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,6,7,8,5,2,3,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[4,5,3,8,2,7,6,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,8,5,4,1,7,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,2,5,8,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,3,8,7,5,1,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,3,6,4,1,2,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[6,8,4,3,5,7,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,2,4,8,7,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,2,4,5,1,8,6,7]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[4,2,5,1,7,8,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[2,5,4,1,3,8,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,4,5,3,8,2,6,7]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[5,1,8,2,4,3,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,5,4,8,2,3,6,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[3,5,1,4,7,8,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[4,8,3,1,6,7,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,2,6,5,7,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,6,2,4,8,7,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[4,7,3,2,6,8,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[7,3,4,6,8,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,6,7,2,5,8,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[1,5,6,8,3,7,2,4]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[6,1,5,8,3,4,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,6,8,1,3,4,7,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[2,8,5,6,3,4,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,1,3,5,4,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,1,6,3,5,4,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,5,8,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,2,4,8,1,7,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,1,7,8,5,4,6,2]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,6,2,7,4,8,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[2,7,1,8,4,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,7,1,8,3,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[2,7,6,3,5,8,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,5,6,8,1,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,7,2,8,1,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[5,1,6,8,7,2,3,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,5,7,6,8,2,3,4]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[7,4,6,8,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,1,5,7,8,3,6,4]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[4,6,2,5,7,1,8,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[3,8,6,7,5,1,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,5,8,6,3,1,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[1,6,8,3,2,5,4,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[7,8,5,1,3,2,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,6,8,1,5,4,7,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,5,4,7,6,2,8,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[2,3,7,6,5,1,8,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[6,1,5,8,3,2,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,1,2,4,8,5,7,6]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[7,1,5,4,8,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,4,1,7,5,3,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[2,7,6,4,8,1,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,2,5,4,8,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,7,2,5,3,8,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,2,3,8,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,2,5,8,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,3,8,4,1,2,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,4,8,3,7,1,5,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[5,2,8,4,1,6,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,6,5,2,1,8,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,5,1,8,3,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,7,1,3,2,4,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[4,2,7,6,3,5,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[8,1,7,4,2,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,3,2,5,1,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[5,1,6,8,3,7,4,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[8,6,5,1,7,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,3,5,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,3,7,1,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,7,4,3,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[8,6,2,7,4,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,2,6,1,4,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,8,5,2,1,4,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[6,8,4,7,3,1,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,6,5,1,2,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,5,1,2,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,4,5,1,7,6,8,2]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[3,8,7,6,5,1,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,6,7,1,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,2,6,1,8,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,2,6,1,3,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,8,2,6,1,4,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,7,5,6,1,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,4,7,2,1,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,4,6,5,1,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,7,3,4,5,2,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,8,2,1,3,5,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,4,3,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,6,7,3,4,8,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[2,1,5,7,4,3,8,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[4,1,8,7,5,6,2,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,5,8,7,4,3,6,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[6,4,1,3,8,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,1,7,4,6,8,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,7,2,4,6,8,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,6,4,2,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,2,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,8,6,2,7,3,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,8,6,2,3,5,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,1,8,3,5,7,6,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,8,1,7,6,2,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,8,1,3,6,7,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,8,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,4,3,2,8,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,2,4,3,8,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,8,4,3,1,6,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,2,8,1,5,7,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,3,7,2,5,4,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,4,7,3,2,6,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,7,2,6,3,4,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[3,7,5,4,6,2,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[6,8,3,2,1,7,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,1,7,5,3,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,7,2,8,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[3,6,5,7,2,8,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[4,6,5,3,8,2,1,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[2,6,5,8,7,3,1,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,3,8,4,1,7,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,8,1,6,4,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,2,8,7,6,4,1,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,2,6,4,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,8,6,3,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[2,8,7,5,3,1,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,3,1,4,8,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[2,4,7,8,5,3,1,6]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[6,5,3,2,4,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,5,8,7,3,2,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,1,4,7,8,5,3,6]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[8,3,1,6,5,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,7,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,1,4,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,4,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,3,7,8,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,1,2,7,5,8,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[2,7,3,1,4,6,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,3,1,6,5,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,6,7,1,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,2,8,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,5,8,1,4,6,7,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,1,8,7,5,4,6,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[7,8,3,4,1,6,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,3,4,2,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,2,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,6,3,1,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,5,2,3,8,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[6,4,7,5,2,8,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[7,5,1,3,6,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,5,2,3,7,8,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[7,2,6,3,1,5,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,6,3,8,7,5,1,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[2,8,4,1,5,7,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,2,5,7,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,5,4,1,7,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,8,3,7,1,6,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,8,5,2,4,7,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,2,8,7,5,3]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[7,8,2,4,1,6,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,4,6,1,8,7,5,3]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,8,4,5,1,7,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,8,2,7,6,1,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,1,6,8,7,5,3,4]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,8,2,4,5,7,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,8,3,5,7,6,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,2,5,7,6,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,1,5,7,6,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,8,7,5,3,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,2,8,7,5,3,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,3,8,7,5,2,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,3,8,7,5,1,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[3,2,8,1,5,7,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,8,2,5,7,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,8,1,4,5,7,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,2,1,4,6,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,3,6,8,7,5,1,4]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[3,1,6,8,7,2,5,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[3,8,4,5,1,6,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,7,2,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[8,1,4,7,6,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,4,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,6,2,7,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,3,6,1,5,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,3,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,5,2,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,5,8,4,6,2,3,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,1,6,5,3,8,4,7]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[5,6,8,1,4,2,3,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,7,4,8,1,2,3,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[8,2,1,5,3,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,8,1,2,6,3,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[8,7,1,5,6,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,8,7,2,3,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[3,7,1,6,2,4,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[5,1,2,7,6,8,3,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[6,1,7,2,5,8,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,7,6,5,8,2,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,6,8,5,7,2,3,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[7,5,1,2,6,8,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,1,5,2,7,8,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,6,3,8,7,2,4,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,7,3,2,4,6,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[8,3,1,4,2,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,7,8,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[5,1,2,6,8,7,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,8,6,2,5,7,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,8,1,2,6,3,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[8,1,5,7,6,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,5,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,7,1,2,8,4,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[8,3,1,2,7,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,6,2,3,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[7,8,6,1,5,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,3,4,5,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,7,4,8,2,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,8,6,1,4,2,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,8,2,4,6,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,8,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,2,8,1,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,5,4,1,7,2,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[6,4,7,3,2,5,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,6,5,3,8,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,4,5,7,8,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[3,7,4,1,6,8,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,1,2,7,6,8,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[6,3,2,8,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,1,8,3,5,4,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,8,5,2,4,6,1,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,8,3,5,2,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,5,4,8,6,3,7,2]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,8,2,5,3,7,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,5,2,6,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,8,6,5,3,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,7,8,4,6,3,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,3,2,8,6,4,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,8,1,2,7,4,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,7,3,6,2,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,5,2,3,4,8,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,5,4,2,8,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,6,1,3,2,4,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[2,5,1,3,7,8,6,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,3,7,2,1,8,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,6,7,2,1,3,5,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[4,6,2,3,1,5,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[3,6,4,2,5,1,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[3,1,6,4,7,5,2,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[3,6,2,7,5,4,1,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[2,4,7,5,3,6,1,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[2,5,7,3,4,1,6,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[2,3,5,8,6,4,7,1]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,3,8,6,5,1]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,4,2,7,5,8,6,1]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[3,1,5,4,7,8,6,2]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[4,5,7,2,3,1,8,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[3,7,8,1,4,6,5,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[2,5,8,7,4,1,3,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,6,4,7,5,3,8,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[6,2,4,7,1,3,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,3,5,1,4,2,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,4,7,1,3,2,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[6,1,4,7,5,3,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[8,7,4,3,1,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,3,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,7,3,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,7,3,6,1,2,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[5,2,1,7,4,3,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[4,7,6,2,3,1,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[7,6,8,2,5,3,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,3,6,1,8,7,5,4]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,6,8,7,5,3,1,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,4,1,7,5,2,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,7,8,2,3,6,1,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,8,7,1,2,5,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,4,1,5,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,2,1,5,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,5,2,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,5,8,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[4,7,3,1,8,5,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[2,6,7,5,3,4,8,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[2,6,4,5,7,3,8,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[6,1,4,5,8,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,1,8,5,3,4,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,1,5,6,8,3,7,2]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[6,4,1,8,7,2,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,5,7,2,6,8,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[1,3,8,5,2,7,4,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,6,7,2,4,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,8,3,7,6,1,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,8,7,6,2,4,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[7,4,6,8,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,3,6,8,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,2,6,7,8,1,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[4,5,6,8,1,2,7,3]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[3,5,8,6,1,2,7,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[4,2,6,8,7,1,3,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[1,4,6,8,7,2,3,5]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[4,5,3,8,1,7,2,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,5,8,4,1,7,2,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,6,5,7,8,2,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,6,4,8,2,3,7,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[6,5,4,8,1,3,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,6,4,8,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,6,5,8,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,7,5,2,4,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[8,1,2,7,4,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,7,4,6,1,3,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[6,1,7,4,5,3,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[8,2,7,3,1,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,3,1,7,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[8,1,3,7,5,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,3,8,6,7,4]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[4,1,6,5,7,8,2,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[6,1,3,7,4,2,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,7,2,4,1,3,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,3,8,4,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,5,3,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,5,6,7,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,8,6,7,2,5,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,8,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,6,7,3,8,5,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[7,3,4,8,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,7,2,4,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,6,7,5,2,8,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[5,4,6,7,8,1,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[5,3,6,7,8,1,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[5,3,7,6,8,4,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[7,5,3,2,8,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,4,8,6,7,2,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,8,6,3,1,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,5,7,3,6,2,8,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[4,5,6,3,8,2,7,1]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[5,4,8,7,2,1,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,5,4,7,8,1,3,6]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[5,3,6,4,8,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,3,7,4,6,2,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[8,2,4,7,3,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,6,2,7,3,8,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[7,4,6,1,5,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,4,6,2,8,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[8,4,6,1,7,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,3,8,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[4,5,6,3,7,1,8,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[6,3,2,8,5,4,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,3,1,5,2,8,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[8,5,4,1,3,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,1,5,2,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,3,8,1,6,7]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,5,7,4,3,1,6,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[5,3,4,2,7,1,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[3,7,5,4,1,2,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[4,2,5,1,3,8,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[4,3,5,1,2,7,6,8]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[5,3,4,1,7,2,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[4,1,6,3,5,2,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[4,2,1,8,6,3,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,2,5,6,4,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,7,5,4,2,1,6,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,2,4,1,6,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[7,3,2,1,6,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,8,6,1,7,4,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,6,1,3,7,8]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[2,5,6,4,1,3,7,8]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[8,5,2,6,1,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,6,3,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,2,5,4,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,4,1,6,5,3,7,8]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[4,1,2,7,5,6,3,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[7,1,2,6,5,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,1,5,6,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,1,6,4,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,5,3,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[3,1,6,5,4,2,7,8]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[3,1,4,6,5,2,7,8]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[6,4,1,5,3,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,8,6,3,7,5,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,8,3,1,7,6,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,6,3,2,8,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,6,3,8,7,4,1,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,2,6,8,7,4,1,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,3,8,5,7,2,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,3,8,5,4,1,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,8,4,5,1,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,2,3,1,4,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,4,1,3,2,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,1,3,4,2,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,2,1,4,3,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[4,2,7,3,8,5,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,7,3,2,8,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,3,7,2,8,5,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[5,3,1,2,4,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,4,3,1,2,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,3,4,1,2,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,2,3,4,1,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,1,7,3,4,6,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,8,7,4,3,1,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,1,3,4,5,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,5,2,8,1,6,7,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,1,7,8,2,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[6,2,3,7,4,1,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,3,7,4,1,2,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,2,6,8,4,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,7,2,8,6,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,6,7,5,1,2,4,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[7,4,5,1,8,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,3,1,8,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,1,4,8,3,7,5,6]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,7,8,4,3,6,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[5,8,1,4,3,2,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,1,3,5,6,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,3,7,8,4,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[6,3,7,8,2,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[8,5,2,4,3,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,2,3,1,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,5,6,4,8,1,7,2]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[3,5,4,6,7,1,8,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[1,4,2,6,5,8,7,3]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,3,2,6,4,8,7,5]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,4,2,5,3,8,7,6]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,5,2,6,4,8,7,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,6,2,5,3,8,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,5,1,4,3,8,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,7,3,5,4,8,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,8,2,6,3,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,6,4,7,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,4,8,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,2,6,3,8,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,5,2,7,4,8,6,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,4,2,8,5,7,6,3]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[4,8,1,3,2,6,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,8,4,7,6,2]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,8,4,7,3,6,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,8,1,5,4,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[8,3,1,4,2,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,5,2,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,8,7,3,5,2,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,3,5,1,2,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,5,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,5,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,4,1,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,4,6,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,3,8,7,4,6,1,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[8,3,5,7,4,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,3,1,2,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,8,7,3,1,5,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,4,1,3,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,5,8,7,4,6,3,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,8,7,6,5,1,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,5,1,6,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,8,7,5,6,1,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,8,7,1,3,6,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,5,4,7,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,5,2,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,5,8,6,4,2,7,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[6,8,4,1,5,2,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,1,7,5,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,4,6,1,2,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,4,8,6,5,1,7,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,8,7,6,5,2,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,5,1,6,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,1,8,6,7,3]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[4,5,8,3,1,6,7,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,7,2,8,4,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[6,7,3,2,4,8,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[7,2,8,6,4,5,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,2,6,5,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,8,4,1,3,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[2,7,8,6,4,1,3,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,6,3,5,2,8,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,2,7,4,8,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[8,6,5,1,7,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,7,3,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,6,8,3,7,4,2,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,1,6,3,4,8,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[3,5,2,6,4,8,1,7]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[3,5,2,4,8,1,7,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[6,3,8,2,4,1,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,6,3,8,7,5,2,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[6,3,8,7,5,4,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,4,2,1,7,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,2,6,4,3,8,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[6,5,3,1,4,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[3,1,7,8,6,4,2,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[3,8,1,7,6,2,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,7,6,4,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,8,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,8,6,4,1,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,7,5,8,2,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,5,2,4,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,5,6,3,8,2,4,7]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[8,7,1,3,6,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,4,3,8,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,2,4,7,3,8,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[1,5,8,7,2,4,6,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,8,7,3,6,5,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[8,3,7,2,5,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,2,8,1,5,4,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,2,6,1,5,8,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[7,2,1,5,8,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,8,1,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,7,8,3,2,6,5,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,4,8,3,2,6,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,5,4,8,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,5,4,3,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,7,4,5,6,8,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,6,4,2,3,5,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,8,7,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,8,6,2,3,4,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,6,5,7,2,3,4,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,7,5,6,2,3,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,3,2,7,6,4,5,8]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,2,3,7,6,4,5,8]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,5,4,2,3,7,6,8]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,5,4,2,3,8,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,3,2,8,6,4,5,7]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,7,5,8,2,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,8,7,5,2,3,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,8,6,3,7,4]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,5,8,4,6,1,7,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,5,3,8,6,1,7,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,6,3,5,8,1,7,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[6,3,2,5,8,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,3,2,8,6,1,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,8,4,6,1,3,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,3,8,6,1,4,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,6,5,4,8,1,7,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[8,3,5,7,2,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,6,8,5,3,7,1]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,8,1,7,6,5,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,1,5,7,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,8,4,1,5,7,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,8,5,2,7,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[8,5,4,7,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,5,4,2,7,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,6,4,8,5,2,7,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,6,4,1,8,2,7,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,6,4,1,5,2,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[4,8,6,5,1,3,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,5,6,7,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,4,7,1,8,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[2,7,5,4,6,1,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,3,7,4,6,1,8,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,6,7,4,1,3,8,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[6,5,7,4,1,3,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[2,4,6,3,5,7,8,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[4,1,6,3,5,7,8,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[3,6,4,2,5,7,8,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[2,3,6,1,5,7,8,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[4,3,6,2,5,7,8,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[4,6,1,2,5,7,8,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[2,6,4,1,5,7,8,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[2,4,1,6,5,7,8,3]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[7,5,4,2,6,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,7,3,1,8,6,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,6,4,2,7,1,8,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[4,2,7,5,3,1,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[5,3,6,4,8,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[7,3,2,5,4,1,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,3,2,5,1,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,6,3,8,7,2,1,5]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,7,6,3,8,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,7,3,8,6,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[5,7,3,2,6,1,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,7,3,2,6,4,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[2,7,5,3,1,8,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,5,2,8,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,2,4,1,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,3,7,5,8,2,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,3,7,5,2,6,1,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[8,4,5,3,7,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,2,8,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[4,5,3,6,8,2,1,7]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[1,2,8,6,4,5,7,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,8,5,3,4,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,4,1,6,3,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,6,1,3,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,4,1,8,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[2,8,6,5,3,1,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,8,6,2,3,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,8,7,5,2,3,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,6,8,3,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[3,4,2,8,7,5,1,6]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[8,5,7,6,3,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,8,7,3,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,8,5,4,2,7,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,1,5,8,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,6,5,8,2,7,4,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[8,3,2,7,4,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,6,2,3,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,7,1,3,2,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,1,3,8,7,2,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,7,1,6,2,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,5,2,4,7,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,4,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,8,5,1,4,7,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,5,4,1,3,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,8,1,6,3,2,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,4,8,5,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,6,1,3,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,4,5,8,6,3,2,7]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[8,4,5,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,6,7,3,1,8]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[8,1,7,5,3,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,3,6,1,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,6,3,1,7,8,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[4,3,5,1,6,7,8,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[5,7,6,1,2,3,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[3,6,7,5,1,2,8,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[1,7,6,8,5,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,7,6,8,1,2,4,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,6,3,7,1,4,8,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[5,3,2,1,8,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[3,8,6,4,5,7,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,6,1,4,5,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,8,5,4,6,7,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,8,3,7,2,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,8,4,3,2,6,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,8,2,1,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,4,8,3,2,1,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,8,4,3,2,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,8,3,1,2,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,8,6,7,3,2,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,6,1,3,2,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,8,4,3,2,7,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,8,2,1,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,8,4,3,2,5,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,8,2,6,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,4,2,3,5,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,2,3,6,1,4,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[5,2,3,8,6,4,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,2,3,7,4,8,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[8,6,3,2,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,4,5,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,2,8,1,5,3,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,8,6,4,7,2,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,8,6,4,5,7,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,8,2,5,7,3,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,3,4,7,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,3,4,7,8,2,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[3,8,5,1,4,7,6,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,1,3,6,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,6,8,5,2,7,3,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[3,7,8,5,2,6,4,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,8,6,2,7,4,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,5,4,7,1,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,6,2,8,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,1,5,2,3,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,3,7,8,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[8,4,2,3,6,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,3,7,2,1,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,7,2,8,4,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,5,1,8,4,6,2,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,1,5,6,8,3,7]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[4,1,2,6,5,8,3,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[4,1,8,3,2,6,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,2,7,5,8,1,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,6,2,7,8,3,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[4,6,1,3,8,2,5,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,3,6,2,1,8,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[3,7,4,5,1,6,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,6,4,5,8,2,1,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[6,1,4,5,2,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,2,4,5,1,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,4,1,6,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,5,4,8,6,3,2,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[7,5,4,8,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,8,7,5,3,6,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,7,4,1,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,1,6,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,6,5,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,2,1,5,6,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,4,7,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,1,4,8,6,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,1,8,5,6,7,2,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,7,4,8,6,2,1,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,3,6,8,2,7,1,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,3,7,4,8,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,3,6,1,4,7,2,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[4,3,6,8,2,7,1,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[5,3,7,4,8,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,3,8,4,1,6,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,3,8,1,4,7,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,4,1,6,3,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,3,8,4,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,5,8,3,6,7,4,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,8,2,5,6,7,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,4,1,6,5,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,3,8,1,5,7,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,3,1,2,5,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,6,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,7,4,8,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,1,3,4,7,8,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[2,5,8,7,4,3,6,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,1,7,8,3,4,2,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[2,5,4,8,3,7,6,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,6,8,2,3,4,1,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[2,3,5,7,4,6,8,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[4,5,2,3,8,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[3,7,4,5,8,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,8,1,4,5,2,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[5,8,2,1,6,3,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,1,3,7,5,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,8,5,3,6,1]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[5,3,1,4,7,2,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[4,3,8,5,1,2,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,4,7,5,8,3,6,1]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[4,3,5,8,2,1,7,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,8,5,3,7,1,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,7,3,1,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,5,1,3,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,2,8,5,1,3,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,7,8,4,1,5,2,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,4,7,5,8,2,1,6]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[1,8,5,7,2,4,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,4,2,3,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,8,5,4,2,7]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,6,3,8,2,7,4,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,4,2,7,5,8,3,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,8,2,3,6,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,8,2,7,5,4]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,6,5,4,3,8,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,8,3,4,5,6,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,6,2,4,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,8,3,6,2,7]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,2,7,8,4,5,3,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[7,2,8,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,3,8,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,2,8,7,5,4,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,8,4,3,7,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,2,8,4,3,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,4,7,3,2,6,8,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,5,7,3,6,2,8,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[3,6,2,7,1,5,4,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[1,2,5,4,8,3,7,6]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,4,3,5,8,2,7,6]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,4,3,6,8,7,2,5]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,5,3,7,6,8,2,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,6,4,5,7,8,2,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[4,2,6,5,7,8,1,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[3,2,5,7,6,8,1,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[3,2,4,6,8,7,1,5]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[5,3,2,6,8,4,7,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[3,1,8,6,4,7,2,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,8,5,4,2,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[5,3,2,8,7,6,4,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,3,8,2,7,6,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,5,4,8,3,7,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,8,5,1,3,7,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,8,7,2,6,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,7,5,1,8,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,8,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,6,4,8,1,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,4,8,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,8,5,6,2,7,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,8,7,3,1,6]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[2,4,5,8,6,7,1,3]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[4,3,1,5,6,2,8,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[4,1,5,8,6,7,2,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,3,7,6,1,2,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,7,5,6,1,2,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[4,3,7,5,6,2,8,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,5,1,8,6,7,3,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,4,5,8,6,7,2,1]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[2,1,5,8,6,7,4,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[3,4,5,8,7,1,2,6]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[4,7,1,5,6,2,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[2,6,4,7,1,3,8,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,3,8,6,4,7,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,4,1,5,7,8,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[3,6,4,7,2,1,8,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[3,8,4,6,1,7,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,6,4,7,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,5,6,7,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,5,2,7,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,5,2,1,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,5,1,7,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,7,3,2,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,1,4,6,7,2,8,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[6,5,4,7,1,3,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[2,1,6,5,3,7,8,4]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[6,1,4,7,2,3,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,6,2,5,4,8,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[4,1,2,7,5,8,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[6,1,3,5,8,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,6,4,3,1,8,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[6,2,3,5,8,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,7,2,3,8,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,2,1,3,8,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,7,4,1,8,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[4,1,7,5,8,3,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[6,7,1,3,8,4,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,6,7,4,3,8,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[6,1,7,4,2,8,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[2,1,6,7,4,3,8,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[6,7,3,2,1,8,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[2,5,7,3,1,4,8,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[6,7,3,2,8,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,2,6,7,4,3,8,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[2,7,1,8,4,6,3,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,5,8,1,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,7,1,8,4,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[8,2,5,7,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,7,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,6,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,7,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,6,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,5,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,2,7,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,5,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,2,7,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,7,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,3,7,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,7,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,3,1,6,7]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[2,7,4,6,1,5,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,4,3,8,5,1,6,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[7,8,3,2,5,4,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,5,6,7,3,8,2,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,6,5,4,8,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,7,3,5,8,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,2,1,6,4,8,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,8,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,8,7,2,4,6,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,6,4,8,5,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[3,1,8,7,6,4,2,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,8,7,5,4,2,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,7,6,5,4,2,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[4,7,1,6,5,3,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,8,1,6,5,3,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,4,1,7,6,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,8,6,3,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,4,1,7,6,3,2,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[6,4,1,8,5,3,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,4,1,7,5,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,6,5,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,6,1,4,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,5,6,1,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,4,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,1,4,3,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,8,6,1,4,3,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,4,3,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[8,7,5,1,4,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,7,2,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,4,2,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,6,4,5,8,7,2]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[3,1,6,4,5,8,2,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[3,1,6,4,5,7,2,8]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[4,6,8,7,2,5,1,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[7,6,3,8,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,2,7,6,1,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,8,1,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,6,3,8,4,1,2,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[8,2,7,6,1,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,4,7,1,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[5,2,3,7,1,6,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[5,2,3,4,7,8,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[8,7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,8,5,2,3,6]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,2,6,7,4,1,5,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[5,8,3,7,6,4,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,2,4,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[3,6,7,1,4,2,5,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[4,7,5,8,2,1,3,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[8,1,2,7,5,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,3,7,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,8,7,5,3,2,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,1,5,4,2,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,7,5,1,4,6,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[5,7,6,1,4,3,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[6,8,1,7,5,4,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,6,3,1,2,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,3,5,7,1,4,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[5,2,6,7,4,8,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[1,7,5,2,6,4,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[7,1,3,6,8,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,2,5,7,8,4,6,3]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,1,2,7,5,4,8,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[6,7,4,1,3,2,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,7,2,8,4,3,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,6,3,5,7,8,2,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[8,6,1,7,5,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,8,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,4,1,6,5,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,7,8,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,2,1,5,7,8,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[5,4,1,6,7,8,2,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[5,1,4,6,7,8,2,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[4,1,5,3,7,8,2,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[8,1,4,6,5,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,4,6,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,1,6,7,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,6,3,8,5]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[6,7,4,1,8,5,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[8,6,4,1,5,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,3,7,1,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[6,1,5,4,8,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,2,8,7,4,3,6,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,7,5,8,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[1,3,6,4,7,8,2,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[4,5,1,3,7,8,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[5,2,3,1,7,8,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[1,6,4,3,7,8,2,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[7,6,4,3,1,5,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,4,6,1,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,4,6,5,1,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,7,8,2,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[6,8,3,5,7,2,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,5,2,4,3,8,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[8,6,5,7,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,8,4,5,7,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[7,5,4,2,6,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,3,8,4,7,5,6,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,7,2,8,6,4,5,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,7,5,8,2,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[4,3,7,8,6,2,5,1]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[3,8,1,7,5,2,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,8,6,1,5,3]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[2,4,8,5,1,7,3,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,8,3,5,1,6,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,4,6,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,2,1,7,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,8,3,2,5,1,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,3,8,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[1,4,6,2,7,5,3,8]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[8,2,7,5,1,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,6,8,3,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[8,2,1,4,5,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,5,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,4,1,5,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,8,2,1,5,4,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,4,2,8,6,5,3,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,4,8,5,2,6,3,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,5,2,4,6,3,8,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,8,5,3,2,6,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,1,3,2,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,2,3,7,8,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,2,8,6,3,1,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,2,3,5,1,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,6,3,4,2,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,2,4,5,7,8,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[8,6,3,2,5,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,3,7,1,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[8,5,3,6,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,8,6,2,1,3]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[1,2,8,4,3,6,7,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,8,3,2,4,6,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,7,5,3,4,6,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,2,7,4,5,3,8,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,7,3,2,6,8,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,2,7,1,4,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,3,6,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,2,1,7,8,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[4,7,8,1,6,5,3,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,5,8,6,1,4,2,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,8,4,2,7,6,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,8,1,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,3,8,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,3,8,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,1,3,7,6,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,7,3,6,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[7,3,8,6,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,5,1,7,8,2,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[5,4,7,8,2,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,3,6,1,8,4,2,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[6,3,8,7,1,5,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,6,4,7,1,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,5,3,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[3,4,6,2,1,8,5,7]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[4,5,7,2,1,6,3,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[5,6,4,8,3,2,1,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,7,4,8,2,1,6,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,7,5,8,2,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[5,7,4,2,6,3,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,7,4,1,6,2,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[8,5,6,1,7,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,6,7,8,3,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[4,5,2,6,1,3,8,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[8,4,6,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,2,5,8,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[7,1,4,6,8,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,1,2,4,8,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,6,3,4,7,8,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[2,3,6,4,7,5,8,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[7,8,1,3,4,5,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,8,2,6,7,3,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,2,8,1,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[7,1,2,6,3,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,1,2,6,3,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,6,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,3,1,6,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,8,3,1,6,2,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[7,4,3,1,6,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,3,1,8,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,7,6,2,4,8,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[4,3,7,2,8,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[6,1,2,7,4,3,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,1,2,6,3,8,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[5,1,2,7,3,8,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[6,1,2,7,3,5,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[8,3,6,2,1,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,1,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,2,1,5,3,6,7,8]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[6,2,5,4,1,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,6,3,2,1,8,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[6,5,3,2,1,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,4,3,2,7,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,4,7,6,3,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,2,7,4,8,6,1,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[7,4,3,2,8,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,8,3,7,5,2,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,7,8,4,3,2,1,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[6,4,3,8,5,2,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,2,5,4,7,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,4,8,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,5,3,2,8,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[3,2,5,4,8,6,1,7]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[3,2,8,6,5,4,1,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,4,3,6,5,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,5,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,7,8,5,4,1,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[6,8,7,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,6,1,4,8,7,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[5,8,1,3,7,2,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,7,5,1,8,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[6,3,2,1,8,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,2,3,1,8,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,4,7,1,8,5,6,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[3,4,8,1,7,5,6,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[7,2,5,1,8,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,1,5,8,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,2,8,1,7,5,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,3,6,4,1,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,5,2,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,6,4,2,8,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,7,4,1,5,8,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[5,8,6,1,2,7,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,1,4,3,7,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,1,4,3,8,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[4,7,1,5,3,8,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[6,8,1,2,4,7,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,1,6,4,8,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,6,4,1,3,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,1,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,1,4,5,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,5,6,1,2,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,4,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,4,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,3,6,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,2,4,5,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,3,2,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,8,3,6,7,2,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,8,3,7,4,6,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,2,6,5,4,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,4,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,2,1,8,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[3,7,1,8,2,5,4,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[4,5,8,6,1,3,7,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,6,2,7,3,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,6,7,1,5,3,8,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[4,6,7,2,1,8,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[4,2,5,6,7,8,3,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[4,1,3,5,6,7,8,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,7,8,4,5,1,6,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,6,8,3,2,7,1,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,8,2,3,7,1,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[3,8,1,7,4,5,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,8,3,7,1,2,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,7,8,4,6,2,5,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,6,1,5,7,8,2,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[3,8,2,5,4,7,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,2,5,1,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,8,6,2,1,7,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,6,1,2,7,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,6,8,5,2,7,1,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[3,7,8,5,2,6,1,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,8,5,4,1,6,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,6,8,5,3,1,7,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[7,8,2,3,5,4,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,1,3,7,6,4,8,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[4,6,5,2,7,8,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[1,6,5,2,3,4,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[4,6,5,1,7,3,8,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[5,7,3,1,2,4,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[6,3,2,5,1,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,1,2,4,8,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,3,1,7,2,5,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[3,7,2,8,5,1,4,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,6,5,2,4,7,1,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[3,6,5,8,1,7,2,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,7,3,4,6,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[1,3,5,8,6,4,7,2]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,3,5,8,6,7,2,4]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[6,1,7,4,8,5,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,7,4,1,3,6,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[7,4,3,1,6,5,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,6,1,7,5,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,6,5,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,6,1,4,5,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,1,7,6,3,4,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[6,2,7,3,8,5,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,2,7,5,3,4,8,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[7,2,8,3,6,4,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,7,8,3,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,7,8,2,5,3,4,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,8,1,2,5,6,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,2,8,7,3,4,6,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,2,7,4,5,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,7,2,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,4,8,6,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,8,6,4,5,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,5,1,4,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,8,3,4,2,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[6,8,4,3,1,7,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,4,1,3,7,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,7,5,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,7,4,2,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,6,8,5,3,4,7]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[4,5,1,3,8,6,7,2]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[1,2,6,8,5,3,4,7]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[5,6,8,7,3,1,2,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,7,5,3,8,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,2,3,4,7,1,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,8,5,7,3,1,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,7,8,6,3,1,2,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,1,4,2,6,8,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[6,3,2,4,7,1,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,5,6,8,4,2,3,7]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[5,7,8,3,6,1,2,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,5,8,6,2,4,3,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,5,3,7,2,6,8,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[5,1,8,6,2,4,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,6,3,7,1,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,5,2,4,8,6,7,3]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,5,4,2,6,8,7,3]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[5,7,6,3,8,1,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,6,8,3,1,2,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[6,8,7,5,3,1,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,2,5,3,6,8,7,4]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[6,8,7,2,1,5,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,3,6,1,4,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,8,1,6,5,3,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,3,2,1,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,6,4,3,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,8,6,3,4,1,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,2,8,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[1,7,2,3,5,8,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[4,6,2,3,5,1,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[2,8,3,7,5,1,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,8,7,2,1,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,8,4,3,6,7,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,5,6,1,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,6,7,8,2,4,3,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[4,1,2,8,5,3,7,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,8,4,2,5,1,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,6,4,3,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,5,6,4,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,6,8,2,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[7,6,8,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,1,4,5,3,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,5,2,7,4,3,6,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[5,1,3,8,4,6,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,5,8,7,1,3,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,7,3,5,1,6,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,7,6,8,2,1,4,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[1,3,6,5,2,7,4,8]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,2,6,5,3,4,7,8]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,7,2,5,6,8,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,2,4,8,3,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,6,2,4,5,3,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,3,2,8,4,5,7,6]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,6,8,2,4,3,5,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,6,7,2,5,3,4,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,2,8,3,6,7,4,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,5,3,4,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[7,1,5,6,2,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,1,4,6,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,1,3,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,1,3,7,2,5,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[6,2,7,5,1,3,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,7,5,6,2,3,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,7,6,1,2,4,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[8,6,1,3,5,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,8,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,5,3,4,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[3,6,7,5,2,8,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[7,8,4,1,5,6,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,8,1,3,6,7,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,8,4,3,7,1,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,6,7,1,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,3,8,4,7,1,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,2,5,4,8,3,6,7]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[7,1,3,8,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,1,3,7,2,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,7,8,1,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[8,3,1,4,7,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,8,2,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,2,3,6,7,8,1,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[6,2,7,3,8,5,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,3,7,8,5,6,2,4]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[8,2,6,7,5,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,4,6,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,7,1,3,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,7,1,2,3,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,1,8,5,7,2,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,8,7,4,6,2,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,1,8,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[6,2,5,1,4,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,5,4,1,3,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,3,5,4,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,3,8,7,4,2,6,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[8,7,4,3,1,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,1,4,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,4,5,1,6,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,5,4,1,3,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,5,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,5,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,7,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,8,5,7,6,3]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[8,2,1,4,7,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,4,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,2,3,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,8,7,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[8,5,1,2,4,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,4,1,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,5,7,6,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,1,8,7,6,4,5]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[4,2,8,7,3,1,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,3,4,8,7,2,5,6]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[8,1,3,4,6,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,2,6,7,1,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,6,8,2,5,1,7,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,8,2,5,7,4,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,2,1,7,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,6,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,5,4,1,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,5,4,1,7,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,1,5,7,6,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,8,2,7,5,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,5,7,1,6,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,3,6,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,7,2,1,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,6,5,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,8,1,7,4,6,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[8,4,7,1,3,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,6,8,1,5]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[3,8,1,2,5,6,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,2,5,6,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[8,5,2,1,4,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,6,5,2,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,2,6,3,8,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,5,2,6,7,1,8,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[8,3,5,4,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,4,7,3,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,8,6,5,2,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,3,1,5,2,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,4,1,5,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,2,4,1,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,2,6,8,4,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,3,2,4,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,2,4,6,1,3,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[7,2,3,4,6,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,3,4,6,7,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,4,7,5,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,6,1,3,4,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,1,5,7,6,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,6,8,2,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,7,1,6,8,3,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,5,2,8,1,7,3,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,7,5,2,8,6,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,8,5,2,6,7,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,4,8,6,1,2,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,4,6,5,2,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,7,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,6,4,8,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[8,6,2,3,5,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,7,4,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,6,8,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,3,5,6,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,5,8,4,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,3,8,4,7,1,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,1,4,3,2,8,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,3,6,1,4,2,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[5,7,2,1,4,3,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[7,1,8,3,5,2,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,4,8,1,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,8,4,2,5,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,4,2,5,8,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,1,7,5,8,3,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[7,3,8,5,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,4,8,1,5,6,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,4,8,3,1,5,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,5,8,3,7,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,6,3,5,8,7,4,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[8,6,5,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,3,7,2,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,4,8,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,5,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,8,4,1,3,5,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,3,4,1,5,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,3,1,8,2,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,3,8,1,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,4,8,7,3,2,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,7,4,8,6,3,1,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,4,8,2,3,1,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,1,8,3,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,1,6,3,8,2,4,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[3,6,5,1,4,8,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[7,3,6,2,8,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,1,8,4,7,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,5,4,8,1,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,3,5,8,7,1,2,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[3,5,6,8,1,4,2,7]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[4,3,5,8,2,1,6,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[6,4,7,2,3,1,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,8,1,5,4,2,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,6,3,1,4,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,2,8,5,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,8,4,7,2,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,6,4,3,7,1,8,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[6,5,3,7,2,4,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,6,2,8,4,3,7,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,1,2,6,8,3,7,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[7,1,3,6,5,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,7,4,3,6,8,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[4,6,2,7,8,3,5,1]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[5,1,2,4,6,7,8,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[4,6,3,5,2,8,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[5,6,3,4,8,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,2,6,4,1,7,8,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[5,8,4,6,3,2,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,4,3,8,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,7,8,2,4,3,6,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,6,2,4,8,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[6,4,7,8,2,3,5,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[3,7,5,2,4,8,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[4,7,5,2,3,8,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[6,4,7,3,2,5,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,7,3,2,8,4,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,3,7,2,8,4,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[4,3,7,2,5,8,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,7,3,2,5,8,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,7,3,2,6,8,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[7,5,3,2,6,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,5,2,6,7,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,3,8,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,6,2,8,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,7,6,2,8,3,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[4,7,6,2,3,8,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[7,6,3,2,5,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,4,2,5,8,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,3,8,5,4,7,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,4,6,3,8,7,5,1]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,1,8,7,3,5]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,3,6,8,7,1,5]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[2,4,6,3,8,7,1,5]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,5,8,7,1,3]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,8,5,7,3,1]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,5,7,1,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,3,7,1,5]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,1,7,3,5]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,5,1,8,7,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[2,4,6,5,8,3,7,1]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,5,8,1,7,3]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,8,5,1,7,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,7,3,5,1]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,7,1,5,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,7,1,3,5]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,5,1,3,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,5,1,8,3,7]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[2,4,6,5,1,3,8,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[2,4,6,5,3,8,1,7]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[2,4,6,5,8,3,1,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,8,5,3,1,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,7,3,1,5]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,6,8,7,5,1,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[4,8,7,5,2,1,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,7,5,8,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,8,6,5,3,2,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,8,2,4,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[4,6,1,7,8,5,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[6,1,2,7,8,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,1,3,2,7,8,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,6,3,1,7,4,8,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[4,8,3,7,1,6,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,7,2,6,5,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,2,1,7,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,4,3,8,1,7,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,5,3,8,7,1,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,3,8,2,7,6,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,2,7,6,5,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,8,2,6,5,4,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,8,7,6,2,5,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,7,2,1,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,6,3,1,7,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,7,1,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,7,6,2,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,7,6,4,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,4,2,1,7,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,2,5,3,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,8,6,2,7,3,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,4,5,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,5,2,6,4,3,7,8]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,5,2,4,6,3,7,8]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,8,6,2,3,7,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,8,6,3,4,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,3,6,8,2,7,4,5]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,4,3,8,2,5,6,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,7,2,3,8,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,3,8,4,2,5,6,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,8,5,4,3,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,7,2,3,8,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,5,3,8,2,7,4,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,4,8,2,5,6,3,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,5,7,3,2,8,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,2,7,3,6,8,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,7,2,3,6,8,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,4,8,3,2,5,6,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,7,2,5,8,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,3,5,8,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,2,4,8,1,6,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[2,6,4,5,7,3,1,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[2,5,6,3,4,7,1,8]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,3,7,5,6,8,4,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,3,6,7,4,5,8,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,5,6,3,4,2,7,8]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,5,6,3,4,7,2,8]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,5,3,6,4,2,7,8]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,7,5,6,8,3,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,5,6,3,8,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,3,7,5,2,8,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,3,7,2,5,8,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,5,3,7,4,6,2,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,5,3,7,6,4,2,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,5,3,6,7,4,2,8]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,5,6,3,7,4,2,8]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,5,7,6,3,4,8,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,5,7,3,6,4,8,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,3,7,2,5,6,8,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,3,7,5,6,2,8,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,5,7,4,1,3,8,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[6,7,3,1,8,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,3,1,5,8,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,3,5,1,7,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,5,8,2,1,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[7,2,4,8,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,3,6,4,1,8,7,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[7,4,5,2,1,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,7,5,2,1,8,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[8,5,3,6,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,3,1,2,8,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[4,5,1,8,3,2,7,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[5,7,4,6,3,2,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[3,6,1,2,4,8,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[2,5,3,8,4,1,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[8,6,2,3,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,1,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,3,1,2,4,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,7,5,2,3,6,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[3,6,8,4,5,1,2,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,2,3,7,6,4,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[6,2,7,3,5,4,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,2,6,5,3,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,6,5,4,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,5,1,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,3,1,7,8,5,6,4]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[7,2,8,5,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,6,7,1,4,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,1,4,3,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,5,3,1,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,7,8,5,1,4,2,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,8,7,3,1,2,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,6,2,3,1,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,4,2,1,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,8,2,1,6,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,7,4,1,8,2,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,8,4,1,7,6,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,8,4,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[8,7,1,6,5,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,7,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,1,7,6,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,7,8,2,4,6,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[7,8,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,5,3,7,8,2,6,1]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[1,5,4,7,3,6,2,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,7,3,6,8,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[4,6,8,2,7,3,5,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,7,6,3,5,1,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[7,8,3,6,1,5,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,5,7,8,4,6,1,3]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[3,7,5,6,2,1,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,1,7,4,5,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,2,6,4,7,5,3,8]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[7,5,6,3,8,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,5,4,2,1,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,7,5,1,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,7,5,1,4,8,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[7,4,1,6,5,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,8,2,7,3,6,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,6,5,7,3,8,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,5,6,8,4,2,7,3]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[7,5,4,1,8,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,4,1,8,2,7,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,8,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,2,5,1,7,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,3,8,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[3,4,2,7,8,6,1,5]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[7,8,6,1,4,3,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,4,7,8,6,1,3,5]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,7,8,6,5,2,4,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,5,2,7,8,6,3,1]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[4,6,2,5,3,1,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[4,1,5,6,3,2,7,8]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[2,6,7,5,4,1,3,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[4,1,6,7,5,3,2,8]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[6,7,4,3,1,5,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,7,5,6,4,3,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[7,6,5,3,1,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,8,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,1,7,8,6,5,3,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[4,5,7,3,8,6,1,2]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[6,8,5,3,7,2,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,7,1,5,8,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[3,7,6,2,1,8,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,5,8,3,6,4,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,4,8,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,4,8,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,3,8,1,6,5,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,3,6,5,7,8,1,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[8,3,4,1,2,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,5,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,4,5,1,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,1,2,8,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,8,2,3,5,7,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,3,8,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[6,7,4,8,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[4,3,5,6,1,7,8,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[3,5,2,6,4,7,8,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[4,1,2,8,5,7,6,3]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,1,5,6,4,7,8,2]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[3,1,4,6,7,5,8,2]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[2,6,4,5,8,1,3,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[6,4,1,3,5,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[3,4,1,7,2,6,8,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[2,4,7,5,8,1,3,6]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[3,1,6,4,8,7,5,2]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[3,7,6,2,1,5,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[4,2,6,1,3,7,8,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[8,5,4,2,7,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,6,7,1,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,2,1,4,6,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,4,6,1,2,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,2,6,5,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[5,6,2,8,7,1,3,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[7,1,3,8,4,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,8,1,4,3,5,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,6,7,2,8,1,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[2,6,7,1,3,5,8,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[3,6,7,1,8,2,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[3,4,1,8,7,2,6,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,5,7,2,8,6,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[3,8,1,4,7,2,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,3,2,7,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,8,3,2,7,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,1,2,7,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,2,1,7,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,8,4,2,7,1,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,3,7,6,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,4,7,1,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,8,7,1,6,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,2,5,7,1,8,6,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[4,2,8,3,1,7,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,2,1,3,7,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,2,8,1,3,7,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,3,4,6,8,7,1,5]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[5,6,4,7,1,2,8,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[4,6,7,5,8,2,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[4,5,7,1,6,8,3,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[3,2,7,6,8,1,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[4,5,1,7,6,8,2,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[6,7,2,8,3,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[7,6,3,1,2,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,2,7,8,4,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[6,3,7,8,4,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,8,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,6,2,3,1,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,2,5,1,3,7,8,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[3,5,1,4,2,7,8,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[3,4,1,7,8,5,2,6]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[4,1,3,7,8,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[4,3,1,8,5,2,7,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,1,8,5,4,2,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,6,3,5,8,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,5,1,3,2,7,8,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[5,1,3,2,4,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[2,3,7,8,5,4,1,6]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[8,3,5,6,1,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,2,6,7,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,3,6,7,8,2,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,3,4,8,6,2,7,5]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[7,2,4,1,3,8,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,8,2,5,4,1,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,5,2,6,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,2,3,7,5,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,5,7,2,3,6,1,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[2,7,3,4,1,5,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,7,2,3,4,8,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[3,5,2,4,6,7,8,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[4,2,6,3,5,7,8,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[1,4,8,5,6,2,7,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,5,6,1,7,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,3,5,8,4,7,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,8,7,4,5,1,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,8,5,2,6,7,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[7,2,8,4,5,1,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,3,5,1,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[8,6,2,4,1,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,3,2,7,8,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[8,5,3,2,1,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,2,3,6,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[7,1,5,2,3,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,2,5,3,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,3,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,3,8,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[5,2,6,8,3,7,1,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,2,5,8,6,7,1,3]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[5,8,6,3,4,1,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,7,2,4,1,8,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[2,4,7,8,5,1,3,6]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[2,5,3,8,4,1,6,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[3,1,7,4,5,6,2,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[2,4,8,3,5,7,1,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[8,1,7,2,4,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,2,4,7,5,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,7,2,4,6,5,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,7,3,2,4,6,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,3,7,4,2,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,3,1,4,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,5,7,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,7,4,1,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,7,4,6,5,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[3,2,6,5,1,7,8,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[5,3,2,6,7,1,8,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[3,2,8,6,7,4,1,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,4,6,2,7,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,7,2,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,6,2,8,7,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[3,8,4,7,6,5,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,2,7,8,6,4,5,1]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[3,2,7,5,6,8,4,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[5,7,8,6,3,2,4,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[6,5,4,2,1,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,4,2,1,7,6,3,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[4,1,6,5,2,7,8,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[5,4,1,6,7,2,8,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[6,8,5,3,1,7,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,2,6,3,8,7,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[8,6,1,7,3,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,6,7,4,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,5,2,7,8,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,5,7,3,2,6,4,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[5,1,3,7,2,6,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[8,1,6,7,2,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,8,2,7,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,4,8,3,7,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,7,2,6,3,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,5,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,6,8,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,7,1,5,2,4,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,6,1,5,2,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,6,3,5,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,6,7,3,5,4,8,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,7,3,5,6,8,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,8,3,6,4,5,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,8,7,6,4,5,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,7,4,6,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,6,4,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,1,6,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,1,7,5,6,8,3,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[5,6,7,4,3,1,8,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[6,7,8,5,3,1,4,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,4,6,2,5,3,7,8]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,6,3,2,5,4,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,6,8,2,5,4,7,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,5,4,2,6,3,7,8]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,2,6,4,3,5,7,8]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,6,8,2,7,5,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,7,4,3,2,6,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,5,4,7,2,6,8,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,3,7,6,2,8,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,7,6,2,8,4,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,5,2,8,4,3,7,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,2,8,4,3,6,5,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,5,6,3,4,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,3,5,2,8,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,6,7,2,5,8,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,5,8,3,2,7,4,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,5,8,2,6,3,7]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,7,6,4,8,2,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,4,8,6,5,2,7,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,3,8,2,6,5,4,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,7,6,3,8,2,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,5,2,7,6,4,8,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,2,4,3,8,7,5,6]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,4,3,8,7,2,5,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,3,8,6,2,4,5,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,5,4,2,6,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,7,2,4,8,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,6,5,3,2,8,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,3,2,8,7,5,4,6]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,2,8,6,5,4,3,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,1,3,4,6,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,6,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,2,6,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,1,7,5,2,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,7,5,2,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,5,1,4,2,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,5,6,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,1,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,4,2,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,4,1,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,1,5,2,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,1,5,2,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,6,8,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,8,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,8,7,5,4,1,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,7,5,1,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,6,8,4,1,5,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,6,1,5,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,1,6,5,3,4,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,3,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,1,3,4,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,3,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,3,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,5,4,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,3,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,8,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,3,8,2,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,4,2,5,3,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,3,7,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,4,8,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,3,1,6,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,6,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,4,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,2,7,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,7,8,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[7,6,3,4,1,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,7,3,1,6,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,2,4,6,5,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,1,7,3,5,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,4,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,7,6,4,2,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[7,5,3,2,1,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,5,3,1,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,8,6,4,3,2,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,6,4,2,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,6,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,7,5,3,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[7,6,2,5,8,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,7,3,6,8,5,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[8,6,2,5,7,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,6,8,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,8,3,6,7,5,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,7,6,4,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,6,4,5,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,6,2,7,4,5,3,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,8,2,6,4,3,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,4,3,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,2,5,4,6,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5,7,2,8,3,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,5,7,2,8,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,2,7,5,8,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,7,2,5,8,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,5,7,3,8,1,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,3,7,4,8,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,3,7,4,8,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,2,7,4,8,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[8,7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,1,4,3,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,8,5,1,4,3,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,7,6,8,3,5,1,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,2,1,5,3,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,8,2,7,6,1,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,1,8,7,3,4,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,2,3,6,7,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,1,5,8,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[2,4,8,7,5,3,1,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,6,8,7,5,3,4,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,6,5,1,4,3,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[6,5,1,2,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,6,5,3,1,2,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[4,8,7,5,3,1,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,6,8,7,5,3,1,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[6,8,7,5,3,1,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,6,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,8,7,3,6,5]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[4,8,7,3,1,2,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,7,3,4,1,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,6,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,3,4,6,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,3,6,5,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,1,6,5,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,2,6,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,4,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,7,3,4,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,7,5,1,2,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,4,3,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,3,4,1,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,5,6,3,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,8,7,3,1,6,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,8,7,3,1,4,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,3,1,8,7,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[4,3,1,2,6,8,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[2,8,7,5,6,3,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,5,3,1,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,5,3,6,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,5,6,1,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,8,7,5,1,4,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,8,7,5,1,2,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,7,5,6,1,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,4,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,7,3,6,5,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[8,7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,7,1,2,6,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,3,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,4,1,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,3,5,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,2,6,4,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,2,4,3,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,7,3,6,5,1,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[7,5,4,2,8,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,3,6,1,5,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,5,7,2,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[5,7,2,1,8,4,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[7,2,8,6,4,3,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,3,8,7,4,2,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,6,3,2,8,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,6,1,3,2,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,7,4,2,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,1,7,3,5,8,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[8,4,7,3,5,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,1,3,2,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,5,8,2,1,3,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[8,1,3,5,2,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,7,2,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,2,1,3,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,7,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,3,6,8,2,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,3,4,7,6,8,2,5]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,2,4,7,8,5,3,6]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[5,1,7,3,6,8,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[1,8,2,7,5,4,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,1,7,3,2,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,7,1,2,8,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[2,1,3,8,6,5,4,7]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,3,2,8,6,5,4,7]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,5,7,1,8,4,3,6]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[3,5,7,1,6,8,2,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[5,4,7,6,8,3,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[8,4,6,7,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,8,6,7,3,1,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,3,8,7,5,4,1,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[8,1,7,6,4,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,8,1,7,4,3,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,1,8,7,3,6,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,6,8,4,1,7,3,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,5,8,7,3,1,6,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,1,8,4,7,6,5,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,5,8,4,3,7,6,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[8,1,7,2,5,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,5,2,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,4,8,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,6,2,4,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,6,7,5,8,3]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[8,1,4,5,6,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,6,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,6,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,7,8,6,4,3]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[3,5,6,2,8,7,4,1]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[2,4,5,1,7,6,3,8]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[7,3,1,5,6,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,3,2,5,6,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,2,8,1,7]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[3,7,4,2,8,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[7,3,4,1,6,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,6,3,1,4,7,5,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[7,2,1,6,3,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,3,4,1,6,5,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,7,4,2,5,8,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[2,3,5,1,4,8,7,6]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[2,7,1,3,6,8,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,1,3,8,4,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,8,7,1,6,2,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,1,4,5,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,1,8,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[4,8,5,7,2,6,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,4,5,7,3,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,4,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,1,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,1,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,6,2,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,7,4,6,1,5,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,4,7,6,1,2,8,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[4,5,8,7,6,1,3,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[8,6,3,7,5,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,6,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,1,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,5,2,7,6,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,4,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,1,5,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[8,4,2,5,1,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,1,6,4,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,1,4,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,5,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,7,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,1,7,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,1,6,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,8,1,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,8,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,4,7,3,1,5,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[8,5,3,1,6,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,5,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,2,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,2,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,2,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,2,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,7,4,2,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,6,3,8,4,2,5,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[4,7,2,5,3,6,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[1,8,3,4,5,2,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,4,2,5,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,6,4,1,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,6,1,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,8,7,5,3,1,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,1,4,8,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,1,8,5,3,2,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,1,6,4,2,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,4,2,5,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,2,7,4,3,5,6,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[6,1,8,5,2,4,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,2,5,1,4,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,5,2,1,6,8,7,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[7,2,8,6,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,6,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,7,2,6,1,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,2,4,3,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,6,3,1,2,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,5,3,1,2,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,5,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,5,6,2,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,4,1,5,2,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,2,8,1,6,4,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[5,2,1,3,7,6,4,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[5,4,1,2,8,3,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,8,4,1,2,3,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,1,2,5,3,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,6,7,3,2,8,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,8,6,3,2,7,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,3,7,2,8,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,4,6,2,8,5,3,7]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,5,6,2,8,4,3,7]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[2,4,6,3,1,7,5,8]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[3,4,8,6,5,7,2,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,2,4,7,3,6,5,8]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,2,5,7,4,3,6,8]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,2,5,7,4,6,8,3]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,2,4,7,6,8,3,5]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[3,5,8,6,1,7,2,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,3,6,8,1,7,4,5]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[2,3,7,1,8,6,4,5]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[2,6,1,7,8,5,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[2,4,8,5,6,7,1,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,4,8,5,6,7,3,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,2,1,6,8,4,7,5]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[4,8,3,1,6,5,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,6,8,5,4,2,7,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,5,8,4,2,1,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,7,8,6,5,4,2,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,8,7,4,5,1,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,1,3,5,4,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[3,6,4,2,5,1,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[2,1,5,8,6,4,7,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[4,2,8,5,6,3,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,3,7,2,6,8,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,7,2,3,4,6,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[1,8,7,3,2,5,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,1,2,3,8,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[7,8,6,2,4,1,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,2,8,4,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,6,2,8,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,5,8,2,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,4,8,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,1,8,4,2,3,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,3,6,2,1,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,8,6,4,2,5,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,2,1,8,4,7,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[2,8,1,6,5,7,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,6,4,3,8,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[5,4,6,8,1,3,7,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[3,7,1,6,4,5,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[3,5,2,1,4,6,7,8]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[1,3,8,7,5,4,6,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[6,7,3,4,8,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,4,1,8,2,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,1,7,2,5,6,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[4,1,5,7,3,2,8,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[6,4,1,7,2,8,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[7,3,1,6,2,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,8,2,5,3,1,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,1,3,4,8,2,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,1,4,5,7,8,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,3,4,7,1,8,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[7,8,5,1,3,4,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,3,4,5,6,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,5,2,7,6,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,5,6,2,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,2,5,6,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,1,6,8,7,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[5,4,2,7,8,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[6,8,7,2,1,3,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,7,6,8,5,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,8,5,2,6,3,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,6,1,2,5,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,2,4,8,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,5,7,3,8,6,2,4]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[6,7,5,1,8,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,6,1,2,4,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,2,1,5,3,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[4,3,2,8,7,1,6,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,8,3,2,7,1,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,1,7,6,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,3,8,7,1,6,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,7,3,1,6,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,3,8,2,1,7,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,8,7,2,6,5,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,8,6,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,4,2,8,1,7,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,8,4,2,1,7,6,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,4,7,1,6,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,4,8,3,1,7,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,5,6,1,4,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,1,2,5,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,6,7,4,2,5,8,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[3,6,7,5,8,1,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[1,6,7,5,8,3,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[3,8,6,5,7,4,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,5,7,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,8,4,7,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[6,5,8,7,4,2,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,5,7,4,2,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,6,7,5,8,2,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[4,7,5,3,8,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,7,5,3,6,1,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,7,5,3,1,6,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[2,7,5,3,6,4,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,7,5,3,8,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[2,7,5,8,6,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,5,6,8,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,5,6,8,3,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[4,7,5,3,6,8,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[2,7,5,6,3,8,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,7,5,3,6,8,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,3,1,4,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,7,5,3,4,8,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,7,6,2,8,3,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,1,6,3,2,4,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[5,7,6,1,8,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[3,8,7,2,1,5,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,8,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[4,8,5,6,7,3,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,8,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[6,1,7,3,8,5,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,1,8,3,2,5,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,8,3,1,5,4,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[4,8,5,6,7,2,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,2,7,4,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,4,6,7,8,5,1,3]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[2,4,6,7,8,3,1,5]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[4,7,6,2,8,5,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,8,7,3,2,4,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,6,5,8,7,3,1,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[8,3,1,7,2,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,2,8,7,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[5,6,1,2,8,3,7,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,8,7,1,6,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,4,5,1,7,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,4,8,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,5,6,1,7,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,1,3,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,7,6,1,3,8,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,7,1,4,2,8,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[2,1,6,4,8,3,7,5]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[7,4,5,1,3,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,5,7,8,4,2,3,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,3,6,4,2,5,7,8]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,4,5,7,8,3,6,2]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,5,7,8,3,6,2,4]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,5,7,8,2,4,3,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[6,8,4,7,3,2,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,4,2,7,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,4,6,3,2,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,8,5,3,2,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,5,6,1,4,2,7,8]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[1,6,3,8,4,2,7,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[7,1,3,2,4,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,6,5,7,8,3,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[4,1,8,2,6,7,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,6,7,8,2,1,4,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[2,5,7,1,6,3,4,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[4,2,8,3,6,5,1,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,3,8,7,2,4,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,6,1,8,2,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,5,6,3,4,8,1,7]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[5,2,4,7,8,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[7,2,1,3,4,8,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,4,5,7,1,8,6,3]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[8,1,6,2,3,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,2,5,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,6,7,2,4,3,5,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,8,3,4,5,2,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,6,4,7,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,5,6,3,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[7,3,5,8,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,4,8,6,7,2,1,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,2,5,1,7,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,7,2,5,8,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,4,6,7,8,3,5,2]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[4,1,5,3,6,8,7,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[3,7,5,1,6,8,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[5,8,7,4,6,2,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,8,1,5,7,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,6,8,3,5,2,7,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[7,2,1,8,6,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,4,7,8,5,6,1,3]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[4,1,7,8,5,6,3,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[2,6,3,8,5,1,7,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[4,1,5,8,6,7,3,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,5,8,2,6,3,1,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,3,4,7,6,1,2,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[2,8,5,4,1,3,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,8,7,1,3,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,4,6,3,1,7,2,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[4,3,6,5,1,8,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[1,5,6,8,7,3,2,4]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,4,8,3,6,5,2,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,3,8,6,4,7,2,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,6,4,3,7,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,1,8,7,3,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,1,7,6,8,3,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[8,1,4,5,7,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,6,2,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,2,6,1,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,4,5,2,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[2,6,3,7,4,8,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[4,6,1,7,8,2,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[7,2,3,8,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,2,6,7,8,3,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[6,5,8,1,2,7,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,1,8,7,2,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,8,4,3,7,2,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,1,2,8,7,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,3,2,8,4,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,5,1,7,6,2,8,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[1,5,2,7,6,3,4,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[7,2,6,8,3,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,8,1,7,6,2,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,2,8,6,5,3,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,1,8,7,6,5,2,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[7,6,5,2,8,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,1,8,7,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,5,1,8,6,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,5,1,7,6,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,6,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,6,1,5,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,7,5,4,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,1,8,7,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[3,4,8,1,5,2,6,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[8,6,5,7,1,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,6,2,7,4,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,1,8,5,7,2,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[6,8,5,3,4,2,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,5,2,6,4,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,6,1,4,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,8,1,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,2,6,7,1,8,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[3,4,6,7,8,2,1,5]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[3,2,6,7,8,4,1,5]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[6,2,7,4,8,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,7,1,3,8,5,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,1,8,5,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,2,6,7,8,5,3,4]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,6,7,4,8,3,2,5]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,4,6,7,8,3,2,5]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[6,1,2,4,5,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[8,1,7,3,2,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,1,5,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,8,6,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,6,5,2,4,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,4,3,1,5,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,8,7,2,3,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,6,1,2,7,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,8,2,7,1,5,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[2,8,6,1,4,5,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,7,2,5,4,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,2,6,4,8,7,5,1]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[4,7,2,8,6,5,1,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,1,8,6,5,3,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[2,7,4,8,3,6,1,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[4,7,3,8,6,1,5,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,3,6,8,7,2,5,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,3,8,2,5,7,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,2,6,8,7,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[3,1,6,4,8,7,2,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[4,1,6,8,7,5,2,3]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[3,8,1,4,5,7,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,4,2,5,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,8,3,5,2,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,8,1,2,5,4,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,6,8,7,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[4,2,8,3,5,1,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,2,8,3,5,7,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,8,2,4,5,7,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,2,5,1,4,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,8,5,7,1,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,8,1,5,2,4,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,4,1,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,8,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,4,2,5,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,2,1,4,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,1,4,3,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,1,3,5,6,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,7,1,3,5,6,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,6,2,1,5,8,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[2,3,6,1,5,8,7,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[3,4,7,1,5,6,8,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,7,4,1,2,8,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[4,3,2,7,1,6,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[7,3,2,8,1,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,8,1,5,6,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,6,8,1,5,3,7,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,8,2,1,5,3,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,2,5,3,6,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,5,8,2,3,6,7,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[2,4,8,5,3,6,7,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[5,3,2,6,4,8,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[2,4,5,3,8,6,7,1]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[4,3,5,2,8,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[4,8,5,3,2,6,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,2,8,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[4,1,2,7,5,6,8,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[5,6,7,4,2,8,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[2,5,7,4,6,8,3,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[7,5,2,4,3,8,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,8,1,2,5,4,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,4,1,8,5,2,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,6,1,8,5,4,7,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[7,1,2,8,5,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,3,2,6,8,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[3,7,6,4,8,5,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,1,6,8,5,4,7,2]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[2,3,5,8,4,6,7,1]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[3,5,2,8,4,6,7,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,4,5,8,2,6,7,1]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[5,4,2,8,3,6,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,3,4,8,2,6,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[2,5,4,8,3,6,7,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[6,3,2,5,8,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,1,8,3,5,4,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,4,8,3,2,6,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,2,3,4,6,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,2,1,7,8,5,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[7,4,6,8,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,4,5,2,7,1,6,8]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[7,5,6,1,2,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,5,7,6,3,2,8,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[8,4,6,7,3,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,3,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,1,4,3,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,1,7,8,5,4,2,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[7,6,4,8,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,8,5,6,1,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,8,5,1,3,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,2,7,8,6,1,4,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[6,8,2,5,1,3,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,4,2,1,5,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[5,7,4,1,3,6,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[4,2,7,5,1,8,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,1,6,5,3,8,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[1,5,4,6,3,8,2,7]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,8,6,4,7,3,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,8,6,3,5,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[5,4,8,1,7,3,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,3,8,6,2,1,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,3,6,2,4,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,2,8,5,3,1,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,5,4,8,7,3,6,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[6,4,2,8,7,3,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,6,8,1,7,4,2,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[7,8,6,3,1,4,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,8,6,1,7,5,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,8,3,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,8,7,5,2,1,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,6,2,8,5,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,5,7,6,2,8,4,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,6,5,2,7,8,4,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[4,7,8,5,6,2,3,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[2,7,8,5,6,1,4,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,8,4,2,1,5,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[4,7,8,1,2,5,6,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[8,6,4,1,2,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,4,7,2,5,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,7,8,3,5,4,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,2,1,5,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[5,6,3,2,7,4,1,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[2,6,4,3,7,5,8,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[7,2,3,6,1,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,4,6,5,7,1,2,8]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[7,6,2,3,5,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,5,2,4,3,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,2,1,5,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,3,6,7,8,5,1,4]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[8,3,7,1,6,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,6,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,4,1,6,8,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,5,1,2,8,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,6,8,1,3,7,2,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[3,7,4,8,6,1,2,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,6,8,5,3,2,4,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,8,1,6,7,4,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,2,8,4,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,7,4,3,8,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,7,8,4,6,2,3,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,1,8,4,6,2,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,1,6,5,4,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,6,8,7,3,2,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[5,1,4,6,7,3,8,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[7,1,3,4,6,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,7,2,8,5,3,1,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[8,7,1,4,6,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,8,4,7,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,4,7,5,8,6,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[6,1,8,3,4,7,2,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,8,6,3,5,2,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,6,8,3,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[3,6,5,2,8,4,1,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[8,2,5,6,3,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,2,5,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,4,8,7,5,2,6,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,5,6,4,2,3,7,8]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[5,7,3,6,8,4,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,8,7,4,2,1,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,7,8,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[1,8,7,3,2,5,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,8,7,3,6]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,2,4,8,6,3,5,7]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,5,2,4,7,3,8,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[8,6,3,5,7,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,1,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,7,6,8,4,3,5]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,6,3,2,5,7,8,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,7,3,4,2,6,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,6,3,5,8,4,2,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,5,6,3,2,8,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,2,5,8,4,6,3,7]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,5,3,2,7,8,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,1,8,6,2,3,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[7,5,8,6,2,3,4,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,7,6,4,3,8,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,8,5,7,6,3,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,6,8,5,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,6,3,5,7,8,4,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,5,6,3,2,7,8,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,2,7,6,8,4,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,8,4,7,5,3,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,5,2,1,7,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,2,6,8,4,3,7,5]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[5,3,7,2,6,4,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,3,8,2,6,1,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,6,2,5,3,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,2,4,5,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,2,4,3,5,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,2,3,5,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,4,2,7,1,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,2,8,1,7,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[8,7,6,1,5,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,4,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,3,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,5,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,1,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,2,8,1,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[8,3,5,4,2,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,3,1,5,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,3,7,1,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,2,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,2,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,1,4,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,7,3,8,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[8,7,5,4,1,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,3,4,2,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,3,4,6,1,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,1,3,4,2,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[7,3,5,6,4,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,5,3,7,8,4,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,5,7,3,8,2,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[7,1,5,3,6,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,3,7,5,8,6,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[3,7,5,8,4,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[7,5,6,8,1,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,3,4,7,8,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,3,7,6,8,1,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[3,1,2,7,5,8,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[3,1,2,5,7,8,6,4]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[7,3,5,1,2,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,7,1,2,8,5,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[5,3,1,7,4,6,8,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[7,4,8,3,5,6,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,4,7,3,5,6,1,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[5,7,6,4,2,3,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[7,4,8,2,5,6,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,8,2,4,6,1,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,1,4,8,5,2,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,4,5,8,1,6,7,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[6,8,7,4,2,1,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,6,8,4,7,3,1,2]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[3,1,6,8,5,2,7,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[2,3,8,1,5,6,4,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[5,4,8,1,2,6,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,8,2,4,6,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,1,8,2,3,6,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,2,3,8,1,7,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[2,3,5,7,1,6,4,8]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,5,3,8,2,4,6,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[8,6,2,7,5,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,6,3,5,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,7,6,1,3,2,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[8,1,7,5,3,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,3,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,6,1,7,8,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[8,1,5,4,6,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,6,4,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,4,6,3,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,5,6,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,2,8,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[3,5,6,4,1,7,2,8]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[2,5,6,1,7,4,3,8]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[2,7,1,8,6,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,7,6,1,8,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[6,2,8,3,1,4,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,7,8,3,1,4,5,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,5,3,2,8,6,7,4]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,8,5,3,2,6,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,7,3,2,8,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,7,5,2,3,4,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,7,5,2,4,8,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,6,7,8,3,2,4,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,4,8,6,2,3,5,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,2,8,6,3,4,5,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,6,3,5,7,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,7,8,4,3,5,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,8,6,7,4,2,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,8,4,2,3,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,6,7,8,3,4,2,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,7,4,2,3,8,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,8,4,2,3,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,3,5,6,2,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,7,8,3,4,2,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,2,3,7,8,5,4,6]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,7,4,6,3,8,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,7,8,4,5,2,3,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,8,3,4,5,2,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,2,8,4,5,6,3,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,8,2,7,3,4,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,7,2,3,4,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,7,5,2,6,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,3,2,5,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,3,8,1,6,7,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,2,1,3,7,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,1,8,3,6,7,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,1,8,4,6,2,7,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,4,1,6,5,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,6,4,3,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,8,7,5,3,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,7,3,2,4,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,3,7,5,6,8,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[3,2,4,7,5,8,1,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[2,8,7,6,4,5,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,6,3,1,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,4,7,6,8,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[5,3,2,6,4,7,8,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[5,3,2,6,7,4,8,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[5,3,2,7,6,4,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[7,3,5,2,8,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,5,2,7,4,6,8,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[3,2,5,7,4,6,8,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[3,2,7,5,4,8,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[3,7,5,2,4,8,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[2,3,7,5,4,8,6,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[8,3,5,1,6,4,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,6,1,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,6,8,2,5,1]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[5,2,8,4,1,3,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,8,5,2,1,4,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,8,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,4,2,1,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,1,6,7,3,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,7,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,6,3,7,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,6,8,1,2,5,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,1,3,4,8,5,7,6]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[5,7,1,2,6,8,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[1,5,2,3,6,8,7,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[3,5,7,4,1,8,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[8,6,4,7,5,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,2,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,3,1,6,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,5,6,1,4,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,5,4,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,1,2,8,5,7,4,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[7,3,1,2,5,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,3,5,7,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,5,7,4,6]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[7,3,1,2,8,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,1,4,7,6,3,5,8]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[7,2,4,5,3,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,4,2,5,6,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,6,3,7,8,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[4,5,1,3,6,7,8,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[5,1,7,6,3,4,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[6,1,7,5,4,8,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[3,7,2,1,6,8,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[1,5,8,2,4,7,6,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,8,1,6,4,7,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,6,5,7,2,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,1,4,7,3,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,6,8,2,7,4,5,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,2,1,8,4,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,1,6,8,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,6,2,1,8,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[6,4,1,7,3,8,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[8,2,5,6,7,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,6,8,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,2,4,7,8,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,1,4,3,2,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[2,7,4,8,6,1,5,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,4,8,6,5,7,3,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,7,8,6,4,2,5,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[6,2,8,4,7,5,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,5,7,3,6,8,1,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[3,4,7,8,6,5,1,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,4,7,2,6,8,5,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[2,3,7,6,5,1,4,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[3,2,7,6,4,1,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[6,2,3,5,7,1,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[7,8,1,2,5,6,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,3,6,8,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,2,8,5,1,6,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,5,8,1,4,2,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,8,2,4,5,1,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,2,4,1,5,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[2,3,8,4,1,6,5,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,5,7,3,1,6,2,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[2,3,1,4,8,5,7,6]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[4,2,6,1,5,8,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[7,5,1,8,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,1,8,5,7,6,4,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[5,1,8,7,4,6,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,4,8,7,5,1,3,6]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,5,7,6,1,8,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[3,5,7,6,2,8,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[1,5,3,2,8,7,6,4]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[6,1,4,3,8,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,3,1,8,7,4,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,3,6,2,8,7,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[6,3,5,2,1,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[2,8,4,1,3,7,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,4,7,6,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,8,7,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,1,3,5,8,7,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[3,4,7,5,8,1,2,6]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[2,7,8,3,4,1,5,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,8,6,7,5,4,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,8,1,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,3,6,2,8,4,7,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[8,1,6,3,7,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,7,1,8,6,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[2,6,5,7,3,8,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[6,8,2,7,4,1,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,1,7,8,5,3,2,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[2,6,5,4,7,1,8,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,8,3,4,6,1,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,1,7,4,2,5,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,8,7,1,5,4,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,3,1,5,7,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,3,8,2,7,1,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,3,4,5,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,2,6,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,7,1,5,2,6,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[6,7,1,8,3,4,5,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[3,7,1,6,8,4,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,8,5,2,6,7,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,2,7,1,4,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[6,8,3,4,7,1,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,7,1,6,5,2,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[8,3,5,2,7,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,4,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,8,6,4,7,1,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,1,4,8,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,1,4,5,2,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[2,3,7,6,5,8,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[3,5,7,6,8,2,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[4,2,5,3,7,6,1,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[6,2,4,3,7,5,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,3,6,4,7,5,2,8]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[8,2,5,3,6,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,3,6,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,2,5,3,7,4,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[4,2,6,3,7,5,1,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[5,2,7,3,6,4,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[7,3,6,2,5,4,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,3,8,2,5,4,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,3,1,4,6,5,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,3,7,2,5,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,3,6,4,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,2,8,4,6,5,1,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,4,7,3,6,5,2,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[8,2,5,4,1,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,4,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,3,7,5,2,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,2,1,4,8,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,2,1,4,8,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[3,2,1,5,8,6,4,7]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[4,2,8,3,7,5,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,2,8,3,7,4,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,3,7,2,6,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,8,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,3,7,4,8,5,2,6]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[8,2,6,3,7,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,8,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,2,7,3,8,4,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[3,2,7,4,8,5,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[5,2,6,3,8,4,1,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[6,2,5,3,8,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,2,5,3,8,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,2,5,3,7,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,4,8,5,2,7]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,3,5,4,8,6,2,7]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[8,2,4,3,7,5,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,3,8,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,2,4,3,8,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,2,4,3,8,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[4,2,5,3,8,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[4,2,5,3,1,7,6,8]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[6,2,4,3,1,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[7,2,4,3,1,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,5,1,3,6,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,6,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,4,7,6,3,8]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[7,2,5,3,1,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,2,5,3,1,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[4,2,6,3,1,7,5,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[3,2,6,4,1,7,5,8]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[3,2,7,4,1,6,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[4,2,7,3,1,6,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[5,2,7,3,1,6,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[6,2,7,3,1,5,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,2,6,3,1,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,5,2,4,8,6,3,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[8,4,1,3,7,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,5,3,7,4,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[3,2,1,6,4,7,5,8]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[3,2,8,5,1,6,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[6,2,8,4,1,5,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,3,7,4,1,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,2,5,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,3,5,2,4,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,5,2,8,7,4,3,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,7,2,8,1,4,3,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,8,2,7,1,4,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,3,1,5,2,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,3,2,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,1,5,7,8,6,2,4]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[8,6,2,3,1,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,7,3,6,8,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,2,1,7,8,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[7,3,4,2,1,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,7,6,3,2,4,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,1,6,4,7,8,5,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,6,3,2,4,7,8,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,2,3,7,5,8,4,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,8,5,3,2,4,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,8,1,5,6,2,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,6,7,1,8,4,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[1,3,7,6,2,4,5,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,7,3,8,4,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,1,4,3,8,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,6,2,7,8,3,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[7,4,1,8,5,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,5,8,1,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,4,8,1,5,7,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,7,4,1,3,6,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,2,1,4,7,5,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[2,6,1,5,4,7,3,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[2,3,6,8,4,1,7,5]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,7,2,8,6,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[8,4,2,3,7,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,4,8,7,3,1,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,3,2,6,7,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,4,6,7,8,1,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[5,2,6,8,1,3,7,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,8,1,6,3,7,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,1,5,2,6,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,3,5,2,6,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,5,6,2,7,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,2,4,6,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,7,6,1,8,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[7,2,4,8,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,2,1,8,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,2,1,6,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,6,5,2,1,8,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[6,7,2,4,3,5,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[4,5,3,7,2,1,6,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[4,3,8,2,1,5,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,2,8,1,6,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,5,8,3,2,7,1,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[6,8,5,2,7,3,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,4,7,8,2,3,6,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,3,8,2,1,6,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,6,7,4,5,2,8,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[3,5,7,4,6,2,8,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[5,3,7,6,2,4,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[4,6,7,2,5,3,8,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[6,4,7,8,3,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[8,4,7,3,1,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,7,6,4,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,6,7,1,8,3,4,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[7,1,8,6,2,5,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,5,8,2,6,4,7,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,5,7,4,6,8,3,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,4,7,5,6,8,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[5,6,7,4,8,1,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[8,1,2,6,4,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,2,5,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,1,5,4,8,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[3,2,7,6,5,8,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[1,7,3,4,5,8,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,1,8,4,5,6,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,2,7,4,5,8,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[6,7,3,2,5,8,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,1,8,4,5,3,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,6,2,5,1,8,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[5,1,4,6,2,8,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[7,3,5,2,1,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,5,1,2,6,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,7,4,6,3,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,7,2,1,3,6,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[3,7,2,6,8,1,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[7,4,8,6,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,6,8,5,1,4,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,6,4,5,7,3,8,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,5,4,7,8,6,2,3]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[7,3,1,6,8,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,6,8,5,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,5,8,7,6,4,1,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,5,7,8,6,2,4,3]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[3,6,2,1,4,7,8,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[6,8,2,7,5,4,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,1,7,6,4,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,6,3,2,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,4,3,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,5,1,4,6,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,3,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,6,1,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,5,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,2,8,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,5,1,4,3,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,2,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,1,8,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[7,6,2,4,1,5,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,1,6,3,7,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,2,6,7,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,2,5,1,7,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,6,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,4,3,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,3,6,2,4,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,3,7,2,1,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,3,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,3,8,2,1,5,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,5,7,4,3,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[6,2,5,4,8,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,2,4,8,5,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,2,7,6,8,5,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[7,1,6,2,8,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,6,3,8,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,6,8,1,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,8,5,1,3,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,8,5,3,2,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,8,2,5,6,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,5,8,7,2,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,1,5,7,4,8,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,1,5,7,8,3,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[4,6,7,3,1,8,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[4,2,6,3,1,8,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[6,1,4,2,5,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,5,3,8,4,6,2,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[7,2,3,5,8,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,4,2,8,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,7,6,4,8,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[8,7,4,2,1,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,5,1,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,8,3,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,1,8,5,7,6,2,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,7,5,8,4,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,5,8,3,4,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,7,5,1,3,2,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[5,2,6,1,7,3,4,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[4,2,6,8,3,7,1,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[6,8,5,1,4,2,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,8,4,5,1,3,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,7,8,5,3,4,6,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,5,8,3,6,4,7,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[6,3,8,1,4,2,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,8,1,5,6,3,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,6,5,3,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,7,2,6,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,8,1,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,1,4,2,3,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,6,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,3,7,4,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,3,7,1,5,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,5,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,3,4,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,4,2,5,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,8,4,3,6,2,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,7,2,6,3,4,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[7,5,1,6,3,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,2,6,3,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,5,1,6,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,1,4,6,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,6,5,4,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,8,4,3,1,7,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,6,8,5,2,4,7,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,8,4,3,2,6,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,3,8,4,7,2,6,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,4,5,8,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[6,7,1,3,2,8,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,5,3,2,6,8,4,7]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[5,4,3,1,7,2,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[3,7,6,5,8,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[5,7,4,2,8,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,4,3,7,8,2,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[3,8,5,7,6,2,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,8,7,2,5,4]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[5,8,7,1,4,2,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,6,3,7,1,4,5,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[7,6,8,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,7,6,5,3,2,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7,6,5,4,1,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,3,5,8,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,7,6,1,5,8,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[6,8,7,1,5,4,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,2,6,1,5,8,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,7,3,8,6,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,3,6,8,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,4,7,3,8,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[8,7,2,4,6,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,7,2,6,1,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[1,7,2,8,5,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,4,8,3,6,2,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,8,2,5,7,1,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,6,2,7,5,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,2,7,3,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,2,7,3,4,5,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,4,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,3,4,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,4,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,7,3,4,5,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,7,8,5,6,4,2,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,3,1,2,4,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,5,8,2,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[8,1,3,2,4,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,6,4,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,5,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,5,4,3,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,2,1,7,6,3,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[3,5,8,2,1,4,7,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[4,2,8,5,3,7,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,2,7,5,3,8,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[6,4,5,1,8,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,4,7,8,3,1,2,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,5,8,1,3,7,2,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,5,3,6,8,7,2,4]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[7,6,2,8,1,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,7,2,6,8,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[6,3,2,8,7,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,4,3,8,5,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,1,5,8,7,6,2,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[8,2,1,6,5,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,6,5,7,2,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,7,6,4,5,8,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[7,2,6,5,1,8,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,2,8,5,6,3,1,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,4,2,1,8,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,7,3,2,5,1,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,2,5,3,8,7,1,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[7,2,5,3,8,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,7,3,2,5,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,1,8,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,5,6,2,7,3,1,8]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[5,3,4,7,1,6,2,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[3,5,1,4,6,8,2,7]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[8,5,7,4,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,4,1,8,6,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,4,5,1,8,6,3,7]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[2,4,1,6,7,5,3,8]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[6,3,7,1,5,2,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[4,1,3,7,8,2,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[7,1,4,8,6,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,3,4,2,1,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,3,8,6,7,2]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[4,6,2,7,5,8,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[7,3,2,5,1,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,8,1,4,2,3,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,5,2,4,8,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,5,2,4,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,4,3,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[5,2,1,4,3,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[8,6,2,7,5,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,1,5,8,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,3,8,7,1,5,4,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,3,8,1,5,2,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,3,6,7,2,8,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[7,1,4,5,8,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,1,3,2,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,8,1,6,5,2,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,4,8,6,5,1,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,7,8,6,5,1,2,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[8,4,5,7,2,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,7,3,1,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[6,5,8,2,7,3,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,2,7,3,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,1,3,6,4,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,3,8,2,7,5,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,5,7,8,3,2,1,6]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[5,7,3,4,2,6,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,7,4,2,3,6,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,4,7,3,2,8,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,8,3,2,4,5,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,3,4,6,1,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,3,8,5,1,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,8,2,3,5,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,4,6,8,2,3,1,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[5,6,8,4,1,2,3,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,4,8,5,1,2,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,4,8,3,1,2,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,7,8,2,3,1,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,4,7,8,2,1,3,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,8,6,3,1,2,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,5,2,1,3,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,6,1,3,2,4,8,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[8,1,5,4,6,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,1,2,5,7,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,6,3,2,8,5,7,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[5,3,7,2,1,8,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[7,4,3,2,5,1,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,4,8,3,7,2,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,6,8,5,2,1,7,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[6,1,5,4,7,2,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[5,4,8,3,2,7,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,4,3,7,2,1,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,4,3,7,8,2,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[1,4,8,6,3,2,7,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,1,8,6,2,5,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,3,4,8,1,2,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,8,1,7,4,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,6,3,1,5,8,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[7,1,3,2,6,5,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,3,5,8,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,5,8,7,4,6,2,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[6,8,5,7,3,4,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,3,6,8,4,2,1,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[5,1,6,8,4,7,3,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,2,8,3,4,1,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,4,1,8,7,6,3,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,3,5,8,4,7,2,6]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,3,8,7,5,1,6,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[8,5,4,7,6,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,4,1,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,1,3,5,6,2,8,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[6,3,8,5,1,7,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,2,4,6,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,3,5,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,2,3,5,6,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,5,6,8,2,7,1]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[8,2,3,4,6,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,3,5,2,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,7,4,3,8,1,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,8,2,7,6,4,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,6,2,1,8,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[4,3,8,6,2,7,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,2,1,4,6,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,2,7,5,4]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[5,3,8,6,7,2,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,7,2,4,6,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,5,2,8,7,6,4,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,7,1,4,6,5,3,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[4,7,1,2,6,5,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[4,2,5,6,8,7,3,1]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[6,5,8,3,7,4,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,2,5,1,6,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,1,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,3,5,4,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,1,3,5,2,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,5,7,6,4,8,1,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[1,3,7,8,5,4,6,2]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,3,2,7,8,5,4,6]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,5,7,6,8,3,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[3,5,7,4,6,8,1,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[6,5,8,4,3,7,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,7,3,1,5,2,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[5,2,4,1,8,3,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[2,1,7,4,3,8,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[7,2,3,8,5,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,1,5,7,6,3,8,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[1,4,8,2,3,6,5,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,4,6,7,3,5,2,8]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,4,8,2,6,7,5,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,7,3,2,4,5,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,3,2,4,5,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,6,4,3,2,5,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[4,2,6,5,3,1,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[5,2,1,6,8,7,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,3,5,8,6,2,7,4]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,3,8,4,1,7,6,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,5,7,4,2,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,7,5,4,6,8]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,4,2,8,6,3,5,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,8,6,3,5,7,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,8,2,5,3,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,8,6,4,2,7,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,3,6,8,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[6,1,5,2,3,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,5,2,1,7,3,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[3,1,2,4,8,6,7,5]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[3,1,2,5,8,7,4,6]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[6,5,2,1,8,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,6,2,4,3,8,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[3,7,5,2,8,1,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[5,1,4,7,3,2,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[2,3,5,4,8,6,1,7]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,3,6,4,7,5,1,8]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[2,3,5,7,4,8,1,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[2,3,7,6,1,5,8,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[8,3,2,4,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,1,2,5,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[4,7,1,6,8,5,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,1,8,6,3,5,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,5,8,6,2,3,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[5,3,4,6,2,8,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[5,4,8,6,3,7,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,7,3,4,8,2,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,6,4,2,7,8,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[6,5,2,3,7,4,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,5,2,3,1,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,5,3,7,4,1,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,4,7,5,3,8,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[5,7,6,4,8,3,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,4,8,3,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,1,4,7,5,2,8,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[4,3,5,1,8,7,2,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[2,5,3,6,1,8,4,7]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[2,5,6,8,3,1,7,4]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[7,1,4,5,3,6,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,7,2,4,5,3,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,4,5,3,2,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,6,4,7,3,5,2,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[3,5,6,4,8,2,1,7]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[1,6,4,7,5,2,3,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,5,2,6,7,4,3,8]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[8,5,6,1,4,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,4,7,8,3,1,6]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[6,4,5,8,2,3,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,6,1,3,2,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,4,6,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,6,7,8,1,5,3]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[3,4,6,7,8,1,5,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[4,7,3,8,5,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,3,2,7,5,8,1,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[4,8,5,3,2,6,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,5,3,6,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,5,3,2,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,4,1,3,6,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,1,3,2,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,2,4,1,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,3,7,8,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,3,7,8,1,5,4,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[2,6,3,7,8,1,5,4]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[7,5,8,1,6,4,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,1,4,3,7,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,5,3,2,6,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[8,2,7,6,4,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,3,8,5,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,8,2,7,3,1,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,2,6,3,4,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,8,5,3,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,1,5,8,3,6,7,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[7,5,2,8,1,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,8,5,7,1,3,2,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,4,7,2,1,5,8,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[4,8,2,7,1,3,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,2,1,7,4,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,3,6,7,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[5,1,6,8,3,2,7,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,1,5,6,8,2,7,3]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[5,7,8,2,4,1,3,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,5,2,8,7,3,1,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,8,5,3,1,6,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,7,8,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,2,3,6,8,4,7,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[6,2,1,7,8,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,2,1,3,8,4,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,2,7,8,4,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[5,2,8,6,4,1,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,2,8,4,3,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,7,8,3,2,5,4,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[5,7,2,6,4,8,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,2,3,4,7,8,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[7,2,1,8,4,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,2,1,3,7,5,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,8,7,3,4,5,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,2,3,7,8,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[7,4,3,2,5,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,2,4,3,5,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,7,6,4,2,3,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,3,2,5,8,6,4,7]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[6,1,4,7,2,8,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,7,5,8,4,2,3,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,6,7,2,4,8,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,7,2,4,3,6,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,7,3,4,6,2,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[2,8,3,6,1,7,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,8,5,2,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,8,4,5,6,2,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,8,2,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,2,5,3,1,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,8,1,7,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[3,5,4,8,6,1,7,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[7,5,2,3,8,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,7,5,1,4,8,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,7,6,1,2,8,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[7,4,6,5,1,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,3,2,6,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,3,5,2,8,1,6,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[1,7,3,8,2,4,6,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,4,8,5,3,1,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,1,3,8,4,2,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,4,1,8,6,2,7,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,4,6,8,1,3,2,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[3,6,1,5,8,4,7,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[6,4,8,3,5,7,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,5,8,2,4,1,7,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[7,2,8,4,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,8,1,2,4,3,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,4,3,5,7,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,2,3,8,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[6,3,5,8,2,4,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,8,7,1,4,6,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,3,7,4,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,8,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,7,6,2,8,1,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,3,8,1,2,5,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,6,4,8,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,5,3,8,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,5,4,2,8,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,5,4,8,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,6,5,3,2,8,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,5,7,2,4,3,6,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,6,5,3,2,4,7,8]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,7,2,4,6,5,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,4,7,2,6,5,3,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,2,6,8,7,4,3,5]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,7,4,3,5,8,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,6,2,8,7,4,3,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,7,4,2,3,5,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,5,2,3,6,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,8,5,2,3,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,4,7,5,2,8,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,6,3,7,4,2,8,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,8,5,2,7,4,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,8,7,5,3,2,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,2,5,8,6,3,7,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,4,7,5,8,6,3]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,5,8,7,6,2,4,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,3,5,8,7,6,2,4]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,5,2,4,3,6,8,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,6,8,7,5,3,2,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,2,5,7,4,3,8,6]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,5,3,2,6,8,7,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,4,2,6,8,7,5,3]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,5,8,6,3,2,7,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,8,5,2,6,3,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,4,6,3,2,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,6,3,2,8,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,3,8,6,4,2,5,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,5,7,4,2,3,8,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[6,3,7,5,4,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[7,5,2,6,3,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,8,2,7,5,4,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,8,6,7,1,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,7,3,6,8,5,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,2,8,1,6,4,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[8,5,2,4,6,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,7,1,4,3,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,4,6,5,8,2,7,1]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[5,2,4,1,6,7,8,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[4,2,7,1,6,8,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[5,2,8,6,4,7,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,1,3,4,7,2,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[8,4,7,2,5,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,7,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,7,2,8,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[5,3,6,7,2,4,8,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[8,6,1,4,7,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,6,7,4,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[7,1,3,6,5,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,1,4,5,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,5,2,3,8,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[6,1,7,5,4,2,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[2,7,3,6,5,1,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[8,6,5,1,3,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,2,4,8,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[3,7,5,6,4,8,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[7,6,8,1,3,5,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,8,4,6,1,7,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,4,7,3,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,4,6,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,6,7,1,4,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,2,4,6,8,5,3,7]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,1,5,8,6,2,4,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[2,5,4,6,8,1,3,7]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[6,5,2,4,7,8,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[7,2,5,8,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,2,8,3,4,7,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,4,3,8,7,1,6,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,5,8,7,4,2,6,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[6,8,7,5,4,3,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,3,4,8,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,4,5,8,6,2,7,1]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[5,4,2,3,6,1,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[5,1,7,4,3,6,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[4,3,7,6,8,2,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[6,1,8,5,2,7,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,7,2,6,3,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,6,4,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,1,3,7,2,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[3,1,8,7,5,2,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[6,5,8,7,2,4,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,3,6,5,8,2,1,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[7,6,3,2,8,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,2,6,8,7,1,4,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[4,3,7,1,8,5,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[3,2,8,5,6,7,1,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,3,2,1,4,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,1,8,5,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[3,7,8,2,5,6,1,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[7,5,1,4,2,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,8,6,1,2,4,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,5,3,4,7,8,6,2]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[5,1,2,4,7,8,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[5,1,7,8,6,2,3,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[8,5,1,6,7,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,1,2,4,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,5,2,7,3,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[7,1,2,6,4,5,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,7,3,6,4,5,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,3,6,4,5,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,2,7,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,2,5,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,1,6,2,5,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,2,5,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,4,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,4,5,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,7,5,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,6,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,1,2,8,5,6,7,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[6,3,1,2,7,4,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,1,7,4,2,3,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,7,3,4,6,8,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,7,3,8,4,5,6,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,1,8,2,5,3,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,7,2,5,3,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[5,1,7,2,6,3,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,1,8,2,6,3,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,6,3,7,4,5,8,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[2,4,7,3,5,1,6,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[2,4,8,6,3,5,1,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,3,7,5,4,1,6,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[3,4,6,2,1,5,8,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[3,4,7,2,1,6,5,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[2,6,8,3,5,1,4,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,3,6,1,5,8,4,7]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,3,7,1,6,5,8,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,4,7,1,3,6,8,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[5,4,7,8,1,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[2,5,7,1,4,6,3,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[2,4,7,1,6,3,5,8]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[2,3,7,1,6,5,4,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,5,7,1,4,3,6,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[2,5,7,3,1,4,6,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[3,4,7,2,1,6,8,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[4,6,3,7,1,5,2,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[5,7,3,2,8,1,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[2,6,5,7,1,8,4,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[3,6,8,5,4,1,7,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,4,7,8,1,3,6,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[2,5,7,1,4,6,8,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[2,4,7,1,6,3,8,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[2,4,7,1,6,8,3,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[2,4,8,3,1,7,6,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[8,6,5,1,2,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,4,2,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,1,4,8,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,7,1,4,3,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,4,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,5,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,4,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,2,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,4,3,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,7,4,5,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,7,3,1,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[8,2,4,5,3,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,3,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,2,1,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[1,6,7,4,3,2,5,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,4,5,7,3,2,6,8]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[3,5,1,4,7,2,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[2,5,1,4,7,8,3,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,3,7,1,5,2,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[3,5,1,6,4,2,7,8]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[6,4,3,1,7,2,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,2,7,4,3,1,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[2,6,4,1,7,3,5,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[6,3,2,7,4,5,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[7,2,4,1,3,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,3,2,5,7,1,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[3,2,6,5,7,1,4,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[1,7,3,2,5,6,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,1,7,3,5,6,8,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[2,1,6,3,5,7,8,4]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,6,3,2,5,7,4,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,4,6,5,2,7,3,8]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[5,6,2,1,4,3,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[2,5,1,6,4,3,7,8]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[2,5,4,1,6,3,7,8]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[4,6,1,5,2,7,3,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[1,6,5,3,7,2,4,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,2,5,4,7,3,6,8]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,2,5,3,4,8,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[5,2,7,6,1,8,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,8,2,6,1,7,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,5,8,3,6,2,7,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[6,8,7,1,4,5,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,2,6,4,7,3,8,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,2,7,8,3,5,6,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[4,8,7,6,2,1,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,5,8,1,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,6,1,8,5,4,3,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,8,6,2,3,4,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,6,2,1,4,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,5,8,6,2,1,3,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[6,4,7,5,8,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,3,7,4,2,5,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,2,1,5,8,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,5,6,2,4,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,6,2,5,7,3,8,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[4,2,8,5,3,6,1,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,1,7,4,5,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,8,4,5,6,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[8,2,1,4,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,3,1,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,4,1,6,2,8,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[6,2,3,1,7,8,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[3,1,8,6,7,2,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,1,8,6,7,3]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[4,5,3,7,1,6,8,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[4,2,8,5,3,6,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,8,6,3,5,4,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,2,8,6,4,7,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[7,3,5,1,6,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,1,4,7,2,6,8,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[1,8,2,5,6,4,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,4,8,5,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,8,4,6,1,3,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,6,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,7,6,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,6,1,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,3,7,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,6,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,6,3,7,5,4,8,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,4,7,1,3,8,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[2,8,5,1,4,7,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,7,6,3,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,5,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,5,8,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,4,8,5,6,2,7,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[5,8,2,3,4,6,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,1,3,4,2,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,5,6,3,2,4,7,8]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[6,3,5,2,4,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[7,8,3,5,2,4,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,4,5,7,3,6,1,8]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[2,5,3,1,6,4,7,8]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[6,5,1,3,4,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,7,4,3,2,6,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,8,7,4,3,5,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,6,7,8,4,3,5,1]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,7,8,4,5,3,6,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,1,8,5,3,4,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,7,4,2,1,6,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,1,4,7,3,6,2,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[7,4,8,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,7,6,3,5,2,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[1,6,5,8,7,4,2,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,1,3,8,7,5,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,6,2,1,8,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,3,6,8,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,7,5,6,8,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,6,7,5,8,2,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[1,7,4,5,2,8,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,5,4,2,1,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,6,7,4,2,8,5,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[4,6,3,2,7,8,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[7,6,1,3,4,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,8,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,2,5,4,6,1,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,2,4,5,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,3,2,1,5,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,6,2,1,7,5,4,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[2,6,7,3,1,5,4,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[2,1,6,4,7,5,3,8]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[7,2,8,5,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,8,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,8,4,6,5,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,8,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,6,1,4,5,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,5,6,4,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,1,3,8,6,2,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[5,6,3,2,8,1,7,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[8,2,6,3,1,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,6,7,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,3,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,4,1,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,2,3,6,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,7,2,8,3,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[3,1,8,4,6,5,7,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,3,8,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,1,6,7,4,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,5,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,5,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,2,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,2,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,2,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,5,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,4,7,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,1,5,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,1,4,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,8,2,6,1]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[8,7,1,4,6,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,4,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,6,4,1,7,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,4,5,1,2,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,7,1,8,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,7,4,2,3,8,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[3,8,2,5,1,7,4,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,2,3,7,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,5,2,1,7,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,5,7,6,1,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,5,2,4,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,7,6,8,4,1,3,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[7,3,1,6,8,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,3,1,7,4,8,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[7,3,1,8,6,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,6,4,1,7,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,7,1,2,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[3,5,2,8,4,7,1,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[6,4,8,3,7,2,1,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,6,2,8,7,4,1,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[6,8,4,2,7,3,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,4,7,8,5,1,2,6]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[4,7,3,2,5,6,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,2,7,6,4,5,8,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,7,3,6,8,4,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,3,6,5,1,8,7,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[8,3,1,2,6,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,4,3,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,6,4,7,1,2,8,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[5,7,4,8,1,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,3,7,8,1,5,2,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[8,5,4,2,6,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,8,7,4,1,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[2,3,7,5,1,8,6,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[6,3,1,2,8,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,2,1,3,8,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[7,2,1,5,3,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,5,8,2,4,3,6,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,3,6,8,1,5,2,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[5,4,6,8,3,1,7,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[3,6,8,4,5,1,7,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[8,6,1,7,2,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,2,8,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,3,7,6,1,8,5,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[3,2,7,8,6,4,1,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[6,2,8,3,1,4,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,1,2,8,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,8,7,4,6,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,8,7,4,5,6]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,8,3,2,4,7,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[8,5,1,7,2,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,3,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,6,2,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,8,7,6,4,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,8,7,6,4,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,6,3,7,2,5,4,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,7,2,4,6,3,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[5,7,2,8,4,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,6,2,8,4,1,3,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[2,4,8,3,1,6,7,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,5,8,4,2,1,6,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,5,8,3,1,4,6,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,8,1,3,5,7,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,7,8,3,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[3,4,8,5,7,1,2,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,6,8,2,5,1,4,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,6,8,7,2,5,4,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,4,6,5,8,2,1,7]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[2,4,6,7,8,3,5,1]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,4,2,5,7,6,3,8]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,4,2,6,8,5,3,7]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,2,6,8,3,5,4,7]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,6,8,3,5,4,2,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,5,3,2,4,6,8,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,5,8,7,6,3,2,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,5,7,6,3,2,4,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,6,3,2,4,7,5,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,6,3,2,4,8,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,2,7,6,4,3,5,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,8,7,5,2,4,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,4,6,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,4,2,5,3,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,8,4,7,5,2,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,3,6,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,5,2,6,3,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,6,3,7,4,2,5,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,6,3,2,7,5,4,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,4,7,5,2,6,3,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,3,6,4,8,7,5,2]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,3,7,6,4,2,5,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,3,2,4,8,5,7,6]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,3,8,7,5,2,4,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,4,6,3,2,7,5,8]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,4,6,3,2,8,7,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,5,7,6,4,2,3,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,6,3,2,8,4,7,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,6,3,5,2,7,4,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,6,3,5,2,8,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,8,3,7,5,2,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,5,3,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,3,8,2,6,4,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,3,8,2,6,5,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,6,1,8,3,4,7,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,7,1,4,8,2,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,5,7,1,4,3,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[4,8,3,5,7,6,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,1,2,4,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[4,8,3,5,7,6,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,3,4,2,8,5,7,6]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[5,7,6,2,4,8,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,7,5,2,3,8,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,7,5,3,8,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[3,2,1,4,8,5,7,6]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[7,3,1,4,2,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,1,6,2,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,4,1,8,2,6,3,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,3,1,8,2,6,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,7,1,5,2,6,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[6,5,1,4,2,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,8,7,3,4,5,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,4,5,2,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,6,8,7,3,4,5]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,3,7,8,4,5,6,2]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[8,4,2,3,1,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,2,8,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,8,6,2,3,1,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,1,8,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,2,6,1,5,8,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[6,4,2,3,5,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[2,8,6,4,5,1,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,4,6,7,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,3,1,7,4,8,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[6,5,1,8,3,2,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,4,3,7,2,8,6,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,8,7,4,5,3,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,1,4,5,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,1,7,2,8,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[8,3,2,1,5,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,6,7,8,4,5,1]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[1,7,4,6,3,8,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,6,4,1,3,8,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[4,5,3,1,8,7,6,2]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[6,3,4,2,7,8,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[8,7,4,5,1,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,7,8,1,3,5,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[5,1,8,4,3,7,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,2,8,1,4,5,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,4,8,2,5,6,7,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[8,1,6,7,2,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,3,6,8,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,1,4,6,5,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,6,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,6,7,2,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,2,8,6,1,5,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,7,2,5,8,4,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[6,7,8,4,1,5,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,2,8,3,5,1,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,7,4,5,3,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,8,2,5,3,4,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,7,5,4,1,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,4,5,6,1,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,3,5,2,8,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,1,8,7,4,5,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,8,7,1,6,3,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,7,5,3,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,8,7,4,5]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,3,8,2,5,4,6,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,6,2,5,8,7,3,4]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,6,8,7,2,3,5,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,6,8,7,2,5,3,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,5,2,4,8,3,6,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,2,4,5,8,6,3,7]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,2,8,3,5,4,7,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,2,5,4,7,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,6,7,5,2,4,8,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,5,6,4,7,2,3,8]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,7,4,2,5,8,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,6,4,3,7,5,2,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,6,5,4,7,2,3,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,7,3,2,6,4,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,5,8,2,3,6,7,4]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,3,2,6,8,5,4,7]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,6,3,2,7,4,5,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,7,8,5,4,2,3,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,8,4,2,3,6,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,7,5,3,8,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,5,7,6,2,4,3,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,8,4,7,3,2,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,8,4,2,6,5,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,7,4,2,6,5,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,6,5,8,3,7,4,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,7,4,8,3,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,4,8,3,2,7,5,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,8,3,6,4,5,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,3,2,8,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[8,2,3,7,4,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,2,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,1,6,8,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,1,5,4,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,3,2,1,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,8,7,3,4,6,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,3,7,2,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[8,1,7,3,4,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,3,4,5,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,7,3,4,2,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,7,1,2,4,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,3,4,6,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,5,4,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,3,6,4,5,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,5,3,6,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,5,3,7,8,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,8,7,1,2,6,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,2,3,4,7,1,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,1,7,3,8,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[6,1,3,2,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,2,1,3,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[3,2,5,8,7,4,1,6]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[4,2,5,8,7,3,1,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[8,3,4,1,6,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,5,7,2,1,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,6,4,8,5,7,2,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[5,8,4,7,3,6,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,2,8,7,3,1,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,5,8,2,1,7,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,1,4,3,8,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,1,3,2,6,8,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[6,1,3,8,7,2,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,2,8,4,5,7,3,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,2,1,8,7,6,3,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,2,5,8,7,1,4,6]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[5,6,3,8,7,2,1,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[2,5,8,4,7,1,6,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,6,2,4,8,5,7,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[3,1,6,5,8,7,2,4]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[4,8,5,3,6,7,1,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,3,4,7,6,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,3,6,4,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,1,7,3,5,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,2,5,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,8,5,7,1,6]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[8,1,2,4,7,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,3,1,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,6,2,1,5,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,8,5,3,7,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[8,7,2,4,1,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,4,8,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,8,3,1,4,6,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,6,5,1,2,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[5,8,3,7,6,4,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,3,8,7,6,5,2,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,8,7,2,6,3,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,2,6,3,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,2,1,4,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,1,6,3,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,8,7,6,5,1,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,2,5,7,4,8,6,3]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[6,2,1,8,7,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,8,7,4,5,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,6,5,3,2,8,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[2,8,3,4,1,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,7,5,4,8,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[4,5,6,3,1,8,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[5,2,1,4,3,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,5,6,3,8,4,2,7]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[2,6,5,3,8,4,1,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,7,3,8,4,2,6,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,3,6,2,8,4,1,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[2,3,6,5,4,8,1,7]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[3,7,5,4,8,2,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[5,3,7,1,2,8,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,3,8,7,2,5,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,8,7,6,1,5,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,4,1,7,5,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,1,4,6,7,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,1,4,7,5,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,4,8,1,2,7,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,1,4,6,7,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,7,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,6,7,5,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,1,2,6,4,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,6,2,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,2,6,7,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,1,6,7,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,2,4,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,6,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,8,1,5,2,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[3,6,8,4,1,5,2,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[8,7,1,4,2,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,1,5,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,6,5,7,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,2,8,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[7,1,4,8,2,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,5,3,6,7,1,8,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[1,4,7,8,3,5,2,6]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[4,6,1,3,5,2,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[2,5,1,4,8,3,7,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[6,1,2,5,4,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,4,1,7,3,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,2,5,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,8,3,1,7]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[3,4,5,8,6,2,1,7]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[4,5,1,8,6,3,7,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[8,3,7,2,1,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,6,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,6,4,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,5,6,2,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,5,6,2,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,5,6,4,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,8,2,7,4]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[2,6,3,8,4,7,1,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,3,5,7,8,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,5,6,3,7,2,8,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,7,5,3,6,2,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,5,7,3,4,2,8,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,5,8,3,4,2,7,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,5,3,7,2,8,6]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,4,5,3,8,2,7,6]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[6,5,1,4,2,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,5,1,4,2,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,7,5,4,2,8,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,1,6,8,3,7,2,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[3,8,5,2,1,4,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,4,8,2,6,7,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[5,4,7,1,8,6,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[1,4,8,2,6,5,3,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[7,5,1,8,3,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,2,8,1,7,4,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,4,8,2,6,7,3,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,2,5,6,8,7,3,4]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,5,6,8,2,7,4,3]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[2,6,7,3,4,1,8,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,6,5,7,8,2,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,5,6,7,2,8,4,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[3,7,6,1,8,2,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,3,7,2,6,4,8,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,5,8,6,7,3,4,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,6,5,8,7,2,4,3]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,5,7,6,2,8,3,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,2,5,8,6,7,4,3]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,6,5,7,3,8,4]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,7,5,8,6,4,2,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,6,5,8,1,2,7,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[5,4,7,8,1,6,3,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[2,5,6,8,1,3,7,4]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[5,3,6,8,1,2,7,4]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,6,5,8,3,2,7,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,5,6,8,2,3,7,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[2,5,8,7,1,6,4,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,5,8,3,6,2,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[7,3,6,8,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,3,6,7,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,7,3,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,7,8,5,6,3,1]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,8,7,5,2,4,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[6,4,7,8,5,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,8,4,6,5,3,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,4,7,5,1,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,6,1,2,3,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,8,7,5,1,6,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,2,6,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,7,5,1,2,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,7,1,4,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,7,4,2,6,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,2,4,7,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,3,4,7,2,6,5,8]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[2,5,1,4,3,6,7,8]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[5,3,8,2,4,6,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,5,8,3,2,6,1,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,8,2,1,4,6,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,1,5,8,3,6,2,7]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[4,5,8,3,6,1,2,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,2,7,1,8,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[4,7,8,5,2,3,1,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[6,2,7,8,1,5,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[2,7,1,3,8,5,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,6,7,8,4,1,3,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[2,6,7,8,4,3,1,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[7,1,2,6,3,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,1,2,6,5,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,6,1,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,8,2,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,1,8,3,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,8,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,4,5,3,1,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,6,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,4,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,8,4,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,5,1,6,8,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,2,1,7,4,8,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,7,4,3,2,5,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,4,3,6,2,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7,5,8,2,4,6,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[5,2,1,6,3,4,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[5,1,3,4,6,2,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[3,8,4,5,7,2,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,7,5,6,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,8,6,3,7,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,7,6,3,8,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[7,4,1,8,5,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,5,6,8,4,7,1,2]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[5,4,1,8,6,7,2,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,2,8,4,5,3,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,5,2,1,8,7,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[4,7,3,8,2,6,5,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,3,1,8,6,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[6,2,1,3,7,4,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,3,7,1,2,5,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,1,4,7,8,2,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[7,2,5,8,1,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,3,6,7,2,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,5,2,1,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,6,2,7,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,6,5,8,4,2,7,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[6,8,3,2,5,7,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,1,5,6,8,7,3,2]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[8,4,2,3,6,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,4,5,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,5,1,3,7,6,8,2]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[3,5,4,8,6,2,7,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,6,2,4,5,8,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[8,1,3,7,4,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,6,4,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,8,3,1,5,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,6,4,1,5,8,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[3,5,1,4,6,2,7,8]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[3,6,4,5,2,8,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[8,1,5,4,7,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,1,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,6,4,1,5,7,2,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[8,1,5,4,7,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,4,6,7,3,8]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[3,6,4,1,5,7,8,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[7,6,5,2,8,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,1,6,5,2,8,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[1,7,2,4,3,5,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,8,1,7,4,2,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,7,4,3,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,5,3,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,5,3,6,1,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,1,4,7,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,3,2,7,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,1,8,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,2,8,3,5,6,4,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,5,7,4,8,1,6,2]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[2,8,1,3,5,4,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,2,8,6,4,3,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[7,4,8,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,6,8,4,1,2,5,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[4,7,8,5,2,1,3,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[6,1,5,2,8,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,1,3,5,7,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,5,4,7,2,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,6,4,8,5,2,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[5,1,3,4,2,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[3,2,6,4,1,5,7,8]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[5,4,2,1,8,3,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[4,2,5,1,8,7,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[6,8,2,7,1,4,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,4,7,3,2,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,3,1,5,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,4,7,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,2,5,4,7,8,3,6]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,8,3,2,6,4,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,2,5,3,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[6,8,4,1,3,7,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,2,6,1,7,8,5,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[7,6,4,1,8,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,4,1,6,7,3,2,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[7,4,1,6,5,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,5,4,1,6,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,1,6,4,7,8,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[1,6,2,3,5,7,8,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,3,4,8,5,2,6,7]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[8,2,4,6,1,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,7,2,3,6,8,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[7,3,1,4,2,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,2,5,7,8,4,1,6]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[4,3,5,1,6,2,7,8]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[8,6,3,5,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,7,4,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,6,3,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,5,1,7,4,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,3,1,7,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,4,8,3,2,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,8,1,7,6,5,2,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,8,7,2,6,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,8,7,2,6,4,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,5,7,4,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,6,1,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,6,3,5,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,6,1,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,8,3,1,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,4,8,2,1,3,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,8,7,2,6,1,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,7,6,3,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,7,6,5,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,8,7,2,6,5]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[7,1,5,4,6,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,1,3,6,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,4,3,1,7,6,2,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[4,1,3,7,5,6,2,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[2,6,8,3,1,7,4,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,5,4,8,1,7,3,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[7,5,2,4,8,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,8,2,6,3,5,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,2,6,5,8,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,6,3,1,4,2,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[2,6,5,3,4,8,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,6,1,5,3,4,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[3,4,7,8,5,1,6,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[3,6,2,4,7,8,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[5,3,6,4,8,7,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[1,5,4,8,6,2,7,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,5,2,7,6,3,8,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[5,8,3,1,2,7,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,6,2,5,3,8,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,4,6,1,3,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,1,2,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,6,2,4,5,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,3,8,6,2,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[7,4,2,3,6,8,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,1,6,7,4,8,3,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[7,8,1,3,6,4,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,2,6,8,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,6,8,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,8,1,6,2,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,7,8,1,6,3,2,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[7,2,6,8,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,2,4,8,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,8,3,1,6,2,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,7,8,4,3,1,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[7,8,3,6,4,1,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,3,8,1,6,4,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,7,5,8,2,4,6,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,5,2,8,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,7,8,2,6,5,1,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,8,2,1,6,4,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[7,8,1,6,3,5,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,7,8,2,5,4,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,3,1,5,4,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[7,8,1,6,2,5,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,6,1,4,3,8,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[5,1,6,8,3,4,7,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[7,1,6,8,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,6,8,1,2,3,7,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,8,1,2,7,6,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,6,1,2,8,5,7,3]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[6,4,7,3,5,2,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[5,7,8,4,2,1,3,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[6,4,8,3,5,2,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,1,6,2,5,7,8,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[1,6,4,5,2,7,3,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,4,7,3,2,5,6,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[6,2,1,4,5,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,2,1,5,7,3,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,2,4,6,8,3,7,5]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,5,8,2,6,7,4]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[6,1,3,7,2,8,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,4,5,8,3,7,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,1,4,3,6,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,8,4,3,1,7,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[8,1,5,2,6,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,7,4,2,8,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,7,8,4,3,6,2,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,5,8,7,4,3,2,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,7,2,3,6,8,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[3,1,2,6,7,8,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[3,8,1,6,4,2,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,4,7,8,2,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[3,1,5,7,6,2,8,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[6,3,1,4,2,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[2,4,3,7,6,1,8,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,1,7,6,5,2,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,4,7,6,8,3,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[7,2,1,5,6,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,3,1,8,6,2,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[3,1,5,2,8,7,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[1,2,8,4,3,7,6,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,6,1,8,7,4,3,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[7,5,1,8,3,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,7,6,3,1,8,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[5,3,1,8,6,2,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,1,8,6,3,2,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,5,4,2,8,6,3,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,4,2,8,5,3,7,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[8,3,1,6,4,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,3,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,3,2,4,8,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,7,8,1,4,2,6,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[2,6,3,8,1,7,5,4]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,5,1,8,6,3,7,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,8,6,4,1,7,3,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,2,7,5,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,1,7,2,8,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[2,8,1,7,5,3,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,8,7,6,4,3,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,8,2,6,3,5,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,5,7,1,6,2,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[4,1,8,5,3,6,2,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,4,2,5,3,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[3,1,5,8,2,7,4,6]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[6,4,1,5,3,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,2,1,5,4,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[3,1,8,5,4,6,2,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[6,1,8,4,5,3,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,5,2,7,1,6,3,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[4,3,5,7,1,6,8,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[4,1,8,5,3,6,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,3,8,4,5,1,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,1,6,8,5,7,4,2]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[2,6,1,8,5,7,4,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,3,8,4,5,2,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,7,2,3,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,3,8,4,5,2,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,1,6,8,5,3,7,4]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[3,2,6,8,5,4,7,1]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[4,1,8,5,2,6,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,1,6,8,5,2,4,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[6,5,8,7,4,1,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,7,4,2,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,5,8,7,2,4,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,8,4,5,7,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,1,8,4,5,7,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,2,7,3,5,8,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[3,6,2,4,8,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[2,7,5,4,3,8,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,5,1,8,4,7,6,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,6,1,8,5,4,7,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,4,8,3,7,6,5,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,6,8,2,5,7,4,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[2,6,8,5,4,3,7,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,6,8,2,5,4,7,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[4,6,8,3,2,5,7,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,2,8,3,5,7,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[3,6,1,8,5,7,4,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[5,2,6,8,4,1,7,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,6,3,8,7,2,5,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[3,5,8,2,7,4,6,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,6,8,5,7,4,3,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,4,8,7,6,3,5,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[7,5,1,6,3,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,7,6,3,4,1,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,7,6,3,1,2,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[4,8,2,1,7,5,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,3,8,5,7,2,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,5,4,8,6,2,3,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[8,2,1,7,5,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,7,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,1,7,5,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,5,1,8,7,6,2,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[5,6,2,7,8,1,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[4,7,3,5,6,1,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,7,8,3,5,6,1,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,2,5,6,8,4,7,1]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[8,4,5,2,6,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,8,3,7,1]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[5,3,2,4,7,8,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[4,2,5,7,3,8,1,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[4,7,3,1,6,8,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,2,7,6,8,1,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[1,7,4,6,8,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[4,7,2,5,6,3,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[5,4,1,3,7,8,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[6,1,5,8,3,7,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,1,3,5,7,8,2,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[6,1,5,8,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,2,1,6,8,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,6,4,1,8,3,2,7]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[4,5,2,1,7,8,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[2,3,7,8,5,1,6,4]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,2,6,7,4,3,5,8]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[5,8,6,3,4,1,2,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,2,3,1,8,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,1,2,6,4,8,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[8,6,2,3,7,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,2,8,6,1,3,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,4,8,2,5,6,1,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[2,8,3,6,7,4,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,2,7,5,3,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,3,2,5,8,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,6,7,2,8,4,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[5,8,3,6,4,1,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,3,8,5,2,7,1,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,8,4,5,1,6,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,8,4,7,1,6]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[2,5,8,1,3,4,7,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,1,8,7,4,2,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[4,6,1,3,8,2,7,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[8,6,1,2,3,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,7,8,3,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[3,1,7,6,2,8,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[5,3,6,7,4,2,8,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[5,4,2,8,6,7,3,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,1,4,2,8,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,7,2,6,8,4,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,6,5,2,7,8,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[5,4,6,2,7,8,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[5,1,8,6,4,2,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,2,1,8,5,7,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,4,6,2,3,1,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[6,5,7,8,1,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[2,1,7,6,8,4,5,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[6,4,7,2,8,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,3,2,7,8,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,4,8,2,7,6,5,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,7,3,1,5,2,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[2,1,4,7,5,3,8,6]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[4,7,3,6,5,2,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[4,7,6,3,1,5,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[2,4,7,3,8,5,1,6]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[2,7,3,1,8,5,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,8,3,1,7,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,2,1,4,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,2,6,8,3,4,7,5]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,5,6,8,3,2,4,7]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,7,4,8,6,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,6,3,5,7,4,8,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,5,4,7,2,8,3,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[3,8,5,2,6,1,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,8,5,2,6,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[8,1,2,6,5,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,2,5,6,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[6,8,7,1,3,4,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,4,2,8,6,7,5,1]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,7,8,6,1,4,2,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,6,1,5,2,7,8,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[7,1,6,8,3,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,1,2,6,3,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,4,7,1,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,7,8,4,2,5,6,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,4,2,8,5,1,6,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[6,8,2,7,5,4,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,4,3,7,6,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,8,7,1,2,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,8,4,5,7,6,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,8,5,7,1,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,3,4,8,7,2,1,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,3,8,4,7,1,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,8,7,1,4,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,2,8,7,1,6,4,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,8,3,1,6,4,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,7,8,5,1,4,6,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,5,8,7,4,1,6,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[7,4,6,8,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,7,8,1,3,6,4,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,7,8,1,5,4,6,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,7,8,1,4,5,6,3]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,6,7,8,2,4,1,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[4,5,7,8,6,3,1,2]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[5,4,6,8,7,3,1,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,5,8,6,7,1,3,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,7,6,8,2,1,3,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,7,6,8,2,4,1,5]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[5,4,7,8,6,3,1,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,5,7,8,2,6,1,3]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[4,5,6,8,7,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[5,7,3,4,2,1,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,1,5,3,8,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,8,6,2,5,4,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,1,7,5,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,4,8,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[2,8,5,1,4,3,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,2,7,5,1,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,3,4,5,6,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,6,4,7,2,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[4,2,6,5,7,3,1,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[5,4,6,2,7,3,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[3,2,6,5,8,4,1,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[3,2,6,5,8,7,1,4]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[4,2,6,5,8,7,1,3]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[5,2,6,4,8,7,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,4,7,6,8,2,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[6,4,7,5,8,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[4,2,7,5,8,6,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[3,2,7,5,8,4,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[4,3,7,2,8,5,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[4,3,6,2,8,5,1,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,3,7,6,8,5,1,2]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[5,3,7,6,8,2,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,3,7,2,8,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[3,2,6,4,8,7,1,5]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[4,2,7,3,8,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[5,2,7,6,8,3,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[3,2,7,6,8,4,1,5]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[3,2,7,6,8,5,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[6,2,7,5,8,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[3,7,8,2,5,4,6,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[6,7,1,3,2,5,8,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[8,7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,3,4,8,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,2,5,3,7,8,6,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[5,3,6,2,4,1,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[7,8,6,2,3,5,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,8,2,6,3,7,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,2,3,7,5,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,5,6,2,3,8,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,5,6,4,3,8,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,4,3,7,5,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,7,6,4,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,7,6,3,8,5,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,4,2,5,6,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,2,7,5,3,8,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[2,4,8,3,7,5,6,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,8,3,7,5,6,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,2,5,8,3,7,4,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,7,3,8,2,5,6,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[8,2,5,6,3,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,7,1,2,6,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[8,5,6,4,1,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,2,8,4,3,1,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[6,7,3,2,8,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[4,7,8,3,1,5,2,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,5,8,1,3,2,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,7,8,1,6,3,2,5]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,7,1,3,8,6,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[2,6,7,4,3,8,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[3,7,6,4,5,8,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[5,7,2,8,3,4,6,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,7,2,8,5,6,4,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[3,1,5,8,6,4,7,2]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[2,3,8,6,4,5,7,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,6,4,7,5,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,8,7,4,5,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,5,6,1,8,7,3,4]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[3,6,2,8,4,7,5,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,3,8,5,7,4,6,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,8,6,7,5,4,1]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[8,5,6,3,1,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,6,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,3,4,6,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[3,5,1,8,6,4,2,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[7,5,3,8,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,1,3,8,6,4,2,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,5,8,3,6,4,2,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[7,5,8,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,5,8,6,3,4,2,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,7,5,8,2,6,4,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[5,7,8,1,4,6,2,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,3,7,8,4,2,6,5]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[6,1,2,5,3,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,1,2,5,4,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,1,4,6,7,3,2,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[1,4,6,5,7,2,3,8]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[6,7,3,5,4,1,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[8,1,6,7,3,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,1,6,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,2,5,1,3,7,6,8]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[1,3,2,6,8,4,7,5]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[8,2,5,4,1,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,4,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,4,7,3,5,8]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,6,4,3,7,2,5,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[5,7,8,3,2,6,1,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[8,4,5,1,3,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,7,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,8,1,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,1,8,6,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,7,3,1,4,8,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,1,6,5,7,8,4,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[4,3,1,5,8,7,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[4,7,1,3,2,5,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,1,6,7,3,2,8,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[1,7,2,5,6,8,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[4,7,6,8,3,1,5,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[5,4,8,6,1,7,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,5,4,7,1,8,6,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[7,1,5,4,2,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,3,6,4,5,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,1,3,8,4,5,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,1,8,7,3,6,5,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,8,6,3,1,2,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,2,7,1,3,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,6,5,4,1,3,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[4,1,5,7,6,3,2,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[6,3,4,2,1,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,5,1,7,6,3,2,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[5,4,2,1,8,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,2,1,5,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,4,2,6,7,8,5,3]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,4,2,5,6,8,7,3]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[2,5,3,6,7,8,4,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,8,6,2,4,3,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,5,7,8,1,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[2,3,4,7,5,8,6,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[6,5,2,8,7,4,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,8,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,5,2,8,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,8,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,2,6,3,7,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,5,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,7,8,4,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[8,6,2,7,5,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,2,7,5,3,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[7,6,3,2,8,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,1,7,4,3,8,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[8,6,3,7,2,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,4,2,3,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,2,8,6,4,1,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,5,3,7,4,2,6,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,7,6,4,3,2,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,7,6,3,4,2,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,2,7,4,3,8,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,5,4,2,3,8,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,5,3,2,4,6,7,8]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,5,4,2,3,7,8,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,2,7,6,3,5,8,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[8,1,3,2,6,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,2,8,1,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[3,2,7,5,6,1,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[7,5,6,1,3,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,3,4,1,8,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,5,1,6,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,6,1,4,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,2,7,6,8,3,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[3,2,6,4,8,5,7,1]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[4,2,8,3,6,5,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,1,4,3,5,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,8,5,7,1,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,5,7,1,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,3,4,1,6,2,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[6,5,7,3,4,1,8,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,2,7,6,8,1,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[7,5,6,1,8,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,6,1,8,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,8,1,6,3,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,3,6,5,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,5,8,4,6,3,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,7,1,2,8,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[7,1,4,2,3,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,7,5,6,8,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[8,1,2,5,3,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,4,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,4,1,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[6,8,5,2,4,3,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,4,2,8,6,7,1,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[3,7,1,6,2,5,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[4,6,7,2,5,1,8,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[3,6,2,5,1,7,8,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[3,4,2,7,8,1,5,6]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[3,8,5,2,4,7,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,1,4,2,5,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,8,5,1,2,4,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,8,1,4,3,6,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,2,3,8,6,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,2,3,8,7,4,1,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,7,6,3,1,2,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[4,6,2,7,8,1,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[6,2,3,7,1,4,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[4,6,7,8,2,1,3,5]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[8,6,3,2,1,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,4,1,7,8,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[6,1,3,4,2,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,1,3,6,2,4,8,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[1,5,7,6,8,2,4,3]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[5,7,1,3,8,4,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[2,6,1,4,3,7,8,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,6,2,4,3,5,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,3,7,6,1,8,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[1,5,6,3,7,8,4,2]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,5,7,6,3,8,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[7,3,5,6,1,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,3,6,1,5,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,6,3,7,8,5,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,7,8,6,3,5,4,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,5,6,1,8,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[5,6,2,8,4,7,3,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,7,6,3,4,8,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[3,7,5,4,6,1,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[5,3,4,7,6,8,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,3,7,4,6,1,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[7,3,5,4,6,1,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,8,3,5,4,1,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,3,5,4,1,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,7,6,3,4,1,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[3,5,4,1,2,7,6,8]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[5,7,6,1,3,2,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,3,4,1,2,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[7,8,3,1,2,5,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,5,1,3,2,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,5,6,1,3,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,1,3,8,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,1,3,8,2,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,1,5,4,7,2,6,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[5,7,6,1,3,8,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,6,3,8,1,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,1,3,7,6,2,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[1,6,3,7,2,4,5,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,3,2,4,8,1,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[6,8,5,3,2,7,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,3,7,2,6,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,7,1,3,8,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[3,4,6,5,1,8,7,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[8,7,1,5,3,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,1,4,7,2,8,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[5,1,4,8,7,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,1,3,4,2,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,5,2,3,7,8,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,5,3,8,4,2,7,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,4,2,1,8,3,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[3,1,7,4,2,6,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[7,4,8,2,3,5,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,4,1,3,2,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,3,2,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,5,2,7,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,6,8,4,2,7,5]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[1,5,2,8,3,6,7,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,6,2,3,7,4,1,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[6,2,4,7,3,5,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,4,8,5,3,6,7,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,5,6,3,1,8,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[4,5,1,2,7,8,6,3]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[4,8,5,1,2,6,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,1,2,8,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[7,2,8,1,4,5,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,4,7,3,8,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[7,1,6,3,4,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,8,4,6,3,1,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,6,3,5,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,4,1,5,8,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,8,4,1,7,2,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,5,1,3,8,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[8,5,1,3,6,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,4,1,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,2,4,1,3,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,2,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,8,4,7,2]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[5,6,1,3,7,2,8,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[5,6,1,8,2,3,7,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,6,1,2,8,4,7,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[3,7,8,1,6,4,2,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,8,6,3,4,2,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,3,8,6,4,2,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,8,1,5,6,4,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,8,5,6,4,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,5,8,6,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,1,3,5,6,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,5,6,4,2,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,8,6,4,2,7]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,5,7,8,6,4,2,3]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,8,2,6,5,3,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,1,5,2,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,6,2,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,2,3,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,8,4,1,3,5,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,8,1,2,3,7,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,1,3,5,6,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,5,3,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,6,2,5,8,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[5,2,7,3,4,8,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[4,2,1,6,5,7,8,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[2,7,5,4,1,3,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7,4,6,5,1,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,8,7,5,2,1,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,6,3,5,1,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,8,6,4,5,3,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,8,7,6,3,4,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,7,8,5,6,3,2]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,6,4,8,5,7,3,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,8,5,2,7,3,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,6,8,5,4,2,3,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,3,4,8,5,2,7,6]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[3,5,8,7,6,2,4,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[6,5,3,7,4,1,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[3,1,5,4,6,8,7,2]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[3,1,6,4,2,5,8,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[3,6,1,4,5,7,8,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[1,8,4,7,2,3,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,8,2,4,6,1,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,4,2,3,6,8,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[3,8,1,6,4,2,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,8,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,7,2,4,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,5,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,3,7,4,6,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,3,1,7,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,7,8,6,2,5,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[4,8,1,2,6,5,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,8,3,7,2,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[2,8,1,6,5,3,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,5,7,6,3,8,4]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[4,1,2,5,7,6,8,3]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[4,3,5,1,7,8,6,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[1,8,5,2,3,4,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,8,2,3,4,7,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,2,7,8,4,5,6,3]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[4,3,8,7,6,2,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,4,8,2,7,6,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,2,5,6,4,8,1,7]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[2,3,6,4,1,7,5,8]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[2,3,7,1,5,8,4,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,3,6,1,7,5,8,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[2,3,6,5,1,7,4,8]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[3,6,4,2,1,5,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[4,3,2,6,5,8,1,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[4,6,5,2,1,7,8,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[4,6,1,7,5,8,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[4,2,6,5,1,7,8,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[4,1,5,7,6,8,3,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[3,5,6,2,1,4,7,8]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[4,2,5,7,6,8,3,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[4,3,6,5,2,8,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[4,3,6,5,1,7,8,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[3,6,4,5,2,1,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[3,5,6,4,2,8,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[4,6,5,3,1,7,8,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[5,8,1,4,2,3,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,5,8,2,3,1,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,5,4,8,1,7,2,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[5,3,6,8,1,4,7,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[3,5,1,8,6,4,7,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[4,7,2,8,3,1,6,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[1,2,5,6,8,3,7,4]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[5,3,8,4,6,2,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,4,8,1,5,2,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,3,2,1,6,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,8,7,2,3]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[1,2,5,6,8,4,7,3]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,5,6,8,4,7,2,3]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[5,6,8,1,2,4,7,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,8,1,4,5,7,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,3,5,1,8,6,7,2]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[1,3,5,6,8,4,7,2]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[5,6,8,2,3,4,7,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,5,1,2,4,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,8,7,2,1,3,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,1,7,2,8,6,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[6,1,5,3,4,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,8,6,3,2,1,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,7,1,6,3,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,7,8,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[8,6,7,1,2,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,4,2,8,7,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[7,5,1,4,8,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,2,8,1,7,5,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,4,3,1,7,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,8,4,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,4,3,1,8,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,8,1,6,3,4,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,8,1,7,3,4,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,6,5,3,8,2,7,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,5,6,3,8,1,7,2]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[7,8,3,5,2,1,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,3,7,5,2,4,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,2,4,5,7,3,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[7,8,1,5,6,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,3,7,5,1,4,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,3,8,2,4,6,7,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[6,1,7,3,4,2,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[3,1,7,2,5,8,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[2,8,7,6,3,5,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,1,5,6,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,5,6,2,8,1,7,4]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[5,3,1,8,6,2,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,1,4,6,8,2,7,5]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[4,1,5,7,3,8,2,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[6,2,5,8,4,7,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,2,8,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,1,6,8,2,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,6,5,7,8,4,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[3,6,5,7,4,1,8,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[1,6,5,7,4,2,3,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[3,4,7,5,2,1,8,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[3,6,7,5,8,4,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[3,4,7,2,5,6,8,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[2,5,3,7,8,6,4,1]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[7,2,8,4,5,6,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,2,3,8,5,4,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,8,7,3,2,4,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,6,1,4,5,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,8,6,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,6,3,8,5,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,3,1,8,4,6,5,7]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,3,1,7,6,8,4,5]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[2,3,1,8,4,6,7,5]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[4,2,3,5,1,8,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[5,8,7,2,6,4,1,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,5,1,7,4,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,2,7,4,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,3,8,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,1,6,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,5,8,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,3,2,8,1,7,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,6,8,7,1,3,5,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,3,8,7,6,2,1,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,7,6,1,4,5,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[4,1,6,2,7,5,3,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[7,6,2,5,3,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,3,1,7,6,2,5,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[4,5,3,1,2,8,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[2,4,5,3,1,8,6,7]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[5,7,6,2,3,1,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[4,1,3,7,5,2,6,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[4,1,6,3,2,7,5,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[7,5,4,1,3,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,4,8,5,6,3,1,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,5,7,4,1,3,6,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[5,7,4,1,3,2,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[2,6,8,4,5,3,1,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,2,3,7,4,1,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,5,1,6,3,2,7,8]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[5,1,6,3,2,4,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[4,2,5,1,6,3,7,8]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[5,1,6,2,4,3,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[5,3,4,8,7,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,3,1,6,7,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,5,7,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,6,7,4,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,5,7,2,4,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,6,4,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,5,3,6,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,8,3,4,7,6,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,8,5,2,7,1,3,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,6,4,5,2,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,4,7,6,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,1,4,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,5,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,3,4,7,2,8,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[8,1,7,3,6,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,5,3,4,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,4,3,1,5,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,4,5,8,3,2,6,7]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,5,2,4,7,8,6,3]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[5,2,7,4,3,8,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[2,7,3,4,8,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,6,8,3,5,4,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,4,5,3,8,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,3,7,4,5,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,6,3,2,7,5,8,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[7,3,5,2,6,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,2,7,1,5,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[2,5,3,6,4,7,8,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[4,2,5,3,6,7,8,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[1,6,5,2,4,7,3,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,8,7,2,4,6,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,2,5,4,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,2,7,3,6,8]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,5,4,2,8,7,3,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,6,8,3,5,2,4,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,7,6,2,3,5,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,2,8,3,6,5,4,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,6,5,2,4,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,4,7,3,2,8,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,8,6,5,2,4,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,8,4,3,2,5,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,7,5,3,2,6,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,2,6,5,3,8,4,7]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,7,3,2,8,4,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,6,5,2,8,4,7,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,8,3,7,2,4,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,8,7,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,6,3,2,5,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,1,6,5,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,3,2,6,1,5,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,8,5,2,7,1,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,5,1,7,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,5,7,2,1,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,5,8,2,7,4,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,1,7,5,8,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,6,4,8,5,3,7,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[3,5,6,2,8,7,1,4]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[1,6,5,3,4,7,8,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[4,2,6,7,8,1,3,5]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[4,6,5,1,3,7,8,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[5,1,7,2,6,4,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[4,1,7,6,5,8,2,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[5,2,1,7,6,4,8,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[4,2,3,6,7,8,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[4,7,2,1,6,5,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[2,7,6,4,1,5,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,4,3,6,7,8,1,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[7,5,2,4,1,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,5,1,3,7,8,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[7,2,1,4,3,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,2,4,3,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[8,1,5,4,2,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,4,6,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,2,6,5,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,6,1,2,4,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,4,5,2,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,1,4,8,7,2,3,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,1,8,5,7,2,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,6,7,5,8,3,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[6,1,7,5,8,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,1,4,7,8,2,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[8,1,2,3,7,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,6,1,2,4,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,6,8,7,5,3,4,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,1,8,7,5,2,3,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,3,1,2,4,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,2,4,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,4,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,7,1,4,2,3,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,1,7,4,8,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,7,8,5,1,2,4,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[4,3,8,5,6,2,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,3,8,6,7,2,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[7,6,8,1,5,3,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,6,1,5,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,3,8,1,7,2,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,1,5,4,8,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,2,5,4,7,1,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[8,3,6,7,5,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,6,5,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,8,5,6,4,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[4,6,8,2,3,5,1,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[6,8,2,1,3,5,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,5,1,6,4,8,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[3,5,8,6,2,1,4,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,4,8,5,6,1,3,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,8,2,5,6,1,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,3,8,4,2,7,6,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,8,5,3,1,4,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,8,4,6,3,2,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,7,2,4,6,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,2,1,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,8,2,7,5,4,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,4,5,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,7,4,6,3,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,7,4,6,3,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,4,1,2,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,2,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,6,2,1,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,8,4,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,8,6,4,7,2,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,7,2,6,5,8,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,6,8,5,7,4,2,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[6,7,5,2,4,8,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[8,1,2,7,5,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,4,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,4,8,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[8,3,5,6,4,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,1,3,4,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,4,5,1,3,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,4,8,7,5,3,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,7,1,4,3,2,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,2,5,1,4,8,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,8,1,3,4,2,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,5,6,3,2,8,7,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,3,7,6,8,4,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,6,7,3,2,8,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[3,2,7,6,8,4,5,1]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[1,3,8,5,2,7,6,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[6,4,1,5,2,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,6,5,3,1,8,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,5,1,4,7,3,6,8]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[3,1,6,5,7,2,4,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[2,6,1,5,7,4,8,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[2,5,7,1,6,3,8,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[2,6,1,5,7,4,3,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[3,1,6,5,2,4,7,8]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[3,6,5,1,4,2,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[3,6,5,1,7,2,4,8]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[3,6,5,2,1,4,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[5,4,3,6,1,7,2,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[4,5,2,7,6,1,3,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[4,6,5,3,1,2,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[5,4,1,6,3,7,2,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[5,4,2,6,3,7,8,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[3,6,5,7,1,4,2,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[3,6,5,1,4,7,2,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[4,3,6,5,7,1,2,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[4,2,6,5,1,3,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[4,1,6,5,3,7,8,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[4,2,5,7,6,1,3,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[3,4,7,6,1,2,5,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[4,2,5,7,6,3,8,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[4,1,6,5,2,7,3,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[3,6,5,7,2,1,4,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[3,5,7,6,2,4,1,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[5,4,2,6,3,7,1,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[4,6,5,2,7,3,1,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[4,6,5,2,1,7,3,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[3,5,8,2,1,4,6,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,8,2,4,6,7,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[5,3,8,2,1,4,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,3,1,8,2,4,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,1,3,8,2,4,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,5,8,4,2,3,6,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,8,2,1,4,3,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,2,4,1,6,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,2,4,6,3,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,2,4,3,6,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,1,4,6,2,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,5,8,4,6,7,2,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,1,8,4,6,7,2,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,2,4,6,3,7,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,8,4,6,7,2,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,6,7,2,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,3,6,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,6,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,5,7,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,2,4,5,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,2,3,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,6,2,4,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,2,1,4,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,2,4,1,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,6,2,4,5,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,6,2,4,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,6,2,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,7,2,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,2,1,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,6,4,5,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,6,7,5,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,6,2,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,6,3,5,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[8,4,2,1,5,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,7,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,2,5,8,4,7,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[3,2,1,7,4,5,8,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[2,6,8,5,1,7,4,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,1,5,8,7,3,6,4]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[3,2,1,6,7,4,8,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[4,3,1,7,8,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[5,6,8,2,4,3,7,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[2,8,5,3,6,4,7,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,8,6,4,7,3,5]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,7,8,6,4,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[4,2,7,8,3,5,6,1]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[2,8,3,7,1,4,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,5,6,4,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,8,4,2,7,6,5,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,2,7,5,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,2,4,8,7,5,6,1]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[2,6,8,1,5,3,4,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,2,5,6,8,1,4,7]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[3,8,1,6,4,5,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,3,6,5,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,6,2,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,2,4,8,6,3,7,5]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[7,2,1,5,3,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,7,2,3,1,4,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[7,1,5,2,4,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,2,7,3,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,4,7,5,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,5,8,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,5,8,7,3,1,2,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,3,8,7,6,4,2,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,8,5,1,7,4,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,4,7,5,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,6,3,8,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,2,8,6,4,7,5,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,8,6,3,7,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,4,3,1,6,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,8,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,3,1,6,2,8,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[3,5,4,1,7,8,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[6,4,2,1,5,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[3,1,5,8,7,2,4,6]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[3,2,5,7,8,4,6,1]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[5,3,7,4,2,6,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,3,7,4,2,6,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,3,8,4,2,1,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,8,4,3,1,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,1,8,4,3,2,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,7,4,3,6,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,2,7,4,3,6,8,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,3,7,4,1,6,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[3,1,5,7,8,4,6,2]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[3,1,5,7,8,4,2,6]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[5,2,7,4,1,3,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[6,2,3,7,4,8,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,2,3,7,4,8,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,2,3,7,4,5,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,1,3,7,4,5,8,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,2,8,6,4,3,5,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,7,4,5,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,8,6,3,5,4,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,1,8,5,3,4,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[4,5,7,8,1,6,3,2]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[2,5,7,8,4,6,3,1]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,8,2,7,5,3,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,1,8,6,7,3]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[5,6,8,3,4,2,7,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,1,5,3,8,6,7,2]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[7,3,5,1,4,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,3,2,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,8,7,1,4,2,5,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,8,2,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[8,5,4,6,1,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,1,4,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[5,3,2,4,8,1,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,3,2,4,7,1,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[8,4,5,3,7,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,7,3,5,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,3,2,4,6,8,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[2,7,6,3,1,4,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,7,4,5,6,8,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[8,7,1,4,2,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,3,7,1,5,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,7,3,5,8,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[8,4,3,5,7,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,4,2,5,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[7,6,4,2,8,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,5,2,4,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,4,3,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,1,3,6,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,6,7,2,5,1,8,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[2,6,5,7,1,4,8,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[3,5,1,7,8,4,6,2]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[1,5,2,4,6,8,7,3]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[8,1,2,4,7,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,1,8,6,7,5,2]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[4,3,8,5,1,7,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,1,3,2,8,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,5,3,2,4,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,2,5,8,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[8,5,4,2,6,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,6,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,5,1,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,7,5,2,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[5,3,7,1,4,6,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,7,2,6,1,4,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[3,8,5,7,6,1,2,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,7,5,2,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,7,2,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,4,6,8,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[4,8,6,3,7,2,1,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,1,7,6,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,4,8,1,7,3]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[5,7,2,1,6,8,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[4,7,8,5,1,6,2,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,5,2,1,6,7,8,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[4,5,6,3,1,7,8,2]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[3,5,6,7,4,1,8,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[3,5,1,4,2,8,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[3,5,1,4,2,6,8,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[3,5,1,4,2,6,7,8]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[1,3,8,4,6,2,5,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,8,4,2,3,7,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,8,3,2,7,6,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,3,7,6,5,2,4,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,2,8,6,7,5,4,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,7,5,4,3,2,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[3,8,5,7,4,6,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,2,4,5,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,7,4,5,2,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,4,1,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,6,3,2,5,1,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,2,7,8,3,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[4,6,3,7,5,8,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[4,2,5,7,8,6,3,1]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[3,6,8,4,5,2,1,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[8,2,5,7,3,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,5,8,7,6,3,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[6,7,2,4,5,1,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[5,2,7,8,3,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[7,2,8,3,1,6,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,3,4,1,8,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,4,7,8,1,3,6,5]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[8,5,1,2,3,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,8,3,1,4,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,7,2,5,1,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,3,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,2,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,1,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,2,7,1,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,4,8,2,1,7,6,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,8,4,2,1,7,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,1,7,5,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,5,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,7,6,2,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,6,8,2,5,7,3]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,6,2,4,8,1,7,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[7,3,8,2,4,6,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,5,2,6,8,3,7,4]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,5,3,1,8,2,6,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[5,1,7,8,3,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[7,2,8,4,1,3,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,7,3,2,8,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,2,1,7,3,8,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,8,2,1,3,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,2,5,1,8,3,6,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[7,4,2,8,3,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,4,2,8,3,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,8,5,2,1,4,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,6,2,7,8,4,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[7,3,4,1,8,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,7,6,3,5,8,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,7,6,5,2,4,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,4,7,8,6,2,5,3]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,6,7,8,3,2,5,4]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,3,2,7,8,4,6,5]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[6,8,2,3,5,7,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,7,1,4,6,2,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[6,3,1,4,7,8,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[8,7,1,5,4,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,7,1,8,6,2,3]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[4,3,8,6,5,2,7,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,3,8,6,5,1,7,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[5,4,7,3,1,2,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[7,6,2,1,5,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,1,2,6,5,7,8,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[7,3,2,6,1,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,2,5,6,8,4,1,7]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[7,2,6,8,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,7,5,6,2,4,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[4,2,5,1,3,6,8,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[5,3,4,2,7,1,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[5,6,8,2,1,3,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,5,2,1,3,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[2,4,3,5,6,8,1,7]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[6,3,2,4,8,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,3,1,2,7,8,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[8,4,7,1,2,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,8,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,5,6,7,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,3,8,4,7,1]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[6,8,4,2,3,1,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,7,6,2,8,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,1,5,6,3,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,1,3,8,5,2,7,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,8,5,4,7,2,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,5,6,4,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,6,5,1,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,4,5,8,6,2,7]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[1,8,3,2,5,4,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,2,8,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[5,7,8,1,3,2,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[8,2,4,1,6,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,2,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,8,3,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,8,6,1,3,5,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,7,5,8,4,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,3,1,2,7,8,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[8,2,7,5,3,4,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,2,8,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,4,7,2,6,3,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,7,8,3,6,4]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[7,6,3,4,2,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,6,2,3,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,8,1,7,2,6]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[6,3,4,2,7,8,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,6,3,7,8,2,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[8,6,3,4,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,7,5,1,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,5,6,2,7,8,3,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[4,5,6,2,7,1,8,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[4,5,6,2,1,7,8,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[4,5,6,2,1,7,3,8]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[6,8,7,2,3,1,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,5,1,6,7,3,2,8]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[2,5,1,8,3,7,4,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,7,2,1,3,8,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[3,7,5,4,1,6,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[7,1,5,4,2,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,5,6,3,7,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,6,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,3,4,6,8,1,7,5]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[2,3,5,8,1,6,7,4]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,4,7,5,6,8,1,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[7,3,4,6,2,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,7,6,5,2,8,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[2,5,4,8,6,7,3,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[7,5,4,1,6,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,5,2,1,7,6,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,3,6,4,1,8,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[7,2,1,8,5,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,6,5,1,4,8,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[6,3,5,4,8,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,5,1,4,6,3,8,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[3,1,5,6,4,2,8,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[8,5,6,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,6,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,3,6,8,5]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[5,3,7,6,4,8,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[3,7,6,4,2,8,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[8,6,1,4,3,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,5,1,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,5,3,7,8,6,4]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[5,1,4,7,6,8,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[8,4,1,3,7,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,1,6,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,2,6,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,4,3,7,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,4,3,2,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,6,4,3,8,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[1,6,4,3,8,2,7,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[6,7,4,1,3,2,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,8,1,4,3,2,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,8,4,5,3,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,3,1,8,6,5,7,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,2,7,5,1,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[5,2,3,7,4,1,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[2,1,7,4,3,6,8,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[7,1,2,4,5,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,8,7,1,4,5,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,3,4,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,3,1,4,6,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,7,2,5,4,6,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,5,3,8,1,6,7,4]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,6,4,2,5,7,8,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[6,5,3,4,1,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,6,3,4,1,7,8,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[2,5,3,1,4,7,8,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[6,8,2,3,1,5,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,3,1,5,2,7,8,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[5,2,3,1,4,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[7,2,1,3,5,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,3,6,4,5,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,3,7,5,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[5,2,4,7,8,6,3,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,4,8,7,2,3,1,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,1,4,5,3,6,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,4,6,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,1,7,4,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,5,7,2,1,8,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,5,4,7,3,8,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[7,4,1,3,8,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,6,8,4,1,7,2,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[2,1,8,4,7,6,3,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,7,5,6,8,4,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,5,2,4,7,8,6,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[7,5,6,3,8,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,6,2,7,4,5,8,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[7,4,2,6,1,5,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,1,6,2,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,1,6,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,2,7,6,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,1,2,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,1,2,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,2,1,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,6,2,4,3]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[6,8,4,7,5,2,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,7,1,5,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,7,4,2,5,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,5,7,2,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,2,5,1,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,5,3,7,6,4,8,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[3,1,5,7,6,4,2,8]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[3,1,6,5,4,7,2,8]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[2,5,6,8,3,4,7,1]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[4,1,3,6,5,2,7,8]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[3,6,2,4,5,7,1,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[3,6,2,5,4,7,1,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[3,5,1,7,6,4,2,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[3,6,1,4,5,7,2,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[4,3,1,6,5,2,7,8]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[4,1,2,6,5,3,7,8]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[4,6,1,3,5,2,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[3,6,4,2,5,7,1,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[4,2,6,3,5,1,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[3,4,7,6,5,1,2,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[4,5,2,7,1,3,6,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[4,6,1,2,5,3,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[5,8,4,7,1,3,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,7,1,3,5,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,8,1,3,5,7,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,3,2,7,4,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,3,1,5,4,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,1,2,5,3,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,2,8,3,4,6,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,7,1,6,4,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[4,5,2,6,1,3,7,8]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[4,3,5,8,6,1,7,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[5,1,3,6,7,4,2,8]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[4,2,8,3,6,7,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,1,7,8,5,6,2,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[6,2,1,7,5,3,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[3,7,1,8,5,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[4,2,8,6,7,1,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,1,2,4,7,3,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[5,3,1,6,4,7,2,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[1,2,4,5,8,7,3,6]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,3,4,7,5,8,6,2]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,5,2,3,7,8,6,4]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,2,8,1,6,5,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,6,4,1,7,2,8,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[5,2,6,3,7,8,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[2,4,1,3,7,8,6,5]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[2,6,1,5,7,8,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,1,6,4,7,8,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[8,4,6,3,7,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,6,8,2,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[5,7,4,8,1,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[3,6,7,5,8,1,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[3,7,5,6,8,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,1,6,8,4,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,5,4,7,2,6,3,8]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[2,4,5,8,3,1,7,6]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,4,7,5,8,3,6,2]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[2,6,8,7,3,5,1,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,7,8,6,2,5,1,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,8,7,3,5,6,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,5,4,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[4,3,8,1,6,5,7,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,3,6,2,5,8,7,4]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[5,8,7,1,4,6,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,2,5,1,3,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,6,5,1,3,4,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[4,6,5,1,2,7,3,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[5,6,4,1,2,7,3,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[8,1,5,6,2,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,1,2,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[5,4,6,1,3,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[5,7,1,4,3,2,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[2,6,4,1,3,7,5,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[7,8,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,2,6,7,8,4,5,3]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[6,1,4,8,2,7,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,2,3,7,1,8,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[7,2,3,1,8,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,4,1,7,3,2,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[7,3,4,5,1,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,5,6,7,4,8,2,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[6,3,2,5,7,4,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[5,7,3,8,1,2,4,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,5,2,7,6,3,1,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[4,5,2,1,7,6,3,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[2,6,7,8,3,1,4,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[6,3,2,5,1,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,6,3,7,8,2,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[5,6,7,1,8,4,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[1,7,8,4,6,5,2,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,3,2,8,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,1,2,8,6,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,8,1,6,5,3,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,1,5,7,3,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,6,3,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,8,4,7,6,3,1,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,4,7,6,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,4,6,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,1,8,4,7,6,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[3,4,2,8,1,7,6,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[2,4,5,8,1,7,6,3]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,1,8,2,6,7,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,6,8,1,4,3,7,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,1,8,2,6,7,3,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,6,5,2,8,7,3,4]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,1,5,8,7,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[8,1,7,3,5,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,2,7,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,8,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,8,1,6,2,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,8,4,5,3,1,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,5,3,2,8,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,2,5,3,8,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,6,1,3,5,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,2,4,5,3,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,1,5,4,7,2,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,8,5,4,7,1,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,6,8,4,2,5,7,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[7,5,8,1,3,4,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,4,2,8,3,5,7,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,3,5,4,8,7,2,6]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,6,2,4,8,3,7,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,7,8,5,4,2,6,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,5,2,8,6,4,7,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,6,5,2,7,4,8,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,1,6,7,4,2,8,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[1,5,4,2,8,6,7,3]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,8,5,4,6,2,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,4,6,2,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,8,4,1,6,2,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,4,5,1,7,2,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[4,8,1,3,7,6,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,1,2,8,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[6,4,2,3,1,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,5,2,1,3,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,6,1,8,2,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,4,2,3,7,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,8,1,2,4,3,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,7,6,8,3,5,4,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,7,6,4,2,1,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,5,7,4,1,3,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[4,6,1,8,3,5,2,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[7,1,6,8,2,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,7,1,8,3,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,8,3,6,1,5,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,7,8,6,4,5,3,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,2,8,6,4,5,1,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,4,3,6,2,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,4,3,5,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,1,2,6,8,7,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[5,7,4,2,1,8,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[8,6,5,7,2,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,1,8,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,6,3,8,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,4,8,1,6,3,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,8,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,4,8,2,3,5,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,6,8,2,5,7,1,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[6,4,8,2,5,7,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,2,4,5,8,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,8,2,4,7,3,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,4,6,2,7,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,2,7,1,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,2,4,1,7,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,5,1,6,2,4,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,2,5,7,1,6,8,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[2,4,8,5,6,7,3,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,5,2,3,8,7,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[2,5,4,7,6,1,3,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[5,2,3,7,6,1,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,2,3,7,6,1,5,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[4,2,7,3,5,1,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[5,6,2,3,8,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,6,2,3,1,7,8,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[5,7,2,3,4,1,6,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,2,7,3,5,1,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,2,6,3,5,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,2,3,1,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,5,2,3,8,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,5,2,1,4,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,5,2,3,1,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,3,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,1,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,4,2,7,5,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[8,5,2,7,3,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,4,5,6,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,3,2,5,6,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,8,1,4,6,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,8,1,5,6,3,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,8,2,3,1,5,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,2,3,1,6,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,7,2,1,4,6,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[4,2,7,1,5,6,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[4,2,3,8,1,7,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,2,1,5,3,7,6,8]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[5,1,3,8,4,6,7,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,1,3,2,6,7,8,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[5,1,3,4,2,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[6,1,3,4,2,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[7,2,1,3,5,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,8,7,2,3,4,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,7,2,8,1,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[5,2,3,7,4,6,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[2,5,3,7,4,6,1,8]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[2,6,7,3,4,5,1,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[6,2,7,3,4,5,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[3,8,4,5,2,1,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,6,3,4,5,1,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,8,7,5,1,3,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,2,8,3,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[5,2,1,3,6,7,8,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,6,5,7,2,8,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[7,5,2,6,1,8,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,1,5,2,7,8,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,6,5,7,2,8,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,5,4,6,2,8,7,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,5,4,6,2,8,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,5,6,4,8,2,3,7]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[6,2,1,5,8,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,5,6,8,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,3,7,5,1,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,3,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,6,4,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,7,4,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,2,7,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,6,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,3,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,6,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,5,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,5,3,7,8,1,6,2]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[3,4,2,8,1,6,7,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[8,3,4,1,5,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,5,1,6,2,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[5,2,6,1,4,3,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[3,5,2,8,6,7,4,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[5,3,7,4,2,8,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[7,4,8,2,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,6,2,8,7,1,4,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,6,3,5,2,7,8,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[4,1,6,3,5,7,2,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[3,1,5,7,4,6,8,2]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[7,2,5,8,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,3,6,1,5,7,8,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[3,5,4,1,2,6,7,8]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[5,3,1,4,6,7,8,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[4,6,7,1,3,5,8,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[5,6,1,3,4,7,2,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[2,5,3,7,8,4,6,1]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,6,2,1,3,7,8,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[3,6,2,4,1,7,5,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[3,2,6,7,4,8,5,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[7,1,3,8,4,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,1,8,3,4,6,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,3,2,7,5,8,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,2,7,1,4,5,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[4,2,6,1,5,7,3,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[2,5,4,1,3,6,7,8]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[5,4,1,2,6,7,3,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[6,5,2,7,4,1,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,5,7,3,1,4,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,7,4,3,1,5,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[3,1,6,7,8,4,5,2]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[7,4,5,6,2,1,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,4,5,2,7,1,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[3,7,5,6,2,1,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,7,6,3,8,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,4,1,2,7,8,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,4,1,3,5,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[5,1,8,3,4,6,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,5,8,2,3,7,1,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[7,3,4,8,2,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,8,1,5,4,2,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,7,2,5,1,6,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[6,5,4,7,2,8,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[3,2,4,6,5,8,1,7]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[3,5,4,8,7,1,6,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[7,5,2,1,6,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,3,1,7,4,2,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[8,7,2,1,5,3,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,3,7,4,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,2,8,1,5,6,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,3,6,4,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,1,4,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,7,2,6,3,8,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[8,4,1,2,3,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,2,1,8,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[6,8,1,3,2,7,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,7,3,6,4,1,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[7,2,4,3,8,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,5,4,6,1,3,8,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[2,4,3,5,8,1,6,7]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[5,8,2,6,7,4,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,6,5,3,8,1,4,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[6,1,2,4,3,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,5,8,2,7,3,4,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,7,6,8,4,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,6,5,3,8,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,1,2,4,3,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,6,1,3,7,8,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[8,4,1,5,2,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,6,3,8,7,2,4]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[5,3,2,6,8,7,1,4]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[6,3,5,2,7,1,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[8,5,2,6,7,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,8,7,1,4,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,4,5,3,1,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,5,1,2,3,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,1,5,4,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,2,6,1,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,7,1,2,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,5,4,3,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,4,7,1,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,4,7,6,2,5,8]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[5,3,4,1,6,2,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[2,7,1,4,6,3,5,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[7,3,1,6,5,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,5,2,4,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,1,4,5,2,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,1,5,8,2,7,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,1,2,3,6,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,1,3,8,7,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,8,4,6,5,1,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,1,3,6,5,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,7,2,8,1,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,4,1,2,6,3,8,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[6,5,1,4,7,3,2,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[2,7,8,4,1,3,6,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,4,6,5,7,8,1,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[2,4,6,7,5,8,1,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[2,4,6,3,7,8,1,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[2,4,5,6,8,7,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[2,4,5,6,8,3,7,1]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[2,4,5,6,3,8,1,7]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[2,3,4,6,8,5,1,7]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[5,2,8,3,4,1,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,6,4,1,2,7,8,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[4,1,7,3,8,6,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[8,4,1,2,5,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,2,7,6,8,4,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,7,6,8,3,1,2,5]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,8,2,7,6,5,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,4,2,8,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,6,5,2,7,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,7,1,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,5,8,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,2,1,6,5,8,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[2,6,4,8,5,7,3,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,3,1,4,5,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[3,4,8,5,2,1,7,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[4,8,7,1,3,2,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,4,6,1,3,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,4,1,8,7,6,2,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[1,3,5,6,8,7,2,4]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[2,8,7,5,4,1,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,5,7,4,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,3,4,1,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,6,1,3,2,8,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[2,6,5,8,3,1,4,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,7,8,2,4,5,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[3,2,8,4,5,7,1,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[6,1,8,2,4,5,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,3,6,4,2,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,4,7,6,2,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[8,3,7,5,4,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,8,5,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,4,3,7,6,1,8,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[8,6,3,7,1,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,7,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[8,5,4,1,2,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,1,6,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,4,1,7,5,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,6,1,3,2,7,8,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[6,7,2,5,8,4,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[4,1,7,8,2,5,6,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[3,4,6,7,1,5,8,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[3,4,5,7,8,1,6,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[1,8,7,4,3,5,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,8,1,3,7,6]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[2,7,8,6,5,3,1,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,3,1,5,8,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,8,3,5,6,1,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,2,7,5,8]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[2,3,7,5,8,1,4,6]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[3,2,8,5,6,1,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,2,5,8,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,7,5,8,1,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,7,5,8,1,2,3,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[3,4,7,5,2,8,1,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[4,3,2,5,7,8,1,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[2,4,7,5,8,3,1,6]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[2,5,4,7,3,8,1,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[3,7,8,4,2,1,6,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[8,5,4,7,6,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,4,8,7,6,2,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[3,2,4,5,8,1,6,7]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[3,6,8,4,2,7,1,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,4,7,6,3,8,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,6,5,1,7,2,8,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[7,4,1,6,2,8,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,3,6,8,2,4,7,5]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,6,7,4,3,8,2,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[7,3,1,6,5,2,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,5,4,1,6,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,8,5,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[7,8,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,6,2,7,3,5,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,3,8,7,5,6,4]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[8,1,7,3,6,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,4,7,3,8,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[4,8,1,6,3,7,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,5,4,1,6,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,2,4,8,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,7,3,2,4,8,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[2,6,8,5,4,3,1,7]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,8,4,6,3,5,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,8,3,6,4,5,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,8,1,4,6,5,2,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,4,1,8,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[4,6,1,8,5,3,2,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[3,8,5,2,1,6,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,4,8,2,6,3,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,5,8,1,3,7,6,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[8,6,7,1,4,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,7,8,6,3,5,2]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[8,5,2,6,3,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,2,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,2,5,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,1,8,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[4,3,7,6,1,8,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[8,6,3,2,7,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,5,4,7,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,7,2,5,4,8,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[7,6,2,4,8,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,6,8,7,3,1,2,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,7,5,2,6,3,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,5,6,2,8,1,4,7]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[5,1,2,4,3,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[6,1,8,2,4,3,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,6,8,2,5,3,4,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[8,5,2,7,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,1,2,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,5,6,4,3,8,1,7]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[8,7,3,5,1,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,3,8,5,2,7,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[8,7,1,4,5,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,8,5,6,2,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[5,2,8,3,1,6,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,7,8,6,3,2,5,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,7,2,4,5,6,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,2,8,1,5,7,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,4,6,7,2,1,5,8]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[2,6,7,1,4,3,8,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,7,6,2,1,8,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[4,2,5,3,8,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[3,2,7,4,8,5,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[7,2,5,1,6,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,8,2,7,4,6,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,5,2,8,3,7,1,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[7,8,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,3,1,2,7,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,6,8,3,2,1,7,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,8,3,5,1,2,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[1,4,6,3,7,5,2,8]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[4,5,2,6,8,7,3,1]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[1,7,6,3,8,5,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,3,8,7,4,5,6,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[7,3,1,8,4,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,2,8,7,4,5,6,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,3,7,5,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,4,2,5,1,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[3,8,2,1,5,7,6,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,8,7,4,6,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[7,5,2,8,3,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,4,2,7,3,8,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[4,6,3,7,8,1,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[8,3,5,4,7,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,4,1,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,1,5,6,3,8,7,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[8,5,1,6,3,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,3,2,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,1,5,4,6,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,1,3,7,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,8,3,7,6,1]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[5,6,4,1,8,2,7,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[6,4,5,1,3,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,1,3,5,4,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,3,8,7,2,5,6,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,5,4,1,8,3,7,6]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[5,1,4,8,3,7,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,4,1,2,7,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,7,6,5,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,3,4,6,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,3,1,2,4,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[8,5,7,3,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,2,8,7,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,4,3,8,5,7,2,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[6,7,1,5,2,8,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,5,3,7,6,4,8,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,8,1,3,6,2,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,7,3,4,8,6,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,8,2,4,7,3,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,1,6,5,8,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,3,8,1,5,7,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,5,7,4,8,3,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[8,5,6,2,4,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,6,7,1,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,1,5,7,3,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,1,2,8,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[2,7,6,4,3,8,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,8,6,2,7,5,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,1,6,2,5,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,2,5,7,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,3,1,2,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,4,8,5,2,3,6,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,4,8,5,2,3,7,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[7,1,4,2,6,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,5,8,7,2,4,3,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,5,4,2,8,3,7,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,2,8,7,3,5,4,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,7,1,3,2,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,4,2,8,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[4,1,6,8,7,2,3,5]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,7,5,6,2,8,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[8,4,3,6,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,7,5,2,8,4,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,8,4,3,2,7,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,1,7,3,5,8,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,3,7,6,4,8,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,6,4,8,7,3,1,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,1,8,7,3,5,4,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,8,7,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,1,8,5,7,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,5,1,4,7,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,2,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,3,5,8,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[2,6,7,3,5,8,1,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,3,1,6,4,8,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[2,5,6,7,1,4,8,3]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[4,7,5,3,2,8,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,7,5,2,8,6,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[3,8,6,7,2,5,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,2,7,4,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,3,1,8,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,6,3,7,8,1,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[6,3,1,8,4,5,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,1,4,7,5,8,6,3]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[7,6,2,4,8,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,8,1,4,3,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,1,4,2,7,5,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,3,1,2,5,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,6,4,7,1,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,5,1,8,7,3,4,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[7,2,4,3,8,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,8,4,3,5,1,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,4,7,3,6,8,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,7,1,4,6,8,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[2,4,7,3,6,8,1,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[8,5,7,6,1,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,5,6,1,8,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,2,6,7,4,5,8,3]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[6,5,2,8,7,1,4,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,2,3,6,8,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,6,1,3,8,5,4,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[6,4,1,8,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,8,1,4,2,7,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,3,1,6,8,7,4,5]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[6,4,8,2,1,7,3,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,3,1,8,7,5,6,4]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,5,6,7,2,4,3,8]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[6,8,3,7,1,2,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,6,4,1,5,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,7,3,6,2,4,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[6,7,4,5,1,3,8,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,6,5,3,8,2,4,7]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,6,1,2,4,8,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[8,7,4,5,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,2,7,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,7,2,5,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,2,4,6,1,8,7,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[3,6,7,4,1,2,5,8]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[1,4,7,5,8,2,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,6,8,4,7,3,2,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,6,7,5,4,8,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[4,5,7,2,6,3,8,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[2,1,5,7,4,6,8,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[2,3,5,7,8,1,6,4]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,5,7,4,2,3,6,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[2,4,7,5,3,6,8,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[8,1,7,2,4,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,7,8,6,3,5]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[2,4,7,8,3,5,1,6]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,3,6,2,5,8,4,7]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,5,3,6,8,2,4,7]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,8,1,2,6,3,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,2,6,3,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,6,2,3,7,5,8,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[4,1,2,6,5,7,8,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[1,8,4,2,7,3,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,2,3,8,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,1,4,7,3,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,6,1,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,1,8,3,7,4,5]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[8,4,2,1,3,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,7,6,8,3,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[5,3,1,8,2,4,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,2,6,3,7,5,8,4]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[5,1,8,3,2,4,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,1,5,4,6,7,8,2]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[2,8,5,7,3,1,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,8,7,3,1,4,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[7,4,2,1,3,8,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,2,1,3,8,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,1,7,3,8,6,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,7,5,3,2,4,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,4,2,7,6,5,8,3]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,4,1,6,5,7,8,2]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[2,8,7,3,4,1,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,6,2,3,8,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[4,5,7,6,2,8,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[3,1,8,7,5,2,6,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,5,6,8,7,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[2,8,3,1,5,4,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,1,5,2,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,7,8,3,2,6,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[1,8,6,2,4,3,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,1,6,2,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,1,6,4,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,2,7,1,5,8,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[4,8,5,1,3,2,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,1,2,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[4,1,6,5,2,3,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[7,1,5,2,3,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,1,6,3,7,2,5,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[4,6,1,2,8,3,7,5]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[4,1,3,6,7,2,5,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[2,6,5,1,3,4,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[2,6,7,4,3,1,5,8]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[2,6,3,1,7,4,5,8]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[6,5,3,7,2,4,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[2,3,6,7,1,5,4,8]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[2,7,5,8,1,3,6,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,1,6,7,3,2,4,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[5,6,1,4,7,2,3,8]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[1,2,5,7,8,6,3,4]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,6,7,4,5,3,8]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,2,7,8,4,6,3,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[8,6,5,2,1,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,8,6,7,1,5,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,3,2,4,7,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,8,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,6,8,2,7,4,1,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[7,4,1,2,6,5,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,2,7,4,6,1,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[7,4,1,2,3,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,4,8,6,3,2,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,4,6,7,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,8,5,1,2,7,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,1,3,6,8,5,2,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[6,3,5,7,1,2,8,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,8,5,3,2,4,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,3,4,2,5,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,6,8,3,4,2,5,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,8,7,5,3,4,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,8,5,3,4,2,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,6,8,4,2,3,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,8,6,4,3,2,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[5,1,7,8,4,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[3,8,2,1,6,7,5,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,1,7,5,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,5,6,2,1,4,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,1,5,8,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,1,6,4,7,8,3,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[5,7,8,3,4,2,1,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,7,5,3,8,2,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[2,6,4,7,8,5,3,1]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[7,8,4,5,6,1,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,5,1,8,4,6,7,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,2,8,4,6,7,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,5,8,3,4,2,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,3,5,8,4,6,7,2]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[3,4,5,8,2,1,6,7]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[8,2,7,6,3,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,3,2,1,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,4,8,2,7,1,5,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[7,2,6,1,4,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,8,1,2,4,6,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,2,8,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,8,3,4,2,5,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,5,1,2,4,3,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,8,1,4,2,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,4,3,7,8,5,6,1]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[2,1,7,6,3,4,5,8]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[6,3,5,2,1,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,1,5,3,8,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,3,6,8,5,1,7,4]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[3,2,4,8,6,1,7,5]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[2,1,3,8,4,5,7,6]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[3,1,2,8,5,4,7,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,7,8,4,6,5]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,3,8,4,7,6,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[3,1,2,8,4,5,7,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,2,8,7,5,4,6,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,6,7,2,3,8,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[3,2,6,5,7,8,1,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[3,2,7,5,6,8,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[2,1,8,7,4,6,5,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,5,8,4,7,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,4,6,8,5,7,2,3]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,8,5,1,6,4,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,7,1,8,3,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[6,1,5,4,2,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,4,5,1,2,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[8,4,1,5,7,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,5,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,2,5,3,8,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[4,6,5,2,1,8,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[5,8,4,3,6,7,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,2,1,5,3,4,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,5,3,8,6,7,4,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[3,2,6,5,1,8,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[7,4,5,8,1,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,5,8,1,6,7,3,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,1,8,4,6,7,3,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,5,3,8,1,7,2,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,3,7,1,6,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,6,5,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,6,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,5,3,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,6,8,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,6,3,7,8,1,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[6,3,8,7,2,1,5,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,5,6,3,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,2,8,6,3,1,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,4,5,8,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,8,4,7,2,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,3,6,8,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,8,5,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,5,2,8,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,4,2,8,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,6,3,2,8,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,3,6,8,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,5,4,8,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,8,3,6,1,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,5,2,8,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,1,6,7,4,5,2,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[3,1,5,4,7,6,2,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[7,3,6,8,2,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,1,3,2,4,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[8,4,2,5,1,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,2,5,7,3,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[5,7,8,4,2,3,6,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[6,4,5,2,8,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,2,4,3,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,5,3,4,1,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,4,5,3,8,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,6,4,8,3,1,2,7]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[7,2,4,6,3,8,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,8,3,7,6,1,5,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,2,6,8,7,3,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[3,7,2,5,8,6,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,6,5,3,8,1,7,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[2,4,8,7,6,1,5,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,2,8,7,4,6,5,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,2,6,5,1,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,7,6,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,5,7,1,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,5,1,7,6,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,7,6,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,4,6,2,5,7,1,8]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[1,7,5,2,6,8,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,1,7,2,4,6,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[6,8,2,1,3,4,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,2,1,7,6,4,3,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[7,4,8,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,4,8,5,1,7,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,2,8,1,3,6,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,3,2,7,4,5,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,4,3,8,5,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,2,1,8,7,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,1,8,7,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,2,1,7,6,3,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,2,6,8,5,7,1,3]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[1,3,4,7,8,2,6,5]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,5,4,3,8,7,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,2,5,8,4,3,6,7]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,5,8,2,6,4,3,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,5,6,2,4,7,8,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[3,5,6,7,2,4,8,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[3,5,7,6,8,2,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[3,5,7,2,6,8,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[3,5,2,7,6,8,4,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[3,5,7,4,2,6,8,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[3,5,4,7,2,6,8,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[3,4,5,7,2,6,8,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[3,4,5,7,2,8,6,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[3,5,4,7,8,2,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[3,5,4,7,2,8,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[3,2,5,7,4,8,6,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[3,5,7,4,2,8,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[3,5,7,8,4,2,6,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[2,3,5,7,8,4,6,1]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[3,5,2,7,8,6,4,1]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[3,5,7,8,2,6,4,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[3,5,7,8,6,2,4,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[4,2,5,6,7,3,8,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[8,6,1,4,3,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,4,3,5,2,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,1,6,4,8,2,3,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[8,1,4,2,5,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,5,3,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,1,3,5,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,8,3,5,2,6,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,3,1,2,5,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,5,4,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,2,5,1,8,7,6,3]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[5,2,4,8,1,7,6,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[7,3,2,4,6,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,4,8,6,7,2,5,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,4,5,7,3,8,2,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[4,6,8,1,2,5,3,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[3,5,6,8,2,1,4,7]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[8,2,5,4,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,8,6,3,1,7]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[5,4,8,2,3,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,7,5,8,2,3,1,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,6,7,5,1,8,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[1,7,3,6,5,8,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,3,4,2,6,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,8,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,1,8,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,6,7,5,2,8,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[5,8,7,2,4,3,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,1,2,8,6,7,3,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[2,5,7,8,6,1,4,3]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[7,2,6,8,4,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,1,7,6,8,2,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[4,6,7,2,1,5,3,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[1,7,6,2,4,3,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,7,1,6,2,3,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,2,5,8,3,4,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,6,8,7,1,3,2,4]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,5,3,4,8,2,6,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,1,3,6,5,8,4,7]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[2,8,6,5,7,4,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,5,7,4,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,7,4,3,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,5,2,8,4,3,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,5,8,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,6,8,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,3,7,2,4,1,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[5,1,2,8,6,3,7,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,1,5,7,2,4,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[4,1,8,2,6,5,7,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,1,4,7,8,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,1,5,7,8,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,6,8,3,7,4,2,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,6,1,5,7,2,8,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[2,5,8,4,6,3,7,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,3,7,1,2,6,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[8,1,6,5,2,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,5,2,7,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,5,8,2,3,7,6,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,6,2,7,4,8,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[1,7,3,2,4,8,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[4,3,1,8,2,6,7,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,8,1,3,2,5,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,3,8,6,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,5,3,8,1,4,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,5,8,1,3,7,6]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[8,1,2,4,3,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,1,5,7,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,1,7,4,8,6,5,2]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[6,4,5,3,2,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[2,7,3,8,5,1,6,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[8,7,3,2,5,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,8,2,6,5,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,6,2,8,1,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,3,8,4,1,5,7,6]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[8,4,2,3,1,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,1,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,2,4,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,8,1,4,3,6,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,5,8,1,3,2,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,1,8,5,3,4,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,4,1,3,2,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,3,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,5,2,4,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,8,6,3,1,5,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,2,8,4,1,6,3]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[2,5,6,3,8,1,4,7]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[7,4,5,6,8,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,1,8,4,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,7,8,5,6,4,3,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,8,1,7,4,5,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,3,6,2,5,4,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,6,2,3,5,8,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,8,5,6,4,3,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,8,4,5,1,7,3]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,6,5,7,8,1,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[2,5,8,6,4,7,1,3]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,3,2,1,7,8,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[8,4,1,3,6,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,5,3,8,4,7,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[7,6,2,3,5,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,2,5,3,4,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,2,5,3,4,8,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[2,6,5,3,4,8,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,3,4,8,1,7,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,1,3,4,8,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,5,3,4,8,7,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[5,1,3,8,4,7,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,3,8,1,4,7,6,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,3,5,8,1,7,6,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[3,6,5,4,8,1,2,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,6,5,4,8,2,7,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,5,2,4,8,7,6,1]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[2,5,3,6,8,4,1,7]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,6,2,5,1,7,8,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[2,3,6,5,8,4,1,7]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,3,5,1,7,6,4,8]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[2,3,1,7,4,8,6,5]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[2,3,8,7,6,4,1,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[7,5,2,3,1,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,8,3,6,4,2,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,7,4,8,5,3,6]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[8,1,7,3,2,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,2,8,1,3,6,7,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,1,2,5,7,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,3,1,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,2,5,3,6,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,5,1,4,6,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[6,8,7,4,1,5,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,6,4,7,5,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,4,7,8,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[2,4,6,5,7,1,8,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[4,2,6,7,8,5,3,1]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[6,2,4,7,8,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[3,5,2,1,7,8,6,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[4,2,7,8,6,5,1,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[1,2,7,8,6,4,5,3]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[4,8,1,2,6,5,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,1,6,3,2,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,4,8,1,2,3,7,5]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,4,1,3,6,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,1,8,3,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,5,1,6,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,2,7,1,4,6,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[6,3,8,5,7,1,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,4,3,8,5,7,1,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,8,3,1,4,6,5,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,7,6,1,3,8,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[3,7,1,6,5,8,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[7,4,3,6,8,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,8,5,4,7,6,1,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,8,7,3,5,2]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[4,6,5,1,3,8,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[5,4,6,2,1,8,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[3,2,8,5,1,4,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,5,4,1,2,8,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[5,3,8,1,4,2,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,3,8,1,4,2,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,4,7,5,8,6,2,3]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[8,5,7,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,2,6,1,4,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,4,5,1,8,3,7,6]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[7,2,8,5,3,4,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,4,5,3,1,7,8,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[7,3,5,6,4,1,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,5,6,3,4,1,8,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[4,6,2,1,5,8,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[4,6,7,2,3,8,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[2,3,5,8,7,4,1,6]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,3,5,8,7,4,6,1]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[4,5,3,7,8,1,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[2,3,5,8,1,6,4,7]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,7,4,5,8,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[8,6,1,5,4,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,6,3,1,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,2,6,1,5,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,8,1,5,4,6]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[5,2,6,7,8,3,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[5,6,2,7,8,3,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[2,3,7,5,8,4,6,1]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[3,7,8,5,1,4,6,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[2,5,6,7,1,8,4,3]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[8,5,3,6,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,8,5,4,6,1]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[6,4,7,8,1,2,5,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,5,8,1,2,3,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,2,8,7,4,6,5,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,4,8,7,3,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,3,1,8,7,5,6,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,3,2,7,6,1,5,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[7,2,6,5,3,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,3,7,6,2,4,8,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,3,8,2,7,4,6,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[8,2,7,1,6,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,8,1,7,5,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[7,5,4,1,6,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,6,5,3,2,4,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,7,3,5,2,4,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,3,7,2,5,1,6,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[5,1,4,3,2,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[7,2,1,3,5,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,3,7,5,4,2,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,8,7,5,2,3,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,3,6,1,8,5,2,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[1,3,6,2,5,4,8,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,4,8,7,3,6,2,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,5,7,6,3,1,8,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[4,6,7,5,1,3,8,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[3,6,5,1,4,7,8,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[4,6,7,3,1,5,8,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[5,4,1,8,7,3,6,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[6,2,4,7,5,3,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,2,5,1,8,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[3,2,6,1,5,8,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[4,2,3,6,7,5,1,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[6,2,3,5,7,4,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,6,3,8,4,7,2,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[8,1,5,2,4,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,1,4,2,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,3,4,8,5,6,2,7]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[3,2,7,1,8,6,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[1,3,8,5,6,7,2,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[6,2,4,1,5,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,8,4,1,3,6,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,8,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[3,2,7,4,8,1,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[5,2,8,1,7,4,6,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,5,4,7,3,1,8,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,6,3,1,2,5,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[7,4,6,8,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,5,4,7,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,1,5,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,5,6,4,8,1,3,7]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[5,4,1,6,2,3,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[1,3,6,5,2,4,7,8]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[5,4,1,2,7,6,3,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[5,8,7,3,1,2,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,7,8,1,4,5,3,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[4,1,2,8,7,3,6,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[6,1,2,4,3,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[3,7,8,1,2,4,6,5]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[7,3,4,1,2,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,3,1,2,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,2,7,4,5,1,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,2,3,5,4,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,1,3,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,3,7,2,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,7,4,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,5,1,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,2,4,5,1,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,3,8,1,7,5,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[8,4,3,7,1,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,7,2,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,3,7,6,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,1,4,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,6,1,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,2,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,6,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,1,3,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,8,4,2,3,7,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,2,4,7,3,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,3,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,4,7,3,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,5,7,2,6,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,2,7,3,1,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,1,2,6,7,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,5,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,6,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,6,4,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,2,3,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,3,6,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,4,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,7,6,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,7,3,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,5,3,7,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,4,7,5,6,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,8,4,7,1,6,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,8,2,3,5,6,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,2,3,5,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,7,6,2,3,8,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,8,2,3,7,6,4,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,8,6,2,5,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,8,2,3,7,4,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,2,8,3,7,6,1,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,3,5,6,4,8,2,7]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[3,1,7,8,5,2,4,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[4,6,1,8,2,7,5,3]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[6,3,5,2,8,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,6,3,5,2,8,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,8,6,3,7,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,4,5,8,1,3,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,3,5,1,8,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,6,3,1,5,8,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,5,4,8,6,3,1,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,5,4,8,6,3,7,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,2,5,4,8,6,3,7]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[6,4,5,8,2,1,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,3,4,1,2,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,4,3,5,2,8,6,7]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,3,5,4,8,2,6,7]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[3,5,4,8,2,6,1,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,6,4,5,1,2,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[4,3,5,1,8,6,2,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[3,5,4,8,1,6,2,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,4,8,5,6,1,2,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,5,6,2,1,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,5,4,8,1,6,7,2]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[2,4,3,1,5,8,6,7]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,7,6,2,5,4,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,6,1,7,4,3,8,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[3,7,2,1,5,6,8,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[3,1,5,6,4,2,7,8]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[8,3,4,1,6,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,3,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,7,8,2,6,4,5]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[2,1,6,5,3,8,7,4]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[3,7,5,6,4,2,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[6,1,4,3,7,5,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[3,8,6,4,5,2,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,8,6,2,3,7,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,6,8,5,3,7,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,5,7,2,8,6,3,1]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[3,7,4,5,1,6,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[4,6,8,1,2,5,7,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,8,5,1,3,7,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[3,7,4,5,2,8,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,7,8,4,6,1,5,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,5,7,2,1,6,8,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[4,5,1,6,8,3,7,2]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[8,3,5,4,6,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,5,2,6,8,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,4,2,6,5,3,8,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[3,1,5,8,4,6,2,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[8,2,6,3,4,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,5,8,2,1,3,7]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[1,4,8,3,5,6,2,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,8,7,4,2,3,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,1,8,5,7,2,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[7,3,2,4,8,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,7,2,4,5,8,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,2,7,4,6,1,8,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[8,3,2,4,6,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,4,5,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,2,1,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,6,7,2,4,1,8,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[8,4,7,2,3,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,1,5,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,2,8,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,1,6,3,2,5,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[5,7,1,8,4,3,6,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,4,8,7,6,2,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,4,6,3,1,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,1,5,2,4,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[3,7,6,2,5,4,1,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7,1,5,3,4,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,4,5,1,2,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,3,8,7,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[7,5,2,4,1,3,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,2,6,8,5,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,6,5,4,1,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,4,1,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,3,8,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,5,1,4,3,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,7,6,2,5,8,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[6,3,2,4,5,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[2,6,4,5,8,3,1,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[3,7,4,8,6,2,5,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[7,3,5,2,8,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,5,8,7,4,2,3,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,7,2,4,5,8,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,4,6,8,7,2,5,3]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,6,2,7,5,3,4,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,3,7,2,6,4,5,8]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,7,3,2,8,5,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,6,5,2,4,8,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,7,3,8,4,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,6,2,4,7,5,8,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,6,2,7,4,3,8,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,5,8,2,3,6,4,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,5,3,6,7,1,4,8]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[6,4,1,5,7,2,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,4,1,5,7,3,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,2,7,3,8,5,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[7,4,1,6,3,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,5,7,4,3,8,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[2,7,3,1,4,5,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,5,8,3,2,7,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,4,3,1,7,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,5,3,4,8]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,2,6,8,7,4,5,3]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[3,4,5,6,8,2,7,1]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[7,2,1,4,5,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,5,6,7,3,4,2,8]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[4,6,8,5,2,1,7,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[1,6,7,8,2,4,5,3]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[4,7,8,2,1,3,5,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[5,7,8,3,2,4,6,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,7,8,2,3,1,6,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,5,2,7,8,6,1,3]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[1,3,5,8,7,2,6,4]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[6,4,1,8,5,7,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,1,3,8,7,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[8,5,1,6,7,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,7,2,1,5,8,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[2,5,6,1,3,8,7,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[3,8,5,7,2,4,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,1,4,5,2,8,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,2,5,6,1,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,4,1,2,5,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,6,3,5,7,1,8,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[4,7,3,5,2,6,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[2,3,5,4,7,1,8,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[6,8,4,1,5,7,3,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,1,6,2,3,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,6,4,1,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,8,7,3,2,6,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,5,3,4,8,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,4,8,7,3,6,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,7,6,8,3,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[8,4,5,2,7,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,7,4,5,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[7,3,4,2,8,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,3,6,5,8,2,7,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[8,2,7,4,5,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,5,3,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,3,8,2,7,4,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,2,8,4,7,5,6,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,3,6,2,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,4,3,6,5,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,8,3,6,5,4,2]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,4,5,8,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,8,1,7,2,4,3,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,5,7,3,8,1,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[8,3,5,2,1,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,7,1,8,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,6,5,7,3,8,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,8,5,3,7,6,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,2,3,8,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,1,3,8,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,1,4,2,7,8,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,5,1,3,7,8,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[5,1,3,2,7,8,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[5,6,8,2,4,7,1,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[6,7,4,2,3,8,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,8,7,3,2,4,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,1,3,2,6,8,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[5,7,1,4,6,8,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[2,4,1,7,5,6,3,8]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,4,3,7,6,2,8,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,6,2,5,7,3,8,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,4,3,8,2,5,7,6]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,5,7,3,6,4,2,8]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,6,7,2,4,8,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[3,7,2,8,4,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[5,3,4,1,7,8,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[4,7,6,5,8,2,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,1,8,3,2,6,5,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,2,6,8,4,3,5,7]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[7,2,6,3,1,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,8,4,1,3,7,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,4,2,1,6,8,5,7]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[8,1,3,5,6,4,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,1,5,6,2,8]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[4,8,2,6,5,3,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,2,5,6,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,4,7,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,5,2,3,1,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,3,5,1,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,2,6,4,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,5,3,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,1,4,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,4,6,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,2,5,4,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,4,6,5,2,7,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,7,4,2,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,2,5,1,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,1,2,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,2,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,2,4,6,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,6,4,1,3,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[7,1,3,5,2,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,6,4,7,1,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,2,1,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,1,8,5,4,3,7,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,8,5,4,1,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,5,3,2,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,5,4,6,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,4,7,2,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,5,7,3,4,8,1,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[5,2,4,7,8,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[4,8,5,6,1,2,7,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,5,6,8,7,1,4,3]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,7,8,5,4,6,2,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[4,6,8,1,5,2,7,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[8,2,3,6,4,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,5,8,6,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[3,8,5,1,2,4,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,6,4,8,2,7,5]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,7,6,2,8,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,5,8,6,4,7,2,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,6,2,8,1,7,3,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[6,8,4,5,1,3,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,2,3,8,1,4,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,6,8,3,2,4,5,7]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[8,6,5,2,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,5,3,7,4,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[8,5,4,2,6,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,3,2,6,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,5,8,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,6,5,8,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,6,4,8,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,5,4,8,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,6,8,4,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,6,5,7,4,2,8,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,2,7,4,8,5,6,3]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[2,6,7,4,8,5,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[3,2,7,5,8,4,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[2,5,8,6,4,3,7,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[6,4,2,5,7,1,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[2,7,5,4,6,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,1,4,7,3,5,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,2,4,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,5,7,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,4,2,8,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[2,5,7,4,6,8,1,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[2,5,6,4,1,3,8,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[4,6,1,3,5,7,2,8]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[3,2,7,5,8,1,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[4,3,6,8,5,2,1,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,5,3,2,1,8,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[3,6,5,8,1,7,4,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,1,6,8,5,2,3,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[4,5,2,8,6,7,1,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,5,2,8,6,7,3,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,5,8,6,2,4,7,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,5,1,6,4,8,3,7]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[3,2,4,5,8,6,1,7]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[4,5,2,1,3,8,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[4,2,3,6,8,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[4,5,1,3,2,8,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[3,4,5,8,6,1,7,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,5,8,6,1,2,7]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[6,4,1,3,7,8,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,3,1,2,5,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,3,1,2,5,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,6,4,1,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,8,2,4,3,7,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,8,5,7,2,3,6]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,8,7,3,2,4,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,2,7,3,4,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,7,3,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,3,2,8,7,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,1,6,7,8,3,2,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,5,6,3,7,2,4,8]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,5,6,7,4,2,3,8]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[5,1,6,7,3,4,2,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[8,6,1,7,3,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,7,4,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,4,2,3,5,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,5,2,3,1,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,4,8,3,1,2,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,4,7,3,2,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,7,3,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,2,7,3,8,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[8,4,2,6,7,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,3,6,5,2,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[4,6,7,5,1,8,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[3,5,2,6,8,7,4,1]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[7,3,6,8,4,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,4,2,3,7,5,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,3,7,5,1,2,8,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[7,2,5,4,8,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,2,3,8,7,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,1,2,8,4,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,5,8,1,2,7,6,4]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,4,3,6,8,5,2,7]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[7,6,2,8,5,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,8,3,5,4,7,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,2,7,6,4,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,5,1,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,7,1,4,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,2,5,6,3,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,1,5,7,4,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,5,6,3,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,5,7,1,6,3,8,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[2,7,1,4,8,3,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,7,1,5,6,8,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,3,1,8,7,4,6,5]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[4,6,8,2,1,5,3,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[5,6,8,4,7,2,3,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,5,7,3,6,1,2,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[4,5,8,2,6,1,7,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,4,5,7,2,1,6,8]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[4,5,6,8,3,2,7,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[4,5,7,2,6,1,8,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[4,6,5,7,2,3,8,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[3,6,7,2,5,8,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[5,3,6,7,4,8,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[4,2,7,8,3,6,5,1]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[4,2,7,8,5,6,1,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[5,4,3,7,8,1,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[3,5,7,8,4,2,1,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[4,6,7,3,2,8,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[4,6,5,3,7,8,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[5,6,2,4,7,8,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[5,6,3,2,8,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,6,2,8,3,4,7,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[3,7,4,8,1,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[5,2,4,8,6,7,3,1]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,2,6,4,8,7,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[2,4,7,8,6,5,1,3]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[5,2,6,7,8,1,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[4,8,2,7,5,3,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,2,4,6,5,8,3,7]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[5,4,2,3,1,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[3,5,8,1,7,4,2,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[5,8,6,1,7,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,1,4,3,8,2,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[8,4,7,5,6,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,7,5,2,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,5,4,7,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,7,3,6,5,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,7,8,6,1,4,5,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,6,7,8,2,1,5,3]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[4,7,6,3,8,1,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[3,8,1,4,6,2,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,5,3,8,7,1,6]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[4,7,5,6,2,8,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[8,7,5,1,6,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,2,3,5,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,8,4,6,7,3,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,6,7,8,2,5,3]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[8,6,3,4,1,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,8,4,6,1,3,7]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,8,6,5,1,3,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[6,8,4,7,3,5,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,4,5,8,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,4,7,3,5,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,2,8,1,7,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,4,8,6,2,1,7,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[8,4,6,2,1,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,2,1,7,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,8,2,4,6,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[8,1,7,6,2,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,4,3,7,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,3,6,7,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,5,8,6,1,7,4,2]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[8,1,4,7,5,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,8,6,7,3,5,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,1,6,7,8,5,3,2]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[3,7,8,6,4,1,5,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,6,1,5,7,2,3,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[4,8,5,3,2,7,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,4,8,1,3,7,2,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,4,5,3,1,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,3,1,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,6,8,7,2,4,3,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[5,7,8,6,4,2,3,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[6,8,7,5,1,3,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,8,2,6,7,5,1,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,3,8,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[6,7,4,1,8,2,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[5,7,6,8,3,2,4,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[7,6,4,2,8,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,3,4,8,7,1,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,7,4,8,1,6,3,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,3,1,6,7,8,2,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[3,4,7,8,6,1,2,5]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[2,1,4,7,8,6,3,5]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[2,4,5,8,1,6,3,7]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,6,8,2,5,7,1]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[1,8,5,6,4,2,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,6,2,4,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,4,8,5,7,3,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,6,4,7,2,5,8,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[2,7,5,1,8,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,5,6,4,8,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,3,1,4,6,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,4,5,8,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,2,5,4,6,8,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,1,5,3,8,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[3,5,7,2,8,4,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[2,4,3,8,5,1,7,6]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[7,3,2,1,4,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,8,3,4,1,7,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,8,2,5,3,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[2,6,7,1,4,5,8,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[8,7,1,6,3,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,6,1,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,2,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,2,5,3,4,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[2,7,3,4,1,5,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,5,8,1,6,7,3,4]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[6,2,8,3,4,5,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,3,4,6,8,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,1,3,7,2,8,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,2,4,6,1,7,8,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[3,8,4,6,1,5,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,3,2,5,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,4,1,2,5,8,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[5,2,7,1,4,3,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[6,3,1,4,2,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,2,3,1,4,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[4,2,7,1,3,5,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[3,5,4,1,6,2,8,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[4,5,7,2,8,3,1,6]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[3,5,1,7,6,2,8,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[8,3,6,2,7,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,6,5,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,2,7,1,8,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[4,1,7,6,5,3,2,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[2,3,6,7,1,8,5,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[3,6,1,2,7,8,5,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[4,5,1,8,7,6,3,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[8,4,5,2,7,6,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,7,5,2,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[3,1,4,5,7,6,2,8]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[4,5,1,3,6,8,7,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[3,8,5,1,2,4,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,5,1,2,4,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,1,2,3,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,5,8,1,4,2,7,6]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,8,5,7,1,4,3,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,8,7,5,1,2,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,1,2,4,6,3,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,4,2,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,2,7,8,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[7,8,1,2,5,3,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,8,4,7,5,2,3,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,7,2,1,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,1,6,7,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[7,4,2,5,3,6,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,1,6,7,5,2,4,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[8,4,2,5,3,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,1,5,3,6,7,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,7,5,2,6,3,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[5,1,4,6,3,7,8,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[7,1,5,3,6,8,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,1,5,3,6,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,5,2,4,7,8,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[1,7,5,4,6,8,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[4,7,8,2,5,6,1,3]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[2,8,5,4,6,7,1,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,2,6,1,8,3,7]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[5,1,8,6,7,3,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,8,3,2,4,1,5,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,5,2,4,1,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,4,8,2,1,3,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,4,8,3,2,6,5,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,3,8,4,2,7,5,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[7,2,8,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,1,3,2,7,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,1,8,2,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,4,1,6,7,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,2,1,6,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,6,4,1,2,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,4,2,8,1,6,3,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,8,4,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,7,5,4,8,6,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[4,8,6,3,5,2,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,3,2,7,1,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,7,6,3,2,4,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,7,3,2,8,6,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[4,5,1,6,8,2,7,3]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[1,6,3,7,2,4,8,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[4,3,1,6,7,2,5,8]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[6,3,1,5,7,2,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[5,2,1,4,8,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[4,5,2,1,3,7,6,8]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[8,2,7,4,1,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,8,4,1,6,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,7,6,4,1,5,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[7,1,6,5,4,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,8,4,2,3,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,7,6,4,5,1,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,6,8,1,7,3,5,2]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[3,6,8,1,5,7,4,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[2,8,3,1,6,7,4,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,8,2,1,7,3]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[4,5,6,8,1,3,7,2]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[4,5,8,3,2,1,7,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,1,3,2,6,7,8]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[4,7,3,2,1,6,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,7,8,3,5,1,6,2]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,7,1,3,5,6,2,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,8,3,2,1,6,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,2,8,1,4,6,7,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,6,3,7,8,1,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[5,7,1,4,3,6,2,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,2,3,7,1,5,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,2,8,1,5,4,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,1,3,4,5,2,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[7,1,3,4,5,6,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,2,5,1,3,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,2,7,8,4,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[7,5,3,6,4,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,3,6,5,8,4,7,1]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,3,6,7,5,2,4,8]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,5,2,6,8,7,3,4]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[5,3,4,7,2,1,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,8,5,7,1,2,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,2,3,7,6,1,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[4,2,6,3,1,5,7,8]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[4,6,3,2,5,8,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[5,8,4,3,2,6,1,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,5,7,4,8,6,2,3]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[6,1,5,7,3,8,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,2,7,8,6,4,3,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[3,5,1,7,8,6,2,4]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[5,2,4,1,7,6,8,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[5,4,3,8,1,7,2,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[7,3,1,5,6,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,2,3,1,6,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,1,8,2,5,6,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[5,7,8,1,6,2,3,4]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,6,4,2,7,3,8,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,4,2,5,8,6,3,7]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[4,8,2,1,5,7,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,2,7,1,6,3,4,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[4,8,2,5,1,6,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,1,2,4,6,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,1,7,3,6,4,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[3,2,7,5,6,1,4,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,2,7,1,6,4,5,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[6,3,1,7,5,4,2,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[6,2,8,7,3,4,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,3,4,8,5,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,3,6,8,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,6,2,8,3,1,7,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[1,4,7,5,6,2,8,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,7,4,8,3,5,6,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,3,1,4,8,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[5,2,4,8,3,1,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,7,3,5,4,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,8,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,1,5,7,6,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,7,5,3,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,8,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,1,5,3,7,6,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,7,3,5,1,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,1,4,2,3,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,5,1,8,3,7,4,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,1,4,3,8,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,5,4,1,7,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,1,7,6,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[4,7,6,3,2,8,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[5,7,6,3,8,2,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,8,4,7,1,2,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,3,7,6,8,4,5,2]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[6,1,5,7,2,8,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,8,7,2,5,6,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,6,7,4,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,4,8,7,6,1,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,8,7,6,3,5,4,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,7,6,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,1,8,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,2,1,4,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,7,3,5,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,3,2,1,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,6,1,4,7,8,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[2,5,7,1,3,6,4,8]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,4,7,2,5,3,6,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[4,5,3,1,2,6,8,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[4,5,1,3,8,2,6,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[4,1,5,3,2,7,6,8]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[7,3,5,1,4,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,2,1,7,4,3,8,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[2,4,3,6,7,1,5,8]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[7,3,5,2,1,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,6,5,2,1,3,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[2,5,6,1,4,3,7,8]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[6,1,5,3,7,2,4,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[3,6,5,4,1,7,2,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[6,8,7,5,4,2,1,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,6,8,7,3,2,4,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[8,7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,2,4,6,3,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,5,4,8,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,6,1,8,4,3,7,2]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[1,8,2,6,7,5,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,7,5,1,6,8,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,5,4,2,7,3,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,1,2,4,5,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,5,3,2,7,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,4,7,2,3,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,1,7,5,4,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,1,5,6,2,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,5,1,7,2,3,4,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,6,8,2,7,3,4,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,6,8,7,3,4,2,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,1,3,6,7,8,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[7,4,1,5,6,8,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,1,2,6,7,8,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[3,7,8,2,1,4,5,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[6,3,7,1,8,2,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[3,7,8,1,5,2,6,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,5,4,7,8,3,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[5,2,4,7,8,3,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,1,4,7,8,3,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[4,8,1,5,6,2,3,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,1,7,3,8,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[4,3,7,8,2,5,1,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[3,7,8,5,4,2,1,6]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,4,5,6,8,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,2,4,5,6,8,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,7,4,5,6,8,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,4,7,8,3,1,6,5]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[5,4,3,6,8,1,7,2]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[3,7,4,5,8,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,4,3,5,6,8,2,7]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,4,6,5,8,2,7,3]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[4,6,1,7,3,2,8,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[1,7,3,6,4,2,8,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,7,3,5,1,2,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[1,6,4,2,3,5,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[4,8,3,5,2,1,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,6,8,4,7,5,3,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[8,7,3,1,5,2,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,6,8,2,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,6,5,8,2,3,7,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[7,1,8,2,4,5,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[5,7,8,2,3,4,1,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[5,2,3,8,7,1,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,7,1,3,2,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,6,4,8,3,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[2,6,3,7,5,8,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[7,5,1,2,3,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,6,2,1,3,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,3,6,8,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[4,7,3,2,6,5,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,3,7,8,2,1,6,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[4,8,7,2,1,5,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,3,8,2,5,1,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,5,3,8,6,1,2,7]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[6,3,5,8,4,1,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,3,8,4,5,1,2,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,8,7,5,1,2,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,8,4,6,1,3,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,8,7,5,1,3,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,8,1,2,7]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[7,8,6,2,1,4,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,7,6,4,1,5,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[5,2,8,4,7,1,3,6]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[7,3,1,2,8,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,7,1,3,2,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,5,7,2,8]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[4,1,3,5,7,2,8,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[5,1,8,2,4,6,3,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[6,8,2,1,4,5,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,2,7,3,6,8,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[3,1,5,8,6,7,2,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[6,8,2,1,4,5,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,5,4,8,7,3,2,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[4,3,1,2,6,5,7,8]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[7,1,4,5,8,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,5,8,1,2,4,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,1,5,2,8,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,4,6,3,1,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,1,5,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,4,5,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,6,4,5,1,7,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,6,4,5,1,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[7,4,6,3,1,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,6,2,5,7,8,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[4,6,3,5,7,1,2,8]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[4,7,3,5,8,6,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[4,8,3,5,7,1,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,5,6,1,2,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,2,5,6,8,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[4,8,2,5,6,7,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,2,6,5,8,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,5,7,2,6,4,8,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[7,2,4,6,1,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,2,7,8,3,5,4,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,7,6,2,8,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,2,7,8,3,4,6,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,7,6,8,3,4,2,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,4,1,7,8,6,5,2]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[2,4,8,6,5,7,1,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[5,1,3,4,8,2,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[8,7,3,6,1,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,1,8,3,4,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,2,1,5,6,4,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,5,6,1,3,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,7,2,4,6,1,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[2,1,5,6,3,8,7,4]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[3,2,7,5,8,6,4,1]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[2,4,5,3,8,1,7,6]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[7,2,5,4,3,8,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,5,3,1,2,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,1,3,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,4,7,3,1,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,3,5,2,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,4,8,3,6,5,7,1]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,1,8,2,6,5,7,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,6,7,8,5,2,1,3]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[4,7,2,1,8,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,6,2,8,4,1,7,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[5,7,2,4,8,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,7,2,4,8,5,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[6,7,3,2,8,5,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,2,3,1,8,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,8,3,5,6,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,3,8,4,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,7,3,4,8,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,7,3,8,5,4,2,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,2,8,4,5,3,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,8,6,4,3,1,7,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,3,4,8,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,5,8,3,4,6,2,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,3,8,4,2,5,7,6]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,4,7,6,2,3,8,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,8,4,6,7,2,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,2,3,7,8,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[5,7,1,6,4,8,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[7,4,5,8,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,4,3,6,2,5,8,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,4,6,3,2,5,8,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,3,6,5,8,2,4,7]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,4,6,3,2,8,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[6,8,4,1,5,7,2,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,2,6,7,4,1,8,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[8,5,6,4,1,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,3,1,6,4,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,8,2,6,3,1,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,5,8,1,6,3,7,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[8,1,4,6,2,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,1,6,2,7,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[5,2,6,8,1,4,3,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[6,7,3,8,2,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[2,7,3,5,4,1,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,6,3,7,4,1,8,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[2,1,4,8,5,3,7,6]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,7,3,8,4,1,6,5]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,6,3,1,5,4,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,5,8,3,4,7,2,6]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,3,8,1,4,6,2,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,5,8,1,3,6,2,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[7,4,6,5,2,8,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,1,3,8,5,7,6,2]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[4,1,3,7,2,8,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[4,6,3,1,7,2,8,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[7,2,6,3,1,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,8,7,2,5,3,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,6,3,2,8,7,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,8,1,7,5,4,6,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,3,1,5,7,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,7,3,1,2,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,5,1,2,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,4,3,6,1,7,8,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[3,2,7,8,5,6,1,4]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[4,8,3,2,1,7,5,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,1,2,6,4,7,8,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[1,8,4,5,6,3,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,6,1,5,8,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[8,5,1,7,4,6,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,8,1,6,7,2,5]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,6,7,8,4,1,5,2]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[2,3,7,8,4,6,1,5]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,3,7,8,4,6,2,5]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[3,1,7,8,4,6,2,5]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[4,3,8,1,6,7,2,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,8,7,3,6,1,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,3,7,1,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,1,8,3,7,5,2,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,4,8,3,6,7,1,5]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,6,5,8,7,3,2,4]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,6,4,8,7,2,1,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[7,2,6,8,3,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,8,6,5,3,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,8,3,7,6,1,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,7,1,3,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,3,4,5,2,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,7,1,4,5,6,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,6,1,4,5,2,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[3,8,2,4,5,1,7,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,1,5,6,4,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[3,6,8,1,5,4,7,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,7,4,6,3,5,2,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,3,6,5,7,2,4,8]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,7,2,5,6,4,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,6,8,5,4,3,7,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,5,7,8,4,3,1,6]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[6,8,5,3,2,4,1,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,6,8,5,3,2,7,4]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,6,1,8,7,5,3,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[1,3,7,6,8,5,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[4,1,7,8,6,5,2,3]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[5,4,3,7,6,1,2,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,7,6,1,2,3,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[4,5,2,6,7,8,1,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[1,7,6,2,3,8,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[4,5,1,3,7,6,2,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[7,2,3,8,6,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,5,4,3,8,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,3,7,5,8,4,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[7,8,1,5,3,4,6,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,3,5,4,1,6,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,5,7,1,6,4,2,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,7,5,6,1,4,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7,5,6,3,4,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,3,1,2,7,8,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[5,1,3,7,8,2,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,8,1,2,7,6,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,6,7,4,5,3,2,8]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,4,2,6,7,5,3,8]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,8,2,4,6,5,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,1,6,4,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,4,8,7,2,3,6,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,1,3,6,5,8,2,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[4,3,7,1,5,8,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[1,8,6,5,2,7,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,6,2,7,4,3,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,6,4,1,8,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,1,8,3,7,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,5,8,7,3,6,2,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,5,4,1,7,8,6,2]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[6,8,7,2,1,5,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,1,6,3,7,5,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,1,3,7,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,5,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,3,5,7,2,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[2,8,1,5,6,4,3,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,7,5,8,4,2,3]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[7,4,1,6,5,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,2,8,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,8,4,7,3,2,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,7,3,2,1,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,8,7,2,6,4,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,8,7,3,5,1,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,2,5,6,8,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,6,5,7,8,3,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[8,6,7,2,3,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,6,7,3,1,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,2,7,3,1,6,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[7,3,6,4,2,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,8,5,2,7,3,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,4,3,1,8,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,4,3,1,5,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,4,8,6,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,8,5,2,6,7,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[7,3,2,1,8,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,5,7,2,4,3,8,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,2,7,5,8,4,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[5,1,3,8,2,7,4,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,7,1,3,2,8,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[7,1,6,3,2,8,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,1,7,2,3,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,6,4,3,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,4,7,8,3,2,5,6]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[8,7,1,3,2,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,3,2,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,7,6,3,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,3,2,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,7,6,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,3,5,1,2,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,7,3,5,4,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,8,5,7,2,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,7,3,6,4,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,7,4,6,1,3,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[8,7,2,3,5,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,4,1,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,3,5,2,8,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,4,5,3,1,7,2,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[8,7,2,4,3,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,3,1,4,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,7,6,2,3,1,5,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,7,6,1,3,2,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[2,8,1,3,5,6,4,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,3,4,7,8,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[7,6,3,1,8,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,1,3,6,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,6,3,8,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,6,4,7,8,5,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[7,2,5,8,6,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,1,3,6,2,5,8,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[7,1,4,6,3,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4,5,8,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,7,2,3,8,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[2,7,8,1,5,4,3,6]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,5,2,6,8,7,4,3]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,8,3,7,5,2,6,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,3,6,5,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,5,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,7,1,5,2,6,8,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[7,4,1,5,2,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,1,6,7,5,2,8,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[8,6,2,4,5,1,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,5,2,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,1,6,2,3,8,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[4,1,7,6,5,2,8,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[8,4,1,5,6,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,5,3,6,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,7,3,5,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,5,4,8,3,2,6,7]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,5,7,6,3,8,2,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[2,6,3,1,7,8,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[2,1,7,8,3,5,4,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,5,8,6,7,4,2,3]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,6,5,8,1,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,1,4,7,6,8,3,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[5,6,4,7,1,8,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[5,3,7,4,6,1,8,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[4,1,5,7,8,6,3,2]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[3,6,7,1,5,4,8,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[3,6,4,7,5,8,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[8,1,7,3,2,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,1,5,2,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[4,8,1,3,5,2,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,2,8,7,4,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[4,1,7,2,5,8,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[3,2,5,8,6,1,7,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[4,5,1,7,2,8,6,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[2,8,5,3,6,7,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,5,2,6,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,6,3,4,7,5,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,7,1,8,5,3,6,2]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[6,4,7,2,5,3,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,1,4,3,6,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,8,7,3,5,1,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,3,8,7,1,6,2,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,2,6,7,4,3,1,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[8,5,1,6,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,2,1,5,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,2,1,6,4,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,8,5,4,6,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,7,1,4,8,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,3,2,8,5,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,1,7,3,2,8,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[8,3,5,2,4,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,7,8,6,1,5,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[1,2,6,3,7,8,5,4]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[6,1,3,7,8,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[3,6,8,5,4,2,1,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[2,6,4,7,5,3,1,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[5,6,3,7,2,8,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[4,5,1,8,6,2,7,3]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[5,6,1,8,7,2,3,4]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,5,1,6,8,7,3,2]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[3,8,6,1,5,2,4,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,1,5,6,4,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[5,8,7,3,2,1,4,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,4,7,6,8,2,1,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[2,8,1,3,7,5,6,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,2,5,6,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,1,2,5,8,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,4,7,1,5,8,2,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[4,2,7,1,5,8,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[2,4,6,3,5,1,7,8]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[4,1,6,2,5,8,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[1,8,2,5,7,3,4,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,6,3,8,5,2,7]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[4,5,6,3,1,7,2,8]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[3,4,6,2,5,1,7,8]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[1,4,7,5,2,3,6,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,4,6,5,8,2,3,7]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,4,8,3,7,6,2,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,4,5,3,7,2,6,8]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[2,5,7,6,8,3,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[3,1,6,7,2,8,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[1,5,3,6,8,4,7,2]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[6,5,1,3,8,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,7,4,8,5,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,3,1,6,8,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,5,1,4,6,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,7,5,6,8,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[3,4,7,8,5,2,6,1]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[4,8,1,7,5,6,3,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,5,2,6,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,3,4,5,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,7,4,5,6,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,3,6,4,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,5,8,2,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,4,7,2,3,6,5,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,7,2,5,6,3,4,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,2,6,5,8,3,4,7]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,5,8,2,6,3,4,7]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[6,8,3,2,7,5,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[7,3,6,8,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,1,5,7,2,6,3,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[5,7,2,1,3,6,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[3,5,6,7,2,4,1,8]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[6,4,7,5,2,3,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,5,6,4,8,3,2,7]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[2,1,5,6,4,8,3,7]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[5,1,4,7,8,6,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[1,6,7,2,8,5,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,3,2,1,7,8,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[7,4,3,8,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,3,7,1,5,8,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[8,2,4,5,3,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,3,2,7,5,8,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[4,8,7,2,6,1,3,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,5,8,2,1,7,3,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[6,8,4,1,7,3,2,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,3,1,8,2,7,5,4]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,1,3,2,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[4,1,7,8,3,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[5,4,7,1,3,6,2,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[7,6,2,8,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,8,2,1,3,6,4,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,5,1,7,3,4,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,6,3,4,1,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[7,1,2,6,4,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,1,2,6,5,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,7,8,6,2,3,5,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[7,1,2,4,8,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,7,5,6,4,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,8,3,6,5,7,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,1,6,5,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,5,1,2,6,8,7,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[3,1,2,4,8,7,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[5,4,1,2,3,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[1,6,7,2,5,8,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[7,8,5,6,2,4,3,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,3,8,6,2,4,1,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,7,4,6,3,8,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,4,7,8,6,2,1,3]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[2,7,4,8,3,1,5,6]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[8,2,1,3,7,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,8,2,3,4,7,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,8,2,3,6,4,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,1,2,7,5,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,1,3,7,5,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[7,5,1,8,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,2,4,1,3,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,2,3,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,2,3,6,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,6,7,5,1,8,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[4,7,2,5,3,8,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,5,7,4,2,8,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[2,4,7,6,3,8,1,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[4,6,8,5,1,2,3,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,5,7,1,2,3,8]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[4,6,5,7,1,3,8,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[3,4,7,6,1,8,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[8,5,2,1,6,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,8,5,3,2,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,6,1,3,2,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,5,2,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,5,4,1,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,1,2,7,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,8,5,7,1,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[6,8,7,4,5,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,2,6,7,4,8,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[6,5,8,1,7,3,2,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,8,1,5,2,3,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,2,4,1,6,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,6,1,5,3,4,8,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[3,8,7,5,4,2,6,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,8,2,3,6,4,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[2,8,7,3,1,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,2,4,7,8,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[3,8,6,7,5,4,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,5,1,4,6,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,2,7,5,4,6,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,6,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,7,1,3,2,8,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[6,4,7,5,3,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[8,4,6,3,1,5,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,1,4,5,6,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,7,3,4,2,1,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[6,4,8,3,1,5,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,4,2,3,5,1,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,1,6,5,2,4,8,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[2,5,3,8,6,4,1,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[6,7,1,5,4,3,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[5,8,4,1,3,2,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,3,4,7,6,1,8,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[4,5,2,1,6,3,8,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[4,5,2,1,6,7,3,8]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[5,3,8,6,2,4,7,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,5,1,6,4,3,8,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[3,6,2,8,5,7,1,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,6,8,1,5,7,2,3]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,1,2,5,7,6,3,8]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[4,6,5,8,1,7,3,2]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[2,1,3,6,4,8,7,5]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[4,8,1,2,7,5,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,3,8,7,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[4,5,1,6,8,7,2,3]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[3,4,7,2,5,8,6,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[2,5,1,8,6,4,7,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[2,5,8,7,3,1,4,6]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,8,7,2,6,1,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,4,5,1,6,7,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,1,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,8,3,6,4,7]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[5,8,4,7,3,2,1,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,6,8,4,2,7,1,3]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[7,2,3,5,6,8,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,8,1,3,4,7,2,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,7,5,6,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,4,5,3,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6,3,1,4,5,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,7,4,6,2,1,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[5,4,1,7,8,6,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[5,3,4,7,8,1,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[4,3,7,6,5,1,8,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[5,1,4,8,2,3,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[3,2,8,5,4,1,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,8,3,4,6,5,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,1,2,7,3,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,7,1,2,6,3,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,2,7,5,6,3,4,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[5,1,4,7,2,3,6,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,8,1,2,3,6,5,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,2,3,8,7,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,2,3,6,4,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,3,6,4,8,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[4,5,1,3,2,6,8,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[6,4,7,5,1,3,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[5,3,1,6,2,7,8,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[6,7,2,4,1,8,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[5,1,6,3,2,7,8,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[5,2,1,6,4,7,3,8]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[5,4,1,6,2,7,8,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[6,7,2,5,4,1,3,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[7,1,3,5,4,2,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,6,8,2,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,8,6,5,1,3,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,8,5,4,7,1,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,8,3,6,2,7,5]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,3,2,4,8,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,3,2,7,4,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,5,8,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,6,2,5,7,4,8,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[2,7,1,5,8,6,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[7,2,4,1,6,8,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,4,7,2,3,8,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,1,8,5,7,4,2,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,1,4,3,6,5,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,5,6,3,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,1,8,5,4,7,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,6,1,5,4,2,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,1,6,8,7,2,4,3]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,6,7,5,3,1,8,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[5,3,2,6,8,7,4,1]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[5,4,6,2,8,7,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[4,5,8,6,7,2,3,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,7,6,1,2,8,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[4,6,5,7,2,1,8,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[7,4,8,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,2,4,3,6,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,3,4,7,8,6,1,5]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[6,3,7,1,4,2,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[4,6,3,5,1,8,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[8,5,7,6,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,6,7,8,2,5,1]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[2,5,6,7,3,8,1,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[5,8,4,6,2,1,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,8,6,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,6,8,3,4,2,7,5]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,1,7,6,2,8,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[4,1,8,2,7,5,3,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,7,2,8,5,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[2,5,6,3,7,4,8,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[2,6,5,3,8,4,7,1]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,5,3,7,4,8,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[7,1,6,3,5,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,7,3,2,8,4,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[2,8,6,1,7,5,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,5,2,7,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,4,2,8,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,6,8,1,7,5,3,4]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,4,6,5,3,8,2,7]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[2,4,5,8,7,1,3,6]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,1,6,8,7,5,4,2]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[3,1,8,7,5,6,4,2]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[5,1,8,7,6,3,4,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[8,2,7,5,3,6,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,1,5,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,7,6,1,3,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,2,6,4,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,2,1,6,4,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,4,7,6,2,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,6,4,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,3,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,2,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,1,8,7,3,6,2]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[3,8,5,2,6,7,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,3,8,5,2,6,1,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,6,4,7,5,2,1,8]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[5,7,4,1,2,6,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[2,8,6,7,5,3,1,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,5,2,6,3,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8,6,3,4,5,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,3,5,4,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,4,5,1,3,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,3,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,7,3,1,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,3,5,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,8,3,2,6,1,7,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,7,6,1,5,2,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[7,5,4,3,6,1,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,6,8,5,3,1,2,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[5,6,8,4,3,7,2,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[7,5,8,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,4,8,7,6,2,5,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[7,2,4,1,5,3,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,5,3,4,1,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,5,4,3,6,1,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,5,3,1,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,6,5,3,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,6,7,2,3,8,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[8,4,2,6,5,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,4,2,8,5,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,2,1,7,4,6,8,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[6,2,5,7,1,4,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[4,8,5,3,1,2,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,5,2,4,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,5,3,4,7,2,6,8]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[8,4,6,1,5,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,7,2,1,3,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,7,3,1,2,4,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[3,1,8,7,6,2,5,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,8,6,7,2,5,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[5,2,3,6,1,8,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[3,2,6,4,7,1,5,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[3,6,2,5,7,8,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[2,7,4,6,8,3,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,6,8,1,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,5,7,6,8,4,2,3]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[2,7,4,6,8,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,7,6,8,5,1,4,2]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[7,1,3,8,6,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,7,1,8,6,5,3,4]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,3,4,7,6,2,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,1,8,5,7,2,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,1,8,2,7,5,6,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[7,6,8,2,4,3,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[7,4,5,3,8,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,6,1,4,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,7,2,6,4,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,4,8,5,7,3,6]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[7,1,4,6,8,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,5,1,6,4,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,7,1,5,6,4,8,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,5,7,8,4,6,3,2]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,4,8,5,7,6,3,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,8,1,5,6,4,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,7,2,8,1,5,6,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[7,3,2,5,1,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,7,2,1,3,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,8,1,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,6,2,1,8,4,7,5]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,5,1,7,6,4,8,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[8,7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,7,6,2,1,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[3,5,2,8,7,1,6,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[3,7,6,5,4,1,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[4,6,5,3,1,8,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[4,5,2,6,7,3,8,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[8,6,7,4,3,1,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,1,8,5,3,2,6]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[8,6,7,1,4,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,7,2,1,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,5,6,1,7,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,2,5,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,1,5,4,2,7,3,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[6,4,2,3,1,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[3,4,6,1,8,2,7,5]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[5,3,1,4,7,6,2,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[6,4,5,2,7,1,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[7,4,3,5,1,6,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5,3,6,2,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,4,3,7,1,8,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[3,1,2,7,6,4,5,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[5,1,2,7,6,3,4,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,6,1,7,2,4,3,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[3,5,6,8,1,2,7,4]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[2,6,5,7,1,3,4,8]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[2,3,7,1,5,6,4,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[2,6,5,3,4,1,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[2,6,1,3,5,4,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[4,6,1,5,2,8,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[6,1,5,4,2,7,8,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,6,1,5,2,7,8,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[2,8,6,5,1,3,7,4]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,1,8,6,2,7,4,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,6,8,2,7,5,1,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,6,4,1,7,2,8,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[3,8,6,1,5,7,4,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,3,4,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,2,3,1,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,4,2,3,7,8,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[4,3,6,2,5,8,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[1,6,4,5,7,3,2,8]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,6,4,5,7,2,8,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,7,5,6,4,8,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,5,6,7,3,2,4,8]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[8,2,4,3,1,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,1,4,3,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,2,1,5,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,6,2,5,1,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,6,8,3,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,7,2,6,4,1,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[4,5,6,1,3,8,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[6,3,5,7,4,2,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,6,4,8,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,2,1,6,4,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,8,6,5,2,7,4]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,7,3,8,5,6,4,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,2,8,5,7,4,6,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,6,8,5,4,7,2,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,1,8,3,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[2,1,3,8,6,4,7,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[8,2,5,4,3,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,4,3,7,6,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,1,5,3,4,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,8,7,4,5,3,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,5,8,6,4,3,7,2]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[5,8,6,4,2,1,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,6,1,8,4,7,5,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[5,3,8,6,1,2,7,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,8,1,4,6,2,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,7,6,2,1,4,8,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[4,6,2,3,7,1,8,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[6,8,7,5,1,3,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,4,3,2,7,8,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[2,7,6,1,5,3,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[7,8,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,4,5,8,7,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,1,7,8,3,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,4,3,8,7,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,4,7,2,1,3,8,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[2,6,4,5,7,1,8,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[3,7,4,6,1,5,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[3,4,6,5,2,8,1,7]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[4,6,7,5,8,2,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[2,5,7,6,4,1,8,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[5,1,4,6,2,7,8,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[1,2,5,3,7,8,6,4]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[4,8,3,5,1,2,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,7,2,8,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[3,8,5,4,1,7,2,6]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,8,2,6,7,4]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[2,8,5,3,1,7,4,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,2,3,7,1,8,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[7,2,1,6,4,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,1,3,7,5,8,4,6]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[6,2,4,5,7,1,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[2,3,8,7,1,4,6,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,2,7,5,6,8,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[6,8,2,5,4,7,3,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,7,6,3,8,4,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[4,6,8,2,3,1,7,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,7,2,3,5,1,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[6,4,2,1,3,7,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[5,3,2,7,6,1,8,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[5,6,4,2,8,7,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,7,4,2,6,1,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,4,7,1,6,2,8,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[4,5,8,7,6,2,1,3]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[6,4,7,1,2,3,8,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[6,1,7,3,8,4,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[8,2,3,1,6,4,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,7,2,3,4,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,3,7,6,2,5,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,8,2,5,6,4,7]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,7,4,6,8,5]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,3,8,4,6,2,7,5]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[8,2,3,6,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,2,1,7,3,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[2,5,7,6,3,8,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[6,4,7,1,2,5,3,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,2,7,5,8,6,3,4]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[7,4,5,1,6,8,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,7,8,4,2,6,3,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[6,3,2,5,7,4,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[6,2,1,5,3,7,8,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,2,5,1,3,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,2,8,5,1,3,7,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,1,7,8,3,6,5,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[6,4,2,1,7,3,5,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[5,8,4,2,1,3,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,7,5,8,4,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,8,1,6,4,7,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,4,7,5,1,8,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[2,3,7,1,8,5,6,4]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[6,5,1,2,7,4,8,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[3,6,5,7,8,2,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,6,5,1,8,7,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[7,8,1,2,5,4,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,8,4,3,5,1,7,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,2,4,7,6,8,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[3,1,5,7,4,8,6,2]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[4,1,7,6,8,2,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[7,2,6,4,1,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,2,6,5,8,3,7,4]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[7,3,5,6,1,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,8,3,1,6,7,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,5,8,1,7,3,6,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,7,1,6,8,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,8,7,1,6,4,2,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,7,3,8,2,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[8,4,1,3,6,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,8,6,7,4,2]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[5,7,1,6,4,2,8,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[2,7,1,6,5,8,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,3,6,1,7,5,4,8]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[2,7,1,4,8,6,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,7,5,4,1,3,2,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,2,7,1,4,3,5,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[8,3,2,6,5,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,5,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,6,8,4,7,1,3,5]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[7,8,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,2,8,6,3,1,4,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,6,4,8,2,3,5,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[2,8,5,6,4,1,7,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,3,5,8,6,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[3,7,8,2,5,1,6,4]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[8,6,1,4,3,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,8,2,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,3,7,8,1,2,5,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[7,6,1,5,2,3,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[5,1,8,6,7,2,3,4]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[5,7,1,6,8,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[6,8,4,2,1,7,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,3,2,8,1,7,4,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,4,1,3,7,8,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,8,5,4,3,7,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,7,4,8,3,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[6,1,2,4,8,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[2,5,6,8,1,4,7,3]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[7,4,1,6,5,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,1,6,5,2,3,8,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[4,5,1,7,8,6,2,3]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[8,5,7,3,4,6,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,7,4,3,5,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,7,5,3,4,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,8,6,2,4,7,3,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,8,6,2,5,7,3,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,6,4,7,5,3,2,8]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,6,5,3,2,7,4,8]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,6,8,7,4,5,3,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,4,7,5,3,2,6,8]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,7,5,4,3,2,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,4,7,5,3,2,8,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,7,4,6,8,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[8,5,6,2,4,7,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,4,2,6,1,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[8,1,3,6,4,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,6,2,5,8,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[7,5,2,1,8,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,3,1,4,7,8,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[7,1,2,4,8,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,6,1,3,5,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,5,8,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,6,8,5,1,4,2,7]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,2,4,1,6,8,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[2,5,3,4,6,8,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[4,7,1,2,5,6,3,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[6,7,3,1,8,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[7,3,1,4,6,2,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,4,1,2,5,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,4,1,3,6,8,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[5,7,4,8,1,6,3,2]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,3,1,2,5,7,6,8]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,2,4,7,8,5,6,3]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[5,3,1,8,4,2,6,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,5,3,6,8,7,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[2,1,6,5,8,7,3,4]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[6,1,5,4,7,3,8,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[3,1,8,4,2,7,6,5]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,8,7,4,1,3,6,5]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,2,3,1,7,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,1,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,5,8,3,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,8,2,3,1,7,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,2,5,7,3,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,3,1,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,2,8,7,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[8,6,7,4,1,3,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,6,5,2,8,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[4,6,3,2,5,1,8,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[4,8,3,2,6,5,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,8,3,6,5,2,7,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,2,5,4,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,3,8,6,1,7,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,6,3,8,5,4,7,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[6,1,3,2,5,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,8,4,2,5,3,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,4,3,5,2,7,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,1,4,6,5,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,4,6,1,2,8,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[7,3,5,6,1,8,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,7,6,3,4,2,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[4,6,7,2,3,5,8,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[6,5,4,8,7,2,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,7,4,3,6,2,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,8,5,6,2,3,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,2,4,6,8,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,2,5,4,7,8,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[3,8,2,6,1,7,4,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[8,5,6,1,3,2,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,7,8,2,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,5,8,3,6,1,7,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,8,7,2,3,1,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[8,2,6,4,3,7,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,8,7,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,6,3,2,7,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,6,8,7,4,5,2]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[5,7,1,3,6,2,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[4,7,5,2,3,6,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,6,4,1,2,5,7,8]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[4,7,1,3,2,5,8,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[4,7,1,3,2,6,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[5,7,1,3,6,2,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[6,8,2,5,7,3,1,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,8,5,2,3,6,1,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,6,3,4,7,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,7,5,4,2,8,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[4,6,5,1,7,8,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[4,7,1,3,2,8,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[3,6,5,1,8,2,4,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[5,8,7,3,4,2,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,5,2,3,7,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,1,5,4,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,7,6,3,5,2,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[1,7,5,3,4,8,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,8,2,3,4,7,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,7,3,2,6,4,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,1,4,7,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,3,1,6,4,8,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[3,4,8,5,7,2,6,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[8,5,1,2,7,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,3,1,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,5,6,2,4,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[7,4,3,6,2,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,3,8,7,1,6,2,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,5,3,8,4,7,2,6]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[8,2,3,1,6,5,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,7,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,2,3,1,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,2,3,6,5,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[3,8,2,6,4,7,1,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,5,8,6,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[6,5,1,7,4,8,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[7,6,3,5,1,4,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,5,4,1,7,2,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[8,3,6,1,7,4,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,6,4,8,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,5,1,8,6,2,4,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[1,8,7,5,4,6,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,7,4,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,4,7,5,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,8,1,5,3,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,6,4,3,5,8,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,1,4,3,7,8,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[5,7,1,8,6,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[5,7,6,3,4,2,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[4,1,3,7,6,5,2,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[4,3,6,1,2,7,8,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[7,2,6,1,3,5,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,2,7,1,5,8,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[5,8,3,6,7,2,4,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,1,6,2,5,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,5,3,6,8,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,8,7,3,4,2,5,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,8,6,2,4,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,4,2,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,7,3,6,4,1,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[3,7,5,6,4,1,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,5,7,3,4,6,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,7,2,3,5,8,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[7,4,5,8,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,1,3,8,5,4,6,7]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[5,3,6,8,2,4,1,7]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,7,8,6,3,2,4,5]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,1,2,5,3,8,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,7,4,2,5,1,8,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,8,3,4,5,7,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,6,7,5,3,8,1,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[4,5,2,6,8,7,1,3]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[4,5,2,6,8,3,1,7]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[4,5,7,6,2,1,3,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[7,8,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[5,3,7,8,4,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[7,3,6,8,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,5,8,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[6,5,8,2,3,4,1,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[8,1,5,3,4,6,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,7,2,4,3,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,7,2,4,8,5,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,8,2,3,7,4,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,8,2,3,5,4,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,4,1,3,2,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,2,3,5,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,8,4,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,7,3,1,8,5,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,8,5,2,1,6,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,6,1,5,7,4,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,3,5,1,7,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,5,4,7,1,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,1,5,7,8,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[4,8,7,1,2,5,3,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,7,2,6,1,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,7,3,8,2,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[7,1,8,6,4,2,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,1,3,5,8,2,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[1,8,5,7,4,6,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,7,6,8,3,5,2]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,7,2,8,6,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[5,7,1,6,4,2,3,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[4,8,2,7,5,1,6,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,6,7,1,5,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,5,1,4,2,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,2,5,3,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,7,5,2,4,3,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,8,5,1,4,3,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,2,5,7,6,8,4]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[5,1,7,3,2,6,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[4,7,2,3,5,1,6,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[4,8,2,3,7,5,1,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,7,2,4,3,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,4,3,5,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,4,7,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,2,8,4,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,8,1,5,7,3,2,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,1,7,5,6,8,2,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[3,7,6,2,1,4,5,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,6,8,7,2,5,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,4,8,7,6,3,5,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[3,1,8,4,5,2,7,6]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,7,6,1,8,4,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[4,8,5,2,1,3,7,6]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,8,4,2,1,3,7,6]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,6,7,5,2,3,1,8]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[6,2,5,3,1,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,2,5,3,8,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[6,4,5,3,8,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,6,4,5,8,7,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[8,4,7,5,2,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,7,4,5,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,4,7,5,3,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,6,7,5,3,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,6,7,5,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,4,5,8,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,8,7,5,3,1,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,6,5,3,8,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[6,7,2,4,5,3,1,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,8,7,4,5,3,1,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,8,4,7,5,3,1,6]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,8,7,4,6,3,1,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[6,5,8,4,7,2,1,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[4,8,6,2,5,7,1,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[8,1,6,2,5,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,8,1,2,4,7,3,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,1,5,3,2,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,7,6,2,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6,1,3,5,8,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[4,5,1,3,8,7,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[6,2,7,1,8,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[6,4,5,8,1,7,2,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[6,2,8,5,1,4,7,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,4,7,6,1,8,3,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[7,4,5,8,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,6,2,3,8,5,7,4]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[3,4,2,6,8,5,7,1]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[7,4,1,3,6,8,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,8,1,2,7,3,4,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,6,2,8,7,3,4,5]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,6,8,5,7,4,3,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,8,1,2,4,7,6,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,5,7,3,6,8,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[2,3,8,1,4,6,5,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,6,2,4,7,5,8,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[3,1,8,4,6,2,5,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,2,7,3,5,8,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[3,1,8,4,5,6,2,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,2,7,8,6,3,1,5]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[7,1,4,2,8,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,3,7,4,8,1,6,5]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,6,3,5,8,7,4,2]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[8,4,6,3,5,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,2,6,8,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,4,5,7,1,6,8,3]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[8,4,2,6,7,3,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,7,8,6,2,3]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[6,1,4,8,2,3,7,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,6,2,3,5,8,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,8,5,7,6,3,4,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,5,7,8,6,4,1,3]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[7,4,1,6,2,5,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,7,5,4,6,2,3,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,2,7,5,3,1,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[6,1,7,4,8,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[8,2,4,6,3,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,2,4,8,7,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[8,5,6,2,3,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,1,4,5,6,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,3,1,2,5,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,3,7,4,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,6,7,8,3,5,4]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,4,8,6,7,3,5]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[8,1,2,6,5,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,2,6,5,8,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,4,8,3,5,6,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,6,1,4,7,5,8,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[3,1,5,7,2,6,8,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[3,1,7,5,2,6,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[3,2,7,5,1,6,8,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[5,2,7,3,1,6,8,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[6,7,2,1,3,4,8,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[4,6,3,1,2,7,8,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[2,3,5,6,8,4,7,1]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[2,4,5,8,3,6,7,1]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[4,5,8,7,6,3,1,2]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[8,7,4,6,5,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,4,3,6,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,5,7,6,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,6,3,7,8,4,2,5]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,3,8,4,6,7,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,3,5,8,6,7,2,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[3,2,7,8,5,6,4,1]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[4,7,3,8,5,6,2,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[7,1,4,8,5,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,3,8,7,2,5,6,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,7,3,8,6,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[7,4,2,8,5,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,4,8,2,6,7,5,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,6,3,8,7,4,5,2]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,4,5,8,7,6,2,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[5,2,1,3,8,4,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,4,3,5,8,2,6,7]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[2,1,3,8,6,4,5,7]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,3,6,4,5,8,2,7]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[6,1,4,3,5,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[6,5,1,3,8,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,4,3,8,6,2,5,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[4,1,3,8,6,2,5,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[7,1,5,4,6,3,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,4,7,8,3,5,1,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[3,5,6,7,1,8,4,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[3,5,2,4,8,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[3,7,6,1,4,8,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[8,4,7,1,5,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,3,6,1,5,4]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,7,8,3,6,2,5,4]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[7,4,3,5,8,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,3,6,4,1,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,8,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,6,4,3,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,7,3,4,1,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,4,3,8,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,7,5,4,3,8,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[4,5,8,1,7,3,2,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,6,7,1,3,8,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[2,6,3,1,4,7,8,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[2,7,3,4,1,8,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[8,6,4,5,1,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,8,5,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,4,6,5,1,3,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,3,8,7,1,2,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[8,5,4,7,6,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,7,8,1,4,6,5]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[8,2,3,5,4,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,1,3,8,2,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[7,2,3,6,4,1,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,5,2,4,1,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,7,2,4,1,3,8,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[6,2,5,4,1,8,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,2,6,3,5,8,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[7,4,2,6,8,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,5,2,4,6,3,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,4,1,2,8,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,4,1,8,5,2,3,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,4,1,6,3,5,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,1,6,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,6,2,3,5,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,2,5,7,3,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,4,8,5,1,2,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[8,5,1,2,7,4,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,8,3,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,6,7,5,4,8,2,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,8,5,4,2,6,3,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,6,2,1,4,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[5,8,6,1,2,4,3,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,1,5,7,3,6,8,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[1,4,5,7,6,8,2,3]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[5,7,2,1,6,8,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[2,6,3,1,7,8,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[6,2,5,7,4,1,8,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[3,6,1,8,7,4,5,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,7,1,3,5,6,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[4,3,5,7,8,2,6,1]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[5,3,2,7,6,4,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[5,3,7,4,6,2,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[5,7,3,2,1,8,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,7,6,3,2,1,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[3,2,7,5,4,1,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,7,3,5,4,2,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[5,3,7,4,1,8,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[7,3,5,4,1,6,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,5,1,6,8,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,3,1,7,6,8,2,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[7,1,5,3,2,4,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,8,7,3,2,1,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,6,8,7,2,4,1,5]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,7,3,6,2,1,8,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[3,6,5,2,4,8,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,8,3,6,2,4,7,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,5,6,4,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,2,1,5,4,3,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,3,2,1,5,8,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[4,3,5,6,2,8,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[6,3,5,2,7,8,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[4,5,3,1,6,8,2,7]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[3,4,6,7,5,1,8,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[7,4,1,2,5,6,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,8,2,6,7,1,5,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,5,8,3,7,1,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,5,2,4,7,6,8,3]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[2,5,4,7,1,8,3,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,5,4,7,3,8,2,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,2,6,7,3,5,4,8]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[8,1,2,4,6,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,7,8,4,5,6,1,2]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,3,8,6,7,4,5,2]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,6,5,3,7,1,8,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[5,7,1,3,6,4,8,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[8,2,5,4,1,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,7,6,4,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,6,3,7,4,5,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,7,3,4,2,8,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[5,8,3,4,2,7,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,6,4,2,3,8,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,5,6,8,2,4,7,1]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[4,8,7,3,2,5,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[3,7,4,2,6,8,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[6,4,8,7,3,2,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[5,6,2,8,7,4,3,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[6,2,8,3,7,4,5,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,7,5,6,4,2,8,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[5,2,3,8,6,1,4,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,4,3,8,5,6,2,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[7,8,2,6,4,3,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,5,8,7,2,3,6,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[7,8,6,1,4,2,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[8,3,6,5,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,3,6,4,2,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[6,1,2,4,7,5,3,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[8,3,1,4,6,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,5,1,2,6,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,4,5,1,8,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[8,6,2,1,7,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,8,6,1,4,3,5,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,3,6,2,5,7,1,8]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[1,6,5,7,3,4,8,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[8,2,6,5,1,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,1,2,5,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,6,5,4,8,7,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[5,6,7,1,3,2,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[7,1,8,4,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,8,5,2,7,6,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,8,2,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,7,8,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[4,6,5,7,1,8,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[7,5,3,6,8,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[7,2,5,6,4,8,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[7,4,6,2,8,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,6,3,4,2,5,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,5,7,6,2,3,8,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,4,3,7,6,2,5,8]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,3,7,4,6,8,5,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[3,7,4,6,8,1,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,8,3,1,7,6,2,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,6,1,4,3,8,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[5,8,6,4,3,1,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,1,3,7,8,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[9,1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,6,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[7,1,2,3,4,5,9,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[9,1,2,3,4,5,8,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,2,3,4,5,8,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[6,1,2,3,4,9,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]
[6,1,2,3,4,8,5,9,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]
[9,1,2,3,4,7,5,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,2,3,4,8,5,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,2,3,4,7,5,9,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[6,1,2,3,4,7,9,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]
[6,1,2,3,4,9,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]
[9,1,2,3,4,7,8,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,1,2,3,4,7,8,9,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[5,1,2,3,9,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[5,1,2,3,8,4,6,9,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0]
[9,1,2,3,6,4,5,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,2,3,9,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[5,1,2,3,9,8,4,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[9,1,2,3,6,8,4,5,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,1,2,3,6,9,8,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]
[5,1,2,3,6,7,8,9,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[4,1,2,8,3,5,6,9,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]
[4,1,2,9,3,5,8,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,9,3,8,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[9,1,2,5,3,4,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,2,8,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,2,8,3,4,5,9,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]
[4,1,2,5,9,3,6,7,8]=>[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]
[4,1,2,8,9,3,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]
[8,1,2,5,9,3,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[8,1,2,9,6,3,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[4,1,2,5,9,8,3,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]
[9,1,2,8,6,7,3,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,1,2,5,6,7,9,3,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]
[4,1,2,9,6,7,8,3,5]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[9,1,2,5,6,7,8,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,1,2,5,6,7,8,9,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,1,9,2,4,5,6,7,8]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,8,2,4,5,6,9,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,1,9,2,4,5,8,6,7]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,5,2,7,4,9,6,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[8,1,4,2,3,5,6,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[9,1,4,2,3,5,8,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,1,4,2,3,7,8,9,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[9,1,8,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,7,2,3,4,5,9,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[3,1,4,9,2,5,6,7,8]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,4,9,2,5,8,6,7]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,9,8,2,4,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[9,1,4,5,2,3,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,4,5,2,3,8,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[7,1,4,9,2,3,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]
[9,1,4,8,2,3,5,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,6,5,2,3,4,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,9,6,2,3,4,5,8]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[9,1,8,6,2,3,4,5,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,8,9,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]
[3,1,4,8,9,2,5,6,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[3,1,8,9,7,2,4,5,6]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[8,1,4,5,6,2,3,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,1,4,9,7,2,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[8,1,9,5,6,2,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,1,9,7,6,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[7,1,4,5,6,2,8,9,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[3,1,4,5,6,9,2,7,8]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[3,1,4,5,6,8,2,9,7]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[3,1,4,9,8,7,2,5,6]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,9,8,6,7,2,4,5]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[9,1,4,5,6,7,2,3,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,4,8,6,7,2,3,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,8,5,6,7,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,4,5,6,7,2,9,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[3,1,4,5,6,7,9,2,8]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[3,1,4,9,6,7,8,2,5]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,9,5,6,7,8,2,4]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[9,1,4,5,6,7,8,2,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,8,9,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,9,1,3,4,5,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,4,5,6,9,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,7,1,3,4,5,9,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[2,9,1,3,4,5,8,6,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,3,4,5,8,9,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[2,6,1,3,4,9,5,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[2,9,1,3,4,8,5,6,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,1,3,9,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,9,1,3,8,7,4,5,6]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,1,3,6,7,8,4,5]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,1,3,6,7,8,9,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[2,4,1,6,3,8,5,9,7]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,9,1,8,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,1,6,3,4,8,9,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[2,6,1,5,3,7,8,9,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[2,4,1,5,9,3,6,7,8]=>[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[2,4,1,8,9,3,5,6,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[2,8,1,9,7,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,9,1,8,6,7,3,4,5]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,6,7,9,3,8]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[2,4,1,5,6,9,8,3,7]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[2,9,1,5,6,7,8,3,4]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,1,5,6,7,8,9,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[9,3,1,2,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,3,1,2,4,5,6,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[9,3,1,2,4,5,8,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,3,1,2,4,7,8,9,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[9,3,1,2,6,7,8,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,3,1,2,6,7,8,9,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[9,4,1,2,3,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,4,1,2,3,5,8,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[6,4,1,2,3,7,8,9,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[5,9,1,2,3,4,6,7,8]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[5,8,1,2,3,4,6,9,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]
[5,7,1,2,3,4,8,9,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
[9,6,1,2,3,4,5,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,6,1,2,3,4,5,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[9,7,1,2,3,4,5,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,9,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,7,1,2,3,4,5,9,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[7,6,1,2,3,4,9,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[9,6,1,2,3,4,8,5,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,1,2,3,4,8,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,6,1,2,3,4,8,9,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[5,6,1,2,3,9,4,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]
[5,9,1,2,3,8,4,6,7]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[9,6,1,2,3,7,4,5,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,1,2,3,7,4,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,6,1,2,3,7,4,9,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[5,6,1,2,3,7,9,4,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]
[9,6,1,2,3,7,8,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,6,1,2,3,7,8,9,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]
[5,4,1,2,9,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[8,4,1,2,9,3,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[5,9,1,2,6,3,4,7,8]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[9,7,1,2,6,3,8,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,4,1,2,6,9,3,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]
[9,8,1,2,6,7,3,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,4,1,2,6,7,9,3,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,0]
[5,4,1,2,6,7,8,9,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[4,3,1,9,2,5,6,7,8]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[9,3,1,8,2,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,4,1,5,2,3,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,4,1,8,2,3,5,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,9,1,5,2,3,4,7,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[9,7,1,6,2,3,4,5,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,1,9,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[8,7,1,6,2,3,4,9,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[9,4,1,6,2,8,3,5,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,1,6,2,7,3,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,3,1,5,9,2,6,7,8]=>[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]
[9,8,1,7,6,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,3,1,5,6,8,2,9,7]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,0]
[4,3,1,5,9,8,2,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]
[4,3,1,5,8,7,2,9,6]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]
[8,9,1,5,6,7,2,3,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[4,3,1,5,6,7,9,2,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]
[4,3,1,5,6,9,8,2,7]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0]
[9,3,1,5,6,7,8,2,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,4,1,5,6,7,8,2,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,3,1,5,6,7,8,9,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[2,3,9,1,4,5,6,7,8]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,8,1,4,5,6,9,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,3,9,1,4,5,8,6,7]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,9,1,4,7,8,5,6]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,9,1,8,7,4,5,6]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,8,1,6,7,4,9,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,3,5,1,6,7,9,4,8]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[2,3,9,1,6,7,8,4,5]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,1,6,7,8,9,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[2,9,4,1,3,5,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,4,1,3,7,8,9,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[2,9,5,1,3,4,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,9,1,3,4,5,7,8]=>[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,9,7,1,3,4,5,6,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,8,1,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,6,7,1,3,4,8,9,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[2,9,4,1,6,3,5,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,1,9,3,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[2,9,4,1,6,3,8,5,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,8,1,7,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,5,1,6,7,8,3,4]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,3,4,1,2,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,3,4,1,2,7,8,9,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[9,3,7,1,2,4,5,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,8,1,2,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,5,4,1,2,3,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,5,4,1,2,3,6,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[6,9,4,1,2,3,5,7,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[6,8,4,1,2,3,5,9,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]
[9,7,4,1,2,3,5,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,4,1,2,3,5,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,9,5,1,2,3,4,7,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[6,8,5,1,2,3,4,9,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]
[8,7,5,1,2,3,4,9,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[6,7,9,1,2,3,4,5,8]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[6,9,8,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[9,7,8,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,7,8,1,2,3,4,9,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]
[6,5,4,1,2,8,3,9,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]
[9,8,5,1,7,2,3,4,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,8,9,1,6,2,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,5,1,6,2,3,9,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[5,3,4,1,6,8,2,9,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0]
[9,3,4,1,8,7,2,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,3,4,1,6,7,2,9,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[9,5,4,1,8,7,2,3,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,5,4,1,6,7,2,9,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[5,3,4,1,9,7,8,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[9,3,5,1,6,7,8,2,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,5,4,1,6,7,8,2,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,3,4,1,6,7,8,9,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[2,3,4,9,1,5,6,7,8]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,9,1,5,8,6,7]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,9,1,7,8,5,6]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,6,1,7,8,9,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[2,3,9,5,1,4,6,7,8]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,9,6,1,4,5,7,8]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,9,1,4,5,6,8]=>[1,1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,3,9,8,1,4,5,6,7]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,9,5,1,7,4,6,8]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,9,6,1,7,8,4,5]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,9,4,5,1,3,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,4,5,1,3,8,9,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[2,9,8,6,1,3,4,5,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,9,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[2,8,9,6,1,7,3,4,5]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,9,6,5,1,7,8,3,4]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,3,4,5,1,2,8,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[9,3,4,8,1,2,5,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,3,4,8,1,2,5,9,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]
[7,3,8,9,1,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]
[9,8,4,5,1,2,3,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,8,4,6,1,2,3,9,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[9,8,6,5,1,2,3,4,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,8,9,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,6,5,1,2,3,9,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[8,3,9,6,1,7,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,3,6,5,1,7,2,9,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,6,4,5,1,7,2,9,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[6,3,4,5,1,7,9,2,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]
[6,3,4,5,1,9,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]
[9,3,4,6,1,7,8,2,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,3,4,5,1,7,8,9,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[2,3,4,5,9,1,6,7,8]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,5,9,1,8,6,7]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,5,7,1,8,9,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[2,3,4,9,6,1,5,7,8]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,9,7,1,5,6,8]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,9,6,1,8,5,7]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,9,7,1,8,5,6]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,9,5,6,1,4,7,8]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,8,5,6,1,4,9,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,3,9,5,6,1,8,4,7]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,4,5,6,1,3,9,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,8,9,5,7,1,3,4,6]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,8,9,7,6,1,3,4,5]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,9,7,5,6,1,8,3,4]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,3,4,5,6,1,2,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,3,4,7,6,1,2,9,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,3,9,7,6,1,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,3,7,5,6,1,2,9,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[9,7,4,5,6,1,2,3,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,9,4,5,6,1,2,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,7,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,7,4,5,6,1,2,9,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[7,3,4,5,6,1,9,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[9,3,4,5,6,1,8,2,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,7,5,6,1,8,2,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,3,4,5,6,1,8,9,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[2,3,4,5,6,9,1,7,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,5,6,8,1,9,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[2,3,4,5,9,7,1,6,8]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,5,9,8,1,6,7]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,9,6,7,1,5,8]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,9,5,6,7,1,4,8]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,9,5,6,8,1,4,7]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,9,4,5,6,7,1,3,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,4,5,6,8,1,3,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,4,5,8,7,1,3,6]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,4,8,6,7,1,3,5]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,8,5,6,7,1,3,4]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,4,5,6,7,1,9,3]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[9,3,4,5,6,7,1,2,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,4,5,6,8,1,2,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,4,5,6,7,1,2,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,3,4,5,6,7,1,9,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[2,3,4,5,6,7,9,1,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[2,3,4,5,6,9,8,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,5,9,7,8,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,9,6,7,8,1,5]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,9,5,6,7,8,1,4]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,9,4,5,6,7,8,1,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,3,4,5,6,7,8,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,5,6,7,8,1,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[2,3,4,5,6,8,9,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[2,3,4,5,7,8,9,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[2,3,4,6,7,8,9,1,5]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[2,3,5,6,7,8,9,1,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[2,4,5,6,7,8,9,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[3,4,5,6,7,8,9,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[2,3,4,5,6,7,1,8,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[2,3,4,5,6,1,9,7,8]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[2,3,4,5,1,8,9,6,7]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[2,3,4,1,7,8,9,5,6]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[2,3,1,6,7,8,9,4,5]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,5,6,7,8,9,3,4]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,4,5,6,7,8,9,2,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,2,3,4,5,6,7,9,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,3,4,5,6,7,8,9]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,8,2,3,4,5,6,9,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1,2,3,4,5,6,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[2,1,9,3,4,5,6,7,8]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,1,3,4,5,6,7,9]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,2,3,4,5,6,7,8,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,3,4,5,6,8,9,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,3,4,5,7,8,9,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,3,4,6,7,8,9,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,5,6,7,8,9,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,4,5,6,7,8,9,3]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,3,4,5,6,7,8,9,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,2,3,4,5,6,9,8,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,3,4,5,8,7,9,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,2,3,4,7,6,8,9,5]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,2,3,6,5,7,8,9,4]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,2,5,4,6,7,8,9,3]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,4,3,5,6,7,8,9,2]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,4,5,6,7,8,9,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,9,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,7,9,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,7,6,9,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[8,7,6,5,9,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[8,7,6,5,4,9,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[8,7,6,5,4,3,9,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[8,7,6,5,4,3,2,9,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[7,8,9,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[8,6,7,9,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[8,7,5,6,9,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[8,7,6,4,5,9,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[8,7,6,5,3,4,9,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[8,7,6,5,4,2,3,9,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,7,6,5,4,3,1,2,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,9,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,4,5,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,9,8,7,5,6,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,4,6,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7,4,6,5,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,9,8,6,5,7,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,5,7,6,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,2,1,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,2,3,1,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,2,3,5,6,7,8,9,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,4,2,5,6,7,8,9,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,2,3,4,5,6,9,7,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,3,4,5,8,6,9,7]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,2,3,4,7,5,8,9,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,2,3,6,4,7,8,9,5]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,2,5,3,6,7,8,9,4]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,4,2,5,6,7,8,9,3]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[9,8,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,8,9,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[9,8,7,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,7,8,9,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[9,6,7,8,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,9,6,7,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[9,8,6,7,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,5,6,7,8,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,9,5,6,7,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[9,8,5,6,7,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,8,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,8,9,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[9,7,8,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,9,6,7,4,5,1,2,3]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[9,8,6,7,4,5,1,2,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,4,5,1,2,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,8,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,8,9,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,6,8,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
[1,7,9,8,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[8,1,2,3,4,5,6,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,9,2,3,4,5,6,7,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,9,2,3,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[2,4,1,3,6,5,8,7,9]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[2,4,1,6,3,5,8,7,9]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[2,4,1,6,3,8,5,7,9]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[2,4,1,6,3,7,5,9,8]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[2,4,1,5,3,7,6,9,8]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[2,3,1,5,4,7,6,9,8]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,2,5,4,7,6,9,8]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,4,6,1,3,5,8,7,9]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[2,4,1,6,8,3,5,7,9]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[2,4,1,6,3,8,9,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[2,4,1,6,3,7,5,8,9]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[2,4,1,5,3,8,6,9,7]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[2,3,1,6,4,7,5,9,8]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,4,2,5,3,7,6,9,8]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[7,1,2,3,4,5,6,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[3,4,1,2,5,6,7,8,9]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[3,2,1,4,5,6,7,8,9]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,6,1,2,3,7,8,9]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]
[4,2,5,1,3,6,7,8,9]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0]
[4,3,2,1,5,6,7,8,9]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[5,6,7,8,1,2,3,4,9]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]
[5,2,6,7,1,3,4,8,9]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,1,0]
[5,6,3,4,1,2,7,8,9]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]
[5,3,2,6,1,4,7,8,9]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]
[5,4,3,2,1,6,7,8,9]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[6,2,7,8,9,1,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]
[6,7,3,4,8,1,2,5,9]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]
[6,3,2,7,8,1,4,5,9]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0]
[6,4,7,2,5,1,3,8,9]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]
[6,4,3,2,7,1,5,8,9]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]
[6,5,4,3,2,1,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[7,4,8,2,5,9,1,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]
[7,4,3,2,8,9,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0]
[7,8,5,6,3,4,1,2,9]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[7,5,3,8,2,6,1,4,9]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[7,5,4,3,2,8,1,6,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]
[7,6,5,4,3,2,1,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[8,6,9,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,6,4,3,9,2,7,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[8,6,5,4,3,2,9,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[2,3,1,4,5,6,7,8,9]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,4,1,5,6,7,8,9]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[2,3,4,5,1,6,7,8,9]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[2,3,4,5,6,1,7,8,9]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[2,4,3,1,5,6,7,8,9]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[2,3,4,5,6,8,7,1,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[2,3,4,5,6,7,9,8,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[3,4,1,5,6,7,8,9,2]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,4,5,1,6,7,8,9,2]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[3,4,5,6,1,7,8,9,2]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[3,4,5,6,7,1,8,9,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[3,4,5,6,7,8,1,9,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[3,1,2,5,6,7,8,9,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[3,4,1,2,6,7,8,9,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[3,4,5,1,2,7,8,9,6]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[3,4,5,6,1,2,8,9,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[3,4,5,6,7,1,2,9,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[3,4,5,6,7,8,1,2,9]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[8,7,6,5,4,3,1,9,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[7,9,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,7,6,5,4,3,9,8,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,9,6,5,4,3,2,8,7]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,6,5,4,3,9,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[3,7,6,5,4,9,1,8,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[7,9,1,5,4,3,2,8,6]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[2,9,6,5,4,3,8,1,7]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,1,5,4,3,9,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[1,3,6,5,4,9,8,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,7,6,5,9,3,1,8,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]
[7,9,6,1,4,3,2,8,5]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,9,2,5,4,3,8,7,6]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,9,6,5,4,8,2,1,7]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,9,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[8,9,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,9,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[9,7,6,5,4,3,1,8,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,9,8,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[6,9,8,7,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[5,9,8,7,6,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[4,9,8,7,6,5,3,2,1]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,9,8,7,6,5,4,2,1]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,8,7,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,9,7,8,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[5,9,8,6,7,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[4,9,8,7,5,6,3,2,1]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,9,8,7,6,4,5,2,1]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,8,7,6,5,3,4,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,7,6,5,4,2,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,9,6,7,8]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,4,9,5,6,7,8]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,9,4,5,6,7,8]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,9,3,4,5,6,7,8]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,5,9,7,6,8]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,4,9,6,5,7,8]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,9,5,4,6,7,8]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,9,4,3,5,6,7,8]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,9,3,2,4,5,6,7,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,9,8,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[6,5,4,9,8,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]
[6,8,5,9,7,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]
[6,7,8,9,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[5,4,3,2,9,8,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[5,8,4,3,9,7,6,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]
[5,4,7,6,9,8,3,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[5,7,8,4,9,6,3,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]
[5,6,7,8,9,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[4,8,3,2,1,9,7,6,5]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,3,7,6,2,9,8,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0]
[4,7,8,3,2,9,6,5,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]
[4,6,3,8,5,9,7,2,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0]
[4,6,7,8,3,9,5,2,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0]
[4,5,6,7,8,9,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,2,1,6,5,4,9,8,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[3,6,2,8,5,1,9,7,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[3,6,7,8,2,1,9,5,4]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[3,2,5,4,7,6,9,8,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,5,7,2,8,4,9,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[3,5,6,7,8,2,9,4,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[3,4,5,6,7,8,9,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[2,4,6,7,1,8,3,9,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[2,4,5,6,7,8,1,9,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[3,1,2,4,5,6,7,8,9]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,1,3,5,6,7,8,9]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[2,3,5,1,4,6,7,8,9]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[2,3,4,6,1,5,7,8,9]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[2,3,4,5,7,1,6,8,9]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[2,3,4,5,6,8,1,7,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[7,6,5,4,3,2,9,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[6,5,4,3,9,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]
[6,5,4,3,2,8,1,7,9]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]
[5,4,9,3,8,2,7,1,6]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,8,2,7,1,6,9]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]
[5,4,3,2,7,9,1,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0]
[5,4,3,2,7,1,6,8,9]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,1,0]
[4,8,3,7,2,6,1,5,9]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,3,7,2,6,9,1,5,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0]
[4,3,7,2,6,1,5,8,9]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0,1,0]
[4,3,2,6,8,1,5,7,9]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0]
[4,3,2,6,1,5,7,8,9]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0,1,0]
[3,6,9,2,5,8,1,4,7]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,6,2,5,8,1,4,7,9]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[3,6,2,5,1,4,7,8,9]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[3,2,5,7,9,1,4,6,8]=>[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,2,5,7,1,4,6,8,9]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[3,2,5,1,4,6,7,8,9]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[2,4,6,8,1,3,5,7,9]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[2,4,6,1,3,5,7,8,9]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[8,7,6,5,4,2,1,9,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,7,6,5,3,2,1,9,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,7,6,4,3,2,1,9,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,7,5,4,3,2,1,9,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,6,5,4,3,2,1,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[7,6,5,4,3,2,1,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[8,7,6,5,4,9,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[8,7,6,5,9,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[8,7,6,9,3,2,1,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[8,7,9,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,9,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[9,6,5,4,3,2,1,8,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,9,8,7,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,4,5,6,7,8,1,3,9]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,4,5,6,7,8,2,9,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[9,7,8,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,8,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,5,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,9,5,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[8,9,5,7,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,6,7,3,5,1,4,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,6,7,4,5,1,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[9,7,8,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,5,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,5,9,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[9,8,5,7,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,9,6,8,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[8,9,5,7,4,6,1,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,6,7,3,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[6,5,4,3,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[6,5,4,3,2,1,8,7,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]
[5,4,3,2,1,9,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[5,4,3,2,1,8,7,6,9]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]
[5,4,3,2,1,7,6,9,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[5,4,3,2,1,7,6,8,9]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]
[4,3,2,1,8,7,6,5,9]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[4,3,2,1,7,6,5,9,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[4,3,2,1,7,6,5,8,9]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]
[4,3,2,1,6,5,8,7,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[4,3,2,1,6,5,7,8,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]
[3,2,1,6,5,4,8,7,9]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[3,2,1,6,5,4,7,8,9]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[3,2,1,5,4,7,6,9,8]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,2,1,5,4,7,6,8,9]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[3,2,1,5,4,6,7,8,9]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,4,3,6,5,7,8,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[2,1,4,3,5,6,7,8,9]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[3,1,4,2,6,5,8,7,9]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[3,1,5,2,6,4,8,7,9]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[3,1,5,2,7,4,8,6,9]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[3,1,5,2,7,4,6,9,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[3,1,5,2,4,7,6,9,8]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,1,2,5,4,7,6,9,8]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,1,5,2,6,3,8,7,9]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]
[3,1,6,2,7,4,8,5,9]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[3,1,5,2,8,4,9,6,7]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[3,1,5,2,7,4,6,8,9]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[3,1,5,2,4,7,9,6,8]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[3,1,2,5,7,4,6,9,8]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,3,5,2,4,7,6,9,8]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[4,5,6,7,8,9,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,8,9,2,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[5,6,7,8,9,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[5,6,7,8,9,2,3,4,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[5,6,7,8,9,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[5,6,7,8,9,3,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[6,7,8,9,2,3,4,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,3,4,5,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,3,4,5,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,4,5,2,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,4,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[7,8,9,4,5,6,2,3,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,5,7,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,6,8,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,4,8,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,4,7,3,6,1,2,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,2,4,6,1,3,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,4,6,1,2,3,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,9,4,8,3,7,1,2,6]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[9,5,8,2,4,7,1,3,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,5,8,4,7,1,2,3,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,3,5,7,1,2,4,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,5,7,1,2,3,4,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,9,3,5,8,1,2,4,7]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[6,9,5,8,1,2,3,4,7]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[9,2,4,6,8,1,3,5,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,4,6,8,1,2,3,5,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,6,8,1,2,3,4,5,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,5,7,9,1,2,4,6,8]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[5,7,9,1,2,3,4,6,8]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[7,9,1,2,3,4,5,6,8]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,2,9,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[9,6,5,4,3,2,8,1,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,5,4,3,2,1,8,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,6,5,4,3,9,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]
[8,6,5,4,3,2,9,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[9,1,2,3,5,4,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,6,5,7,8,9,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[9,1,2,3,5,6,4,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,7,5,6,8,9,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[2,3,4,6,7,5,8,9,1]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[8,7,6,4,3,5,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7,6,3,5,4,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,9,8,7,5,4,6,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,7,4,6,5,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,5,8,4,3,2,1,9]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[7,6,5,4,9,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[7,6,5,4,3,8,2,1,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]
[7,6,5,4,3,2,8,1,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]
[6,9,8,5,4,3,2,1,7]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[7,5,8,9,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]
[7,6,4,8,9,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]
[7,6,5,3,9,8,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[7,6,5,4,2,8,9,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]
[7,6,5,4,3,1,8,9,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[6,5,8,7,4,3,2,1,9]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]
[7,5,4,8,6,3,2,1,9]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[5,9,8,7,4,3,2,1,6]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,4,3,9,5,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[7,4,8,9,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]
[7,6,5,3,2,8,4,1,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]
[7,6,3,8,9,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]
[7,6,5,4,2,1,8,3,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]
[7,6,5,2,9,8,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[7,6,5,4,1,8,9,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]
[2,3,4,5,6,8,9,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[8,1,9,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[9,2,8,7,6,5,4,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,9,8,7,6,5,4,1,2]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,9,1,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,2,9,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,1,2,3,4,5,9,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[8,1,2,3,4,9,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[8,1,2,9,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[8,1,9,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[2,1,8,9,3,4,5,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[9,8,7,6,5,2,3,1,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,3,4,2,1,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,4,5,3,2,1,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,5,6,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,6,7,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,2,1,7,6,5,4,3,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[3,2,8,7,6,5,4,1,9]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,3,1,7,6,5,4,9,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,2,9,1,6,5,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[4,2,8,7,6,5,9,1,3]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,9,2,7,6,5,4,1,8]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,4,1,7,6,5,9,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[8,3,2,1,6,5,4,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,2,9,7,1,5,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[5,2,8,7,6,9,4,1,3]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]
[4,3,2,7,6,5,8,1,9]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,1,0]
[3,9,8,2,6,5,4,1,7]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,4,2,1,3,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,9,8,7,6,5,3,2,4]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,7,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,9,8,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,9,8,7,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,9,8,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,9,8,7,6,5,4]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,9,8,7,6,5,4]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,1,9,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,4,3,2,9,8,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,4,3,9,8,7,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,2,4,3,9,8,7,6,5]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,4,9,8,7,6,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,5,4,3,2,9,8,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,5,4,3,9,8,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,2,5,4,3,9,8,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,3,2,5,4,9,8,7,6]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,3,5,4,9,8,7,6]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,3,4,5,9,8,7,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,3,2,6,5,4,9,8,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,3,6,5,4,9,8,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,1,4,3,6,5,9,8,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,4,3,6,5,9,8,7]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,3,4,6,5,9,8,7]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,3,5,4,7,6,9,8]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,3,4,5,7,6,9,8]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[9,8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,4,3,2,1,8,7,6,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,4,3,1,7,6,2,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,4,1,6,2,3,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,4,3,1,9,8,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[9,5,2,1,8,4,3,7,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,3,1,5,2,7,4,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,3,1,9,5,2,8,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]
[6,5,1,9,8,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]
[9,2,1,4,3,6,5,8,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,6,1,8,2,3,4,5,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,1,7,2,9,3,4,6,8]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[7,1,9,2,3,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[9,1,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,9,8,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[6,1,9,8,7,5,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[5,1,9,8,7,6,4,3,2]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,9,8,7,6,5,3,2]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,9,8,7,6,5,4,2]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[9,8,1,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,9,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[7,6,9,8,1,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[6,5,9,8,7,1,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[5,4,9,8,7,6,1,3,2]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[4,3,9,8,7,6,5,1,2]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,9,8,7,6,5,4,1]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[9,1,2,3,4,5,6,8,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,2,3,4,5,7,8,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,9,7,8,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[9,2,1,8,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,9,2,8,7,6,5,4,1]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,2,9,8,7,6,5,3,1]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[9,2,8,1,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,1,8,7,6,5,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,5,6,4,7,8,9,1]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[2,3,6,4,5,7,8,9,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[9,1,2,4,5,3,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,9,6,8,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[6,9,8,5,7,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[5,9,8,7,4,6,3,2,1]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[4,9,8,7,6,3,5,2,1]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,9,8,7,6,5,2,4,1]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,9,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,6,9,4,7,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,6,9,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,6,9,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,6,9,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,7,9,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,6,4,9,7,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[8,6,9,4,2,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,6,9,4,7,2,1,5,3]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,6,9,4,7,3,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,6,9,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,7,9,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[9,6,8,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,9,2,8]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[2,3,4,5,6,7,1,9,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[2,1,4,5,6,7,8,9,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,1,4,5,6,7,8,2,9]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,2,3,4,5,7,9,6,8]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,3,4,6,9,5,7,8]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,3,5,9,4,6,7,8]=>[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,4,9,3,5,6,7,8]=>[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,9,2,4,5,6,7,8]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,9,8,7,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,8,7,1,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,2,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,2,8,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,9,8,7,6,5,2,1,4]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,9,8,7,6,1,2,5,3]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,9,8,7,1,2,6,4,3]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[6,9,8,2,1,7,5,4,3]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[7,9,1,2,8,6,5,4,3]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[8,1,2,9,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[1,9,8,7,6,3,2,5,4]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,7,4,2,6,5,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,9,8,7,6,3,2,1,5]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,8,5,1,7,6,4,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,9,8,7,4,1,2,6,3]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,6,2,8,7,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,9,8,5,1,2,7,4,3]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[1,7,2,9,8,6,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[7,9,6,2,1,8,5,4,3]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[8,7,1,2,9,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[1,6,7,8,9,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[6,7,8,1,2,3,4,5,9]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]
[1,7,8,9,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[5,6,7,1,8,2,3,4,9]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]
[4,6,7,8,1,2,3,5,9]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,6,7,8,2,9,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[1,5,7,8,9,2,3,4,6]=>[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[9,2,3,4,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,2,3,4,5,6,7,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[7,2,3,4,5,6,1,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[6,2,3,4,5,1,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[5,2,3,4,1,6,7,8,9]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[4,2,3,1,5,6,7,8,9]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,3,5,6,7,8,9]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,6,8,9,7,5,3]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,2,4,5,3,6,7,8,9]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[2,4,1,3,6,8,5,7,9]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[8,2,1,3,4,5,6,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[3,2,4,5,6,7,8,1,9]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[8,3,1,2,4,5,6,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,2,3,1,4,5,6,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[4,2,3,5,6,7,8,1,9]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,1,0]
[1,9,3,4,5,6,7,8,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,4,5,6,7,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,9,8,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[7,3,4,5,6,8,1,2,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]
[2,3,4,5,7,6,8,1,9]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,8,4,5,6,7,9,2,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,3,4,5,6,8,7,9,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,2,3,4,5,9,7,8,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,4,9,6,7,8,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,9,5,6,7,8,4]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,9,4,5,6,7,8,3]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,9,7,6,8,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,9,6,5,7,8,4]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,9,5,4,6,7,8,3]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,9,4,3,5,6,7,8,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,3,2,4,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,5,6,7,8,9,4,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,2,3,5,7,4,6,9,8]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,2,3,6,4,7,5,9,8]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,2,3,4,6,8,5,7,9]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,3,4,7,5,8,6,9]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,2,5,7,3,4,6,9,8]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,2,4,5,7,3,6,9,8]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,2,6,3,4,7,5,9,8]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,2,5,6,3,7,4,9,8]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[4,9,1,2,3,5,6,7,8]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,9,1,2,4,5,6,7,8]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,3,4,5,6,7,9]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,9,8,6,7,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[9,8,7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,9,8,6,5,7,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,9,8,5,7,6,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,7,6,5,4,3,2,9]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,1,8,7,6,5,4,3,9]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[4,5,6,7,8,1,2,9,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[4,5,6,7,1,2,8,9,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[4,5,6,1,2,7,8,9,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[4,5,1,2,6,7,8,9,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[7,8,1,2,3,4,5,9,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[2,8,9,1,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[7,1,8,2,9,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]
[6,1,7,2,8,3,9,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]
[5,1,6,2,7,3,8,4,9]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[7,1,8,2,3,9,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]
[6,1,7,2,8,3,4,9,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0]
[5,1,6,2,7,3,9,4,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,0]
[4,1,5,2,7,3,8,6,9]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[2,1,3,4,5,6,8,9,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,3,4,5,6,7,9,8]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,3,1,4,5,6,8,9,7]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,3,2,4,5,6,8,9,7]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[2,3,1,4,5,6,7,9,8]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,2,4,5,6,7,9,8]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[6,7,1,2,3,4,8,9,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]
[7,8,6,5,4,3,2,9,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[9,7,6,5,4,3,1,2,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,4,3,5,6,7,8,9,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,5,6,7,8,9,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[5,6,7,8,9,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[6,7,8,9,2,1,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[7,8,9,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,2,1,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,6,4,3,2,1,9,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[7,5,4,3,2,1,8,6,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]
[8,6,4,2,1,9,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[7,5,3,2,1,8,6,4,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]
[7,4,3,2,1,8,5,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]
[6,4,3,2,1,7,5,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]
[7,5,3,1,8,6,4,2,9]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]
[7,4,2,1,8,5,3,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]
[6,4,2,1,7,5,3,8,9]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]
[6,3,2,1,7,4,8,5,9]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0]
[5,3,2,1,6,4,7,8,9]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]
[7,4,1,8,5,2,9,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]
[6,3,1,7,4,2,8,5,9]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,1,0]
[5,3,1,6,4,2,7,8,9]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]
[6,2,1,7,3,8,4,9,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]
[5,2,1,6,3,7,4,8,9]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]
[4,2,1,5,3,6,7,8,9]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]
[4,1,5,2,6,3,7,8,9]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,1,0]
[3,1,4,2,5,6,7,8,9]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,7,2,3,4,5,6,8,9]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,2,3,4,5,6,8,7,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,3,4,5,7,6,8,9]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[9,2,3,4,5,6,7,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,2,3,4,5,6,9,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[8,2,3,9,5,6,7,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[8,2,9,4,5,6,7,1,3]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,9,3,4,5,6,7,1,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[4,2,3,1,9,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,9,8,6,7,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,4,5,6,7,8,9]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,2,3,5,6,7,8,9]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[8,2,3,4,5,6,7,9,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[7,2,3,4,5,6,9,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[6,2,3,4,5,9,7,8,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]
[5,2,3,4,9,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[4,2,3,9,5,6,7,8,1]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,9,4,5,6,7,8,1]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,9,3,4,5,6,7,8,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,2,3,4,5,1,8,9,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]
[5,2,3,4,1,7,9,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0]
[4,2,3,1,6,9,7,8,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]
[3,2,1,5,9,6,7,8,4]=>[1,1,1,0,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,4,9,5,6,7,8,3]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,9,4,5,6,7,8,2]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,6,4,7,8,1,9]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,3,4,6,7,5,8,9,2]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[2,3,6,5,7,4,8,1,9]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[2,3,5,6,7,1,8,4,9]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,3,4,7,6,8,5,9,2]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,3,4,6,7,8,2,9,5]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[2,3,4,5,6,1,8,7,9]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[2,3,4,5,1,7,6,8,9]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[2,3,4,1,6,5,7,8,9]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[2,3,1,5,4,6,7,8,9]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,8,6,4,2,9,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[8,6,4,2,1,7,5,3,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7,5,3,1,6,4,2,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,9,7,5,3,2,8,6,4]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,6,4,2,7,5,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,5,1,2,4,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[8,6,5,4,3,2,1,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[9,4,3,2,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,7,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,9,2,3,4,5,6,8,7]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,1,2,3,4,6,5,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,9,2,3,4,5,7,6,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,2,9]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[2,1,4,5,6,7,9,3,8]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[2,1,4,5,6,7,8,3,9]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,6,9,8,7,5,4,3,2]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,4,9,8,7,6,5,3,2]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,9,8,7,6,5,4,2]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,7,1,9,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[6,7,9,1,8,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[5,6,9,8,1,7,4,3,2]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[5,4,9,8,7,1,6,3,2]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[3,4,9,8,7,6,1,5,2]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,9,8,7,6,5,1,4]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,7,6,9,8,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,6,9,5,8,7,4,3,2]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[8,7,6,1,9,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[5,1,9,8,4,7,6,3,2]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[6,7,9,5,1,8,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[1,4,9,8,7,3,6,5,2]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,6,9,8,4,1,7,3,2]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[1,3,9,8,7,6,2,5,4]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,9,8,7,3,1,6,2]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[3,4,9,8,7,6,2,1,5]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[9,3,4,2,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,9,8,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,3,4,6,7,9,8,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,3,4,6,8,9,7,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,3,4,6,9,8,7,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,3,5,6,7,9,8,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,2,3,5,6,8,9,7,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,3,5,6,9,8,7,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,2,3,5,7,9,8,6,4]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,3,5,9,8,7,6,4]=>[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,4,5,7,8,9,6,3]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,2,4,5,7,9,8,6,3]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,2,4,5,9,8,7,6,3]=>[1,0,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,2,4,6,9,8,7,5,3]=>[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,2,4,9,8,7,6,5,3]=>[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,3,5,7,9,8,6,4,2]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,3,5,9,8,7,6,4,2]=>[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,5,1,2,3,7,8,9,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[4,1,3,2,5,6,7,8,9]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[6,1,2,4,5,3,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[5,4,1,2,3,6,7,8,9]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[8,1,2,3,5,6,7,4,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[4,1,6,3,5,2,7,8,9]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0]
[8,1,7,3,2,6,4,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[5,7,1,6,2,4,3,8,9]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]
[7,3,4,6,1,2,5,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[6,1,2,9,4,5,7,8,3]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]
[4,1,6,3,8,5,7,2,9]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,0]
[6,8,5,1,7,2,3,4,9]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
[8,3,4,5,7,1,2,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[5,7,1,9,2,8,4,6,3]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]
[7,9,4,6,1,8,2,3,5]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[3,4,1,6,2,5,8,7,9]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[3,4,1,2,6,5,8,7,9]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[3,5,1,6,2,4,8,7,9]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[2,5,1,6,3,4,8,7,9]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[3,5,1,2,6,4,8,7,9]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[2,5,1,3,6,4,8,7,9]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[8,6,4,2,1,3,5,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,6,2,1,4,3,5,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,4,2,1,6,3,5,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[6,4,2,1,8,3,5,7,9]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,0]
[8,6,4,2,9,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[9,6,4,2,7,1,3,5,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,4,2,5,1,3,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,5,2,3,1,4,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,5,3,1,2,4,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,2,1,4,3,6,5,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[4,2,1,6,3,5,8,7,9]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]
[6,4,2,1,8,3,5,9,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]
[6,4,2,7,1,3,5,8,9]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]
[8,9,4,2,5,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[9,6,7,2,3,1,4,5,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,4,5,1,2,3,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,9,3,4,5,6,8,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,8,4,5,9,6,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,2,3,4,9,5,6,8,7]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,4,5,9,6,8,7]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[7,1,2,3,4,8,5,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]
[6,9,1,2,3,4,8,5,7]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[5,1,9,2,3,4,8,6,7]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,2,3,5,8,6,9,7]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0]
[3,1,2,4,9,5,8,6,7]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,4,5,9,6,8,7]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,7,2,3,4,5,9,8,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,6,2,3,4,5,9,8,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[6,1,2,3,7,4,8,9,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]
[1,2,3,8,5,4,6,9,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[5,9,1,2,6,3,4,8,7]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,5,6,9,8,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[4,1,9,5,2,3,6,8,7]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,4,5,6,9,8,7]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[3,4,1,2,5,6,8,9,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[2,3,1,4,9,5,6,8,7]=>[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[8,1,2,3,4,6,9,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[8,1,2,4,6,9,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[6,1,2,3,4,5,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[5,1,2,3,4,8,6,9,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0]
[4,1,2,3,9,6,8,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,1,2,8,4,6,9,5,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[2,1,9,4,6,8,3,5,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,8,2,4,6,9,3,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,3,5,6,7,8,9,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]
[6,7,8,5,4,3,2,1,9]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]
[6,5,7,8,4,3,2,1,9]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]
[6,5,4,7,8,3,2,1,9]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0]
[6,5,4,3,7,8,2,1,9]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]
[6,5,4,3,2,7,8,1,9]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,1,0]
[7,8,9,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[6,7,8,9,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,5,7,8,9,3,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]
[6,5,4,7,8,9,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]
[6,5,4,3,7,8,9,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0]
[6,5,4,3,2,7,8,9,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[8,7,6,5,3,2,1,4,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7,6,4,3,2,1,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7,5,4,3,2,1,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7,6,5,4,1,2,3,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7,6,5,2,3,1,4,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7,6,3,4,2,1,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7,4,5,3,2,1,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,5,6,4,3,2,1,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[6,7,5,4,3,2,1,8,9]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]
[6,8,7,9,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]
[5,8,7,6,9,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]
[4,8,7,6,5,9,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]
[3,8,7,6,5,4,9,2,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,8,7,6,5,4,3,9,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,9,2,4,5,6,7,8,3]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,1,3,4,5,6,7,8,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,8,3,4,5,6,9,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,2,3,4,5,1,9,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[8,1,9,4,5,6,7,3,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[7,9,3,4,5,6,1,8,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,2,8,4,5,6,9,3,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[7,8,3,4,5,2,9,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]
[8,2,3,4,1,6,9,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[8,1,3,9,5,6,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[7,8,9,4,5,6,3,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[6,9,3,4,5,1,7,8,2]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[4,1,5,6,7,8,9,2,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]
[2,3,6,7,1,8,9,4,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[9,8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,9,8,7,6,5,4,1]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[9,1,3,2,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,5,2,4,7,6,9,8,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[2,4,3,6,5,8,7,1,9]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[3,5,1,2,4,7,6,9,8]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[3,4,5,6,7,8,2,9,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[8,7,6,4,5,3,2,9,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[2,9,8,7,5,6,4,3,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,6,9,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,7,5,9,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[8,7,6,4,9,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[8,7,6,5,3,9,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[8,7,6,5,4,2,9,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[5,6,4,7,3,8,2,9,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]
[5,6,4,7,3,9,2,8,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,0]
[5,4,6,3,7,2,8,1,9]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[1,8,3,4,5,6,7,9,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,2,3,4,5,6,1,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[2,1,9,4,5,6,7,8,3]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,8,3,4,5,6,7,1,9]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,9,1,8,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,8,1,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,1,2,3,4,5,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[5,1,2,3,4,6,7,8,9]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[4,1,2,3,5,6,7,8,9]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[9,8,2,3,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,9,2,3,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[9,8,7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,6,7,8,9,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,8,9,3,4,5,6,7,2]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,4,5,6,1,8,9,2,7]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[3,4,5,6,8,1,9,2,7]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[3,4,5,6,8,9,1,2,7]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[2,4,5,1,6,7,8,9,3]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[2,3,4,1,6,7,8,9,5]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[3,4,5,6,1,2,9,7,8]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[3,4,5,6,8,1,2,7,9]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[3,4,5,1,6,7,8,2,9]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[5,6,1,7,8,9,2,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]
[1,3,5,2,6,7,8,9,4]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[2,1,4,3,6,7,8,9,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[2,3,1,5,6,7,8,9,4]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[9,7,8,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,5,7,8,9]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,3,5,4,6,7,8,9]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,8,2,3,4,5,9,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,3,4,5,6,8,9,2,7]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[4,5,2,3,6,7,8,9,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[4,3,2,5,6,7,8,9,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,6,7,2,3,4,8,9,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,0]
[5,3,6,2,4,7,8,9,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]
[5,4,3,2,6,7,8,9,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[6,3,7,8,2,4,5,9,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,0]
[6,7,4,5,2,3,8,9,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]
[6,4,3,7,2,5,8,9,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0]
[7,8,4,5,9,2,3,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]
[7,4,3,8,9,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]
[7,5,8,3,6,2,4,9,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]
[7,5,4,3,8,2,6,9,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]
[7,6,5,4,3,2,8,9,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[8,6,4,9,3,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[8,6,5,4,3,9,2,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[2,4,1,5,3,6,7,8,9]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[4,5,6,7,8,3,9,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[8,9,2,3,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[5,6,7,4,8,9,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]
[7,8,9,2,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[6,5,7,8,9,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]
[7,1,2,3,4,5,8,6,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]
[6,1,2,3,4,7,5,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]
[5,1,2,3,6,4,7,8,9]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]
[4,1,2,5,3,6,7,8,9]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]
[8,1,2,3,4,5,9,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[8,1,2,3,4,9,6,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[9,1,2,3,8,5,6,7,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,2,3,4,6,7,8,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,8,9,6,7]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,3,4,7,9,5,8,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,3,6,9,4,7,8,5]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,5,9,3,6,7,8,4]=>[1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,4,9,2,5,6,7,8,3]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,9,1,4,5,6,7,8,2]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,3,6,5,8,7,9]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,3,4,2,6,5,8,7,9]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[2,3,1,4,6,5,8,7,9]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[4,6,1,2,3,5,8,7,9]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0]
[3,4,5,1,6,2,8,7,9]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[3,1,2,4,6,5,8,7,9]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[2,1,3,4,5,6,9,7,8]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,3,4,5,7,8,6,9]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[7,1,9,3,4,5,6,2,8]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[7,2,1,9,4,5,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]
[6,9,7,3,4,5,1,2,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,2,9,5,6,7,4]=>[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[8,7,9,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[7,2,3,1,9,5,6,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[6,1,2,7,4,5,9,3,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,0]
[5,9,6,3,4,1,7,2,8]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,4,2,9,6,7,5]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[9,7,2,3,8,5,6,1,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,7,8,9,4,5,6]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,6,7,9,3,4,8,5]=>[1,0,1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,2,3,8,9,6,7,4,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,2,3,6,9,4,8,7,5]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[5,6,7,9,1,2,3,8,4]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]
[1,5,8,9,2,6,7,3,4]=>[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[1,5,6,9,2,3,8,7,4]=>[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,2,7,9,5,8,3,6,4]=>[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,2,5,9,3,8,7,6,4]=>[1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,7,9,1,5,8,2,6,3]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]
[4,5,9,1,2,8,7,6,3]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,8,9,6,7,4,5,2,3]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,6,9,4,8,2,7,5,3]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,4,9,2,8,7,6,5,3]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,9,3,8,1,7,6,4,2]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[3,9,1,8,7,6,5,4,2]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,8,9,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]
[5,4,6,7,8,9,1,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]
[1,4,3,2,5,6,7,8,9]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[6,1,2,3,5,4,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[2,3,4,5,6,9,8,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,5,8,7,9,6,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[2,3,6,5,7,8,9,4,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[3,4,5,6,7,1,2,8,9]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[2,3,5,1,4,7,6,9,8]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,4,1,5,2,7,6,9,8]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[4,1,2,5,3,7,6,9,8]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]
[4,2,6,8,1,3,5,7,9]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0]
[4,6,2,8,1,3,5,7,9]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0]
[4,6,8,2,1,3,5,7,9]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]
[4,6,8,2,9,1,3,5,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,6,2,7,9,1,3,5,8]=>[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,2,5,7,9,1,3,6,8]=>[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]
[2,3,5,7,9,1,4,6,8]=>[1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[6,4,2,8,1,3,5,7,9]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]
[8,4,6,2,1,3,5,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[4,6,8,9,2,1,3,5,7]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,6,2,7,1,3,5,8,9]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,0]
[4,8,2,5,9,1,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,0]
[6,2,3,7,9,1,4,5,8]=>[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]
[1,4,5,7,9,2,3,6,8]=>[1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[8,6,4,9,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[7,8,5,9,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]
[8,6,4,2,9,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[7,8,5,3,9,6,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]
[7,4,8,5,9,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]
[6,7,8,4,9,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[7,8,5,3,1,9,6,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]
[7,4,8,5,2,9,6,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]
[6,7,8,4,2,9,5,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]
[6,7,3,8,4,9,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]
[5,6,7,8,3,9,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]
[6,7,3,8,4,1,9,5,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]
[5,6,7,8,3,1,9,4,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]
[6,2,7,3,8,4,9,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]
[5,6,7,2,8,3,9,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0]
[4,5,6,7,8,2,9,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[5,6,1,7,2,8,3,9,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]
[4,5,6,7,1,8,2,9,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]
[2,1,4,3,6,5,9,7,8]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[2,1,4,3,7,5,9,6,8]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[2,1,5,3,7,4,9,6,8]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,3,4,5,9,6,7,8,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,9,5,6,7,8,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,9,4,5,6,7,8,1]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,9,7,6,8,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,9,6,5,7,8,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,9,5,4,6,7,8,1]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,9,4,3,5,6,7,8,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,9,7,8,6,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,9,6,2,3,4,5,8,7]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,8,7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,5,6,7,8,9,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,4,2,1,5,6,7,8,9]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,2,5,6,7,8,9]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[4,5,2,1,3,6,7,8,9]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]
[3,4,2,5,1,6,7,8,9]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[5,3,1,2,4,6,7,8,9]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[4,3,5,1,2,6,7,8,9]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0]
[5,4,3,1,2,6,7,8,9]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[6,5,4,3,1,2,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[8,5,4,3,9,1,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[6,2,3,4,5,1,9,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[2,3,4,5,9,7,1,8,6]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,9,6,7,1,8,5]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,9,5,6,1,7,8,4]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,9,5,1,7,4,8,6]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,3,4,5,6,8,7,9]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,4,5,6,8,7,9,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[8,6,5,4,3,2,7,9,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,9,5,4,3,2,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[7,6,5,4,3,8,9,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]
[9,6,5,4,3,2,7,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,2,3,4,5,6,1,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,5,6,7,8,9,2,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[2,1,3,5,6,7,8,9,4]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[3,4,5,6,7,9,1,2,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[3,4,5,7,8,9,1,2,6]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[3,5,6,7,8,9,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,4,5,6,9,1,2,7,8]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,5,6,1,2,7,8,9]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,2,4,3,5,7,8,9,6]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[3,1,2,4,5,6,7,9,8]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[9,8,7,6,5,1,3,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,1,4,5,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,1,5,6,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,1,6,7,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,7,8,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,2,9,8]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[3,4,5,6,7,1,9,2,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[3,2,4,1,6,5,8,7,9]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[4,2,5,1,6,3,8,7,9]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]
[4,2,6,1,7,3,8,5,9]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[4,2,6,1,8,3,9,5,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[4,2,6,1,7,3,5,9,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0]
[4,2,5,1,3,7,6,9,8]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]
[3,2,5,4,6,1,8,7,9]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[4,2,5,1,7,6,8,3,9]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[4,2,6,1,7,3,9,8,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0]
[4,2,6,1,7,3,5,8,9]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,1,0]
[4,2,5,1,3,8,9,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0]
[3,2,1,6,7,4,5,9,8]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,4,5,2,3,7,6,9,8]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[7,6,5,4,3,1,2,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[7,6,5,4,2,1,3,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[7,6,5,4,1,3,2,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[9,8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,8,6,7,9,5,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,3,8,5,6,7,9,1,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,8,4,5,6,7,9,3,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[8,3,4,5,6,7,9,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[2,3,4,5,7,9,1,8,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[2,3,4,6,7,1,9,5,8]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[2,3,5,6,1,7,9,4,8]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[2,4,5,1,6,7,9,8,3]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[3,4,1,5,6,7,9,2,8]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[3,2,4,5,6,7,9,1,8]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[2,3,4,7,6,9,8,5,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[2,3,4,6,9,1,7,8,5]=>[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,5,4,6,8,7,9,1,3]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[2,3,5,7,1,6,9,4,8]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[4,3,5,8,6,7,9,2,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0]
[2,4,6,1,5,7,9,3,8]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[2,4,8,5,6,7,9,1,3]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[3,5,1,4,6,7,9,8,2]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[4,2,3,5,6,7,9,1,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]
[1,4,2,6,3,7,5,9,8]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[1,3,2,6,4,7,5,9,8]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[2,1,6,3,7,4,8,5,9]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[7,9,6,8,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[7,9,5,8,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[7,9,5,8,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[7,9,5,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[7,9,5,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[7,9,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[6,9,5,8,4,7,2,3,1]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[7,9,4,8,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[7,9,5,8,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[7,9,5,8,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[7,9,5,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[7,9,8,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[9,7,5,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,3,2,7,1,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]
[5,4,3,2,6,1,7,8,9]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]
[4,3,2,5,1,6,7,8,9]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]
[3,2,4,1,5,6,7,8,9]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,3,5,2,7,4,6,9,8]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,3,5,2,7,4,9,6,8]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,2,4,3,6,5,8,7,9]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,3,5,7,2,4,6,9,8]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,3,5,7,2,9,4,6,8]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[5,6,2,1,3,7,4,8,9]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]
[3,2,5,1,6,4,7,8,9]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[6,7,2,1,8,3,4,9,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0]
[3,6,4,1,7,2,8,5,9]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[3,6,7,2,1,4,8,5,9]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[4,2,6,1,7,5,3,8,9]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,1,0]
[4,3,2,6,1,7,5,8,9]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,0]
[4,7,2,5,1,8,3,9,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0,0]
[4,3,7,8,2,1,5,9,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0]
[3,5,2,7,1,8,6,4,9]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[5,4,3,2,7,1,8,6,9]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,0]
[6,4,2,8,1,9,7,5,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0]
[4,3,6,2,8,1,9,7,5]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[6,5,4,3,2,8,1,9,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]
[9,7,5,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,6,3,8,5,2,7,4,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,5,2,9,6,3,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[9,5,1,6,2,7,3,8,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,5,1,8,4,7,3,6,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,4,7,3,6,2,9,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[7,3,8,4,6,2,9,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]
[9,4,7,2,5,8,3,6,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,4,6,1,8,3,5,7,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,3,5,7,2,9,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[7,2,8,3,9,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]
[8,3,7,2,9,4,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[5,8,3,7,2,9,4,6,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]
[4,5,6,9,3,8,2,7,1]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]
[4,5,6,8,2,9,3,7,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]
[9,3,6,5,4,7,1,8,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,2,9,3,6,5,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[6,5,4,8,2,9,3,7,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0]
[5,6,4,8,2,9,3,7,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0]
[9,2,7,4,5,6,3,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,4,5,6,3,9,2,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]
[5,7,4,6,3,9,2,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0]
[4,2,5,6,7,8,9,1,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,6,5,7,4,8,3,9,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,4,6,3,8,2,7,1,9]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0]
[3,4,5,6,7,8,2,1,9]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[4,5,6,7,8,1,2,3,9]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]
[4,3,1,2,6,5,8,7,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[6,5,3,1,2,4,8,7,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]
[8,7,5,3,1,2,4,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[7,5,3,1,2,4,6,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[5,3,1,2,4,7,6,9,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[4,1,2,6,5,3,8,7,9]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]
[6,3,1,2,4,8,7,5,9]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]
[8,5,3,1,2,4,6,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[7,5,3,1,2,4,6,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[5,3,1,2,4,9,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[3,1,2,7,5,4,6,9,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,5,3,2,4,7,6,9,8]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,9,8,7,6,5,1,4,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,6,5,4,3,2,9,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,4,5,6,7,8,9,3,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[9,8,7,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,8,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,5,6,7,8,9,1,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[4,2,5,6,7,8,9,3,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,3,4,5,6,7,2,8,9]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[2,5,6,7,8,9,1,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[2,1,6,7,8,9,3,4,5]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[4,1,2,3,6,5,8,7,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[4,1,6,2,3,5,8,7,9]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]
[2,3,1,9,8,7,6,5,4]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,6,1,7,2,9,8]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[1,4,5,9,6,7,2,8,3]=>[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,5,9,6,1,7,3,8]=>[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,5,7,6,1,9,2,8]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,6,9,7,1,8,2,4]=>[1,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,4,8,5,6,2,7,9,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[2,5,9,6,7,3,1,4,8]=>[1,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[4,1,5,2,7,6,3,9,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,1,0,0]
[3,4,1,6,9,5,7,2,8]=>[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[6,7,9,8,1,3,4,2,5]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[9,1,5,2,8,6,3,7,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,7,4,5,2,6,8,9,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[9,2,3,4,5,6,1,8,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,2,3,4,5,1,7,8,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,2,3,4,1,6,7,8,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,2,3,1,5,6,7,8,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,2,1,4,5,6,7,8,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,2,3,4,1,9,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[4,2,3,1,9,5,7,8,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,9,4,6,7,8,5]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,9,3,5,6,7,8,4]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,8,9,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[5,8,9,1,2,3,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[2,3,4,5,1,7,6,9,8]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[2,3,4,1,6,5,8,7,9]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[2,3,4,5,1,8,6,9,7]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[2,3,4,1,7,5,8,6,9]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[3,4,5,6,7,9,1,8,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[3,4,5,6,7,9,2,8,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[3,4,5,6,7,1,9,8,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[5,3,4,2,1,9,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[6,5,3,4,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[7,6,4,5,3,2,1,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[2,4,1,5,3,6,8,7,9]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[2,4,1,7,3,8,5,6,9]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[8,5,9,3,6,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[9,7,1,5,8,3,6,2,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,5,4,1,3,8,2,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,6,5,4,3,2,1,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,5,4,3,2,1,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,2,3,4,5,8,7,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,2,3,4,8,6,7,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,2,8,4,5,6,7,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,8,3,4,5,6,7,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,2,3,4,7,8,6,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,2,3,6,8,5,7,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,2,5,8,4,6,7,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,4,8,3,5,6,7,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,8,2,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,9,2,1,4,5,6,7,8]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,8,9,1,7,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,6,7,8,9,1,5,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[3,5,6,7,8,9,1,4,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,8,9,1,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[5,4,2,3,6,7,8,9,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[6,5,4,2,3,7,8,9,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[7,6,5,4,2,3,8,9,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[4,6,7,8,9,1,2,3,5]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]
[5,7,8,9,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]
[7,5,1,3,2,6,4,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[9,6,1,3,4,2,7,8,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,3,6,1,4,2,7,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[9,8,1,7,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,4,7,1,5,2,8,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,5,4,6,3,2,9,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,7,4,6,5,3,2,9,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[2,3,4,5,6,1,9,8,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[2,3,4,5,1,9,8,7,6]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[8,9,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,6,7,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7,9,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[9,7,8,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,5,4,3,6,9,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[8,7,6,9,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[8,7,9,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[3,2,1,5,6,7,8,9,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[3,2,6,1,4,7,8,9,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[4,3,2,1,6,7,8,9,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]
[3,2,7,8,1,4,5,9,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[4,7,2,5,1,3,8,9,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,3,2,7,1,5,8,9,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,0]
[5,4,3,2,1,7,8,9,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]
[4,3,2,8,9,1,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]
[8,5,6,3,4,1,2,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[5,3,8,2,6,1,4,9,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0]
[5,4,3,2,8,1,6,9,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0]
[6,5,4,3,2,1,8,9,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]
[6,9,4,7,2,5,1,3,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[6,4,3,9,2,7,1,5,8]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]
[6,5,4,3,2,9,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]
[7,6,9,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[2,3,4,9,6,7,8,5,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,9,5,6,7,8,4,1]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,9,4,5,6,7,8,3,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,3,4,5,6,7,8,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,1,9,7,8,6,5]=>[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,3,1,9,6,7,8,5,4]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,9,5,6,7,8,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,9,4,5,6,7,8,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,4,7,3,9,1,8,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,0]
[5,6,4,9,1,8,2,7,3]=>[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]
[5,9,1,8,2,7,3,6,4]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[9,1,8,2,7,3,6,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,4,9,1,8,2,7,3,6]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[5,4,6,3,9,1,8,2,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0]
[5,4,6,3,7,2,9,1,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,0]
[5,6,4,8,2,9,1,7,3]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0]
[5,7,3,9,1,8,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]
[6,4,9,1,8,2,7,3,5]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[4,5,9,1,8,2,7,3,6]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]
[6,4,5,3,9,1,8,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]
[5,4,7,3,6,2,9,1,8]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[9,8,3,4,5,6,7,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,2,3,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,4,5,6,7,8,2,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,4,5,6,7,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,2,9,8,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[9,8,2,3,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,5,6,7,8,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,3,9,4,5,6,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[9,3,4,5,6,2,1,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,6,2,7,3,8,4,9,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[3,4,5,2,1,6,7,8,9]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[3,4,5,8,9,1,2,6,7]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[3,4,7,8,9,1,2,5,6]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[3,6,7,8,9,1,2,4,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[3,4,5,6,1,7,2,8,9]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[3,4,5,1,6,2,7,8,9]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[3,4,1,5,9,2,6,7,8]=>[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[1,3,7,8,9,2,4,5,6]=>[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[2,6,7,8,9,1,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[4,3,5,2,6,1,7,8,9]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,1,0]
[4,5,3,6,2,7,1,8,9]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]
[1,3,5,7,2,8,4,9,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,3,5,6,2,7,4,9,8]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,3,4,5,2,7,6,9,8]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[3,5,7,1,2,4,6,9,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[3,5,7,8,1,9,2,4,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[3,5,6,7,1,8,2,9,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[7,1,2,3,4,9,6,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]
[7,1,2,3,4,8,6,9,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]
[8,1,2,3,9,5,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[7,1,2,3,9,5,6,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[7,1,2,3,8,5,6,9,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]
[6,1,2,3,8,5,9,7,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0]
[6,1,2,3,7,5,8,9,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]
[6,1,2,8,4,5,9,7,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]
[6,1,2,7,4,5,8,9,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0]
[5,1,2,7,4,9,6,8,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]
[5,1,2,7,4,8,6,9,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0]
[5,1,2,6,4,7,8,9,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]
[4,1,6,3,8,5,9,7,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[4,1,6,3,7,5,8,9,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,0]
[4,1,5,3,6,7,8,9,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,9,8,7,6,4,3,2,5]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,7,5,4,3,2,6]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,6,5,4,3,2,7]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,7,6,5,4,3,2,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,7,6,5,2,3,4]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,7,6,3,4,2,5]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,7,4,5,3,2,6]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,5,6,4,3,2,7]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,6,7,5,4,3,2,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,7,8,6,5,4,3,2,9]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[8,9,2,3,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[7,8,9,2,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[6,7,8,9,2,3,4,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[5,6,7,8,9,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[7,8,9,2,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[6,7,8,9,2,3,1,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[4,5,6,7,8,1,9,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[7,9,3,4,5,6,2,1,8]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[3,9,2,1,5,6,7,8,4]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,1,4,5,6,7,2,9]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,9,3,4,5,2,7,1,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[3,9,2,4,1,6,7,8,5]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,8,9,1,5,6,7,4,2]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,7,1,4,5,6,2,8,9]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[2,8,7,6,5,4,3,1,9]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,1,4,9,8,7,6,5,3]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,9,8,7,6,1,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,9,8,7,6,5,2,1,3]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,9,8,7,6,2,1,4,3]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[6,9,8,7,2,1,5,4,3]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[7,9,8,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[8,9,2,1,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[7,8,1,9,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]
[6,7,8,1,9,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[5,6,7,8,1,9,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]
[9,1,2,3,4,5,7,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,3,4,5,9,6,7,8]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[7,2,6,5,4,3,1,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[3,2,1,9,5,8,7,6,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,5,4,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[4,3,2,1,9,7,8,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[9,1,2,3,4,8,6,5,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,2,3,8,5,6,4,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,2,9,4,5,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[9,1,8,3,4,5,6,2,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,2,3,4,9,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]
[6,1,2,3,8,4,5,9,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]
[5,1,2,8,3,4,6,9,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0]
[4,1,9,2,3,5,6,8,7]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,8,1,2,4,5,6,9,7]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,2,1,3,4,5,6,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[9,1,2,3,8,5,4,7,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,1,2,3,9,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]
[5,1,2,8,3,6,4,9,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0]
[9,8,2,1,4,5,6,7,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,1,8,2,5,3,6,9,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0]
[3,9,1,4,2,5,6,8,7]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,2,3,1,4,5,6,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[1,3,4,5,2,6,7,8,9]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[2,3,4,5,1,6,7,9,8]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[2,1,4,5,3,6,7,8,9]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,3,2,5,4,6,7,8,9]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,4,5,9,8,6,7,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,9,7,5,8,6,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,9,6,4,7,8,5,1]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,9,5,3,6,7,8,4,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,4,2,5,6,7,8,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,1,6,2,8,3,5,7,9]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,0]
[4,1,6,2,8,3,9,5,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[4,1,6,2,7,3,8,5,9]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[8,7,9,1,4,5,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[7,6,9,1,4,5,2,8,3]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[3,9,2,4,5,6,7,8,1]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,5,2,4,6,7,8,9]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[4,1,2,3,5,6,8,7,9]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,2,4,7,3,5,6,8,9]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[5,1,2,3,4,7,6,8,9]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]
[5,6,4,3,2,1,7,8,9]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]
[4,5,3,2,1,6,7,8,9]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]
[6,7,4,3,2,1,5,8,9]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]
[5,6,4,3,2,7,1,8,9]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]
[7,5,4,3,1,2,6,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[6,5,4,3,7,1,2,8,9]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]
[7,6,4,3,5,2,1,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[7,6,3,5,4,2,1,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[9,8,6,1,2,3,4,5,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,4,1,2,3,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,3,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,8,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,2,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,4,6,5,7,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,3,6,5,4,7,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,7,6,5,4,8,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,2,7,6,5,4,3,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,2,1,3,6,5,8,7,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[6,2,1,4,3,5,8,7,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]
[9,2,3,4,1,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,4,5,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,5,4,6,7,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,4,5,3,7,6,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,3,5,7,6,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,5,4,6,3,7,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,4,3,6,7,5,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,3,2,1,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,8,9,1,3,4,5,6,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[6,1,2,9,3,4,5,7,8]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]
[4,1,2,3,5,9,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]
[3,1,2,4,5,6,9,7,8]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,3,4,2,5,6,7,8,9]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,5,6,3,7,8,9]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,2,3,5,6,7,8,4,9]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,5,3,6,7,4,8,9]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,3,5,6,4,2,7,8,9]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[3,5,2,1,6,4,7,8,9]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[2,1,3,6,4,7,8,9,5]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,3,4,6,7,2,8,5,9]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[3,2,6,1,4,7,8,5,9]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[2,4,6,1,7,5,3,8,9]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[4,6,3,2,1,7,5,8,9]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]
[2,4,1,7,5,8,3,9,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[4,3,7,2,1,5,8,9,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0,0]
[1,3,5,7,8,6,4,2,9]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[3,5,7,2,1,8,6,4,9]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[5,7,4,3,2,1,8,6,9]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0]
[2,4,6,8,1,9,7,5,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[4,6,8,3,2,1,9,7,5]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,8,5,4,3,2,1,9,7]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]
[4,5,6,3,7,2,8,1,9]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0]
[1,5,6,7,4,8,3,9,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[3,5,6,7,8,9,2,4,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[2,4,6,7,8,9,1,3,5]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[2,5,6,7,8,9,3,1,4]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[5,4,6,3,8,1,7,2,9]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0]
[1,6,5,7,4,9,2,8,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[5,4,8,1,7,2,6,3,9]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0]
[5,4,8,1,6,3,7,2,9]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0]
[1,6,5,9,2,8,3,7,4]=>[1,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,6,5,9,2,7,4,8,3]=>[1,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,5,6,7,8,1,9,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[4,5,6,7,1,2,8,3,9]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0]
[1,3,6,7,8,9,2,4,5]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[3,5,6,7,8,1,2,9,4]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[2,3,4,5,7,6,8,9,1]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[2,3,4,5,8,7,6,9,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,2,3,4,7,9,5,6,8]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,3,4,6,7,9,5,8]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,3,4,8,5,6,9,7]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,2,3,4,7,8,5,9,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[8,7,9,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,9,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[2,3,4,5,8,6,7,9,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,4,5,9,6,8,7,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[9,3,4,5,2,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,8,2,3,4,5,1,6,9]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,8,9,3,4,5,6,2,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,1,3,4,5,8,6,7,9]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[9,2,3,4,5,1,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,2,3,4,5,6,9,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[6,2,3,4,5,9,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]
[5,2,3,4,9,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[4,2,3,9,1,5,6,7,8]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,2,9,1,4,5,6,7,8]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,6,7,8,1,3,9,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[2,1,9,8,7,6,5,3,4]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,9,8,7,6,4,3,5]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,9,8,7,6,3,5,4]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,7,8,9,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]
[5,3,4,6,7,8,9,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]
[9,5,4,3,2,1,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,7,4,8,5,9,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,2,3,4,7,5,9,8,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,2,6,3,7,4,9,8,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,2,3,8,6,4,9,7,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,2,3,6,4,9,8,7,5]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[5,1,6,2,7,3,9,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,0]
[1,5,2,8,6,3,9,7,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[1,5,2,6,3,9,8,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[1,2,7,5,3,9,8,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,2,5,3,9,8,7,6,4]=>[1,0,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[4,1,7,5,2,9,8,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0]
[4,1,5,2,9,8,7,6,3]=>[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]
[1,6,4,2,9,8,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,4,2,9,8,7,6,5,3]=>[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,5,3,1,9,8,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[5,3,1,9,8,7,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]
[1,3,2,5,4,7,9,6,8]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,3,2,5,7,4,9,6,8]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,2,5,7,9,4,6,8]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,5,7,2,4,9,6,8]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,1,2,7,4,9,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,2,5,3,7,4,9,6,8]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,1,4,2,7,5,9,6,8]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[2,1,5,3,6,4,9,7,8]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[2,1,4,3,7,5,8,6,9]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[2,3,4,5,8,7,6,1,9]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,3,4,5,6,9,8,7,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,2,3,4,5,8,9,7,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,3,4,8,9,6,7,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,3,8,9,5,6,7,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,2,8,9,4,5,6,7,3]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[9,4,2,3,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,2,5,6,7,9,8,3]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[2,1,4,5,6,9,7,3,8]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[3,1,5,2,9,6,7,8,4]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[4,5,1,6,8,7,9,2,3]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0]
[2,3,1,5,9,6,7,4,8]=>[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,4,5,7,9,6,3,8]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[3,4,6,5,7,1,2,9,8]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[3,1,9,4,2,6,7,8,5]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,5,3,9,6,8,7,4]=>[1,0,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[4,5,1,7,6,8,2,9,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,8,7,6,5,3,2,1,9]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,8,7,4,6,3,2,1,9]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]
[8,4,7,6,5,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[6,9,8,5,7,4,1,3,2]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[9,8,7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,8,3,4,5,6,9,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,9,5,2,3,8,4,6,7]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,8,2,9,4,3,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,3,2,4,9,8,5,6,7]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,4,5,9,8,6,7]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[9,1,7,2,3,4,5,8,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,8,5,2,3,4,6,9,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[9,8,1,2,3,5,6,4,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,2,3,9,5,6,8,7]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[4,9,8,1,2,5,3,6,7]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,3,2,4,5,9,6,8,7]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,8,3,9,4,2,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,3,1,4,9,8,5,6,7]=>[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[8,7,6,5,4,1,9,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[8,7,6,5,2,9,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[8,7,6,3,9,2,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[8,7,4,9,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[8,5,9,4,3,2,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[6,9,5,4,3,2,1,7,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[8,7,6,5,2,1,4,3,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7,6,3,2,5,1,4,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7,6,5,1,9,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[8,7,4,3,6,2,1,9,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,7,6,2,9,5,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[8,5,4,7,3,2,1,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7,3,9,6,2,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[6,5,8,4,3,2,1,7,9]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]
[8,4,9,7,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[5,9,8,4,3,2,1,6,7]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,5,6,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,6,5,7,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[9,8,7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,5,6,7,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[6,7,5,8,4,3,2,1,9]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]
[8,9,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[7,6,5,3,2,1,4,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[9,8,7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,6,5,4,2,3,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[2,9,8,6,5,7,4,3,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,6,7,4,5,2,3,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,6,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,6,4,5,1,7,8,9]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[2,3,4,8,5,6,7,1,9]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[3,5,4,7,2,6,1,8,9]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[2,6,4,1,5,3,7,8,9]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[4,5,2,6,3,1,7,8,9]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,1,0]
[3,6,4,5,9,2,7,8,1]=>[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[2,5,4,7,8,6,3,1,9]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[4,6,2,5,8,3,7,1,9]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]
[3,5,7,6,1,4,2,8,9]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[5,6,2,3,7,4,1,8,9]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0]
[5,7,2,3,6,9,4,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0]
[2,8,4,1,6,3,7,5,9]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[4,6,7,8,3,1,5,2,9]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]
[6,7,2,3,4,8,5,1,9]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,1,0]
[3,5,9,7,1,8,2,6,4]=>[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[5,7,8,3,9,4,1,6,2]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]
[7,8,2,3,4,5,9,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]
[5,1,2,4,3,6,7,8,9]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[7,1,2,3,4,6,5,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[9,7,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,4,6,2,5,8,7,9]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,3,2,5,7,4,6,9,8]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,9,8,5,6,7,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,5,4,6,7,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,5,4,6,7,8,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,5,6,9,8]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[9,8,7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,6,1,7,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,1,8,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,7,4,5,6,8,9,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,2,3,4,7,8,5,6,9]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,3,4,6,5,8,7,9]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,2,3,4,8,9,5,6,7]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,7,8,9,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[9,7,5,3,8,6,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,6,9,7,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[8,6,3,2,1,4,9,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[8,6,4,9,7,5,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[9,7,5,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,6,7,8,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,5,6,9,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[8,6,3,2,1,9,7,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[9,7,8,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,6,3,4,9,7,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[8,6,9,7,3,2,1,4,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[9,7,5,2,3,8,6,4,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,6,2,1,3,4,9,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[8,6,4,9,7,5,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[2,5,1,6,3,7,4,8,9]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[2,6,1,7,3,8,4,9,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[3,4,6,1,7,2,8,5,9]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[3,2,6,1,7,4,8,5,9]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[4,2,5,6,1,7,3,8,9]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0]
[3,4,2,6,1,7,5,8,9]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[4,2,5,7,1,8,3,9,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0]
[3,4,2,7,1,8,5,9,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[5,3,6,4,7,1,8,2,9]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[3,5,2,6,7,1,8,4,9]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[4,3,5,2,7,1,8,6,9]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[4,6,2,7,5,8,1,9,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,3,6,2,7,8,1,9,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0]
[4,5,3,6,2,8,1,9,7]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[7,6,5,9,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]
[7,6,5,4,3,9,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]
[7,9,8,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[7,6,9,8,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[7,6,5,9,8,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]
[7,6,5,4,9,8,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[7,6,5,4,3,9,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]
[9,8,7,6,5,2,3,4,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,1,5,6,8,9,4,7]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[5,6,7,8,9,1,3,4,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[6,7,8,9,1,3,4,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,1,4,5,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,1,4,5,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,1,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[7,8,9,1,4,5,6,2,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,1,4,5,6,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,1,5,6,3,4,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,1,5,6,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,1,5,6,7,3,4,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,1,5,6,7,4,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,1,6,7,4,5,2,3]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,1,6,7,4,5,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,1,6,7,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[9,1,7,8,5,6,3,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,7,8,5,6,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,7,9,6,8,1]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[2,3,4,6,9,5,7,8,1]=>[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[2,3,5,9,4,6,7,8,1]=>[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,9,3,5,6,7,8,1]=>[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,9,8,7,6,4,3,1,2]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,8,7,6,3,2,1,9]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0]
[6,5,9,8,7,4,3,1,2]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[9,5,8,7,6,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,1,8,9,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[2,3,4,5,1,7,8,9,6]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[2,9,3,4,5,6,1,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,8,3,4,5,1,6,9,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,7,3,4,1,5,8,9,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[2,6,3,1,4,7,8,9,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[4,2,5,3,7,6,9,8,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]
[4,2,6,3,7,5,9,8,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0]
[4,2,6,3,8,5,9,7,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[4,2,6,3,8,5,1,7,9]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,0]
[4,2,6,3,8,5,7,1,9]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,0]
[4,2,6,3,5,8,7,1,9]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0,1,0]
[4,2,3,6,5,8,7,1,9]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,0]
[5,2,6,3,7,4,9,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,0]
[4,2,7,3,8,5,9,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,0]
[4,2,6,3,9,5,1,7,8]=>[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]
[4,2,6,3,8,5,7,9,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]
[4,2,6,3,5,8,1,7,9]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0,1,0]
[4,2,3,6,8,5,7,1,9]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0]
[2,4,6,3,5,8,7,1,9]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[3,4,5,6,9,2,1,8,7]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,5,8,2,9,1,7,6]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[3,4,7,2,8,9,1,5,6]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,6,2,7,8,9,1,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[5,2,6,7,8,9,1,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]
[3,4,5,6,9,1,7,8,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,5,8,9,6,1,7,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[3,4,7,8,5,9,1,2,6]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[3,4,5,9,2,6,1,8,7]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,6,7,4,8,9,1,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[3,4,8,2,5,9,1,7,6]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[5,6,3,7,8,9,1,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]
[3,7,2,4,8,9,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[6,2,3,7,8,9,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]
[8,9,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,7,9,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[9,7,8,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,2,4,5,6,9,7,8]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[2,3,1,4,5,6,9,7,8]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[4,3,9,5,6,7,8,2,1]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,8,5,6,7,1,9,4]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[7,8,4,5,6,1,3,9,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[3,4,1,9,6,7,8,2,5]=>[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,8,9,5,6,7,2,1,3]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,2,3,8,6,7,1,9,5]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]
[6,8,4,5,1,3,7,9,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]
[3,5,1,4,9,7,8,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[8,3,4,9,6,7,2,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[4,7,9,5,6,2,1,8,3]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]
[5,6,7,8,9,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[6,7,8,9,3,4,1,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,3,4,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[7,8,9,3,4,5,1,2,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,3,4,5,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,4,5,2,3,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,4,5,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,4,5,6,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,4,5,6,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,5,6,3,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,5,6,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[8,9,5,6,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[9,6,7,4,5,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,2,6,1,3,5,8,7,9]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]
[4,2,6,1,8,3,5,7,9]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,0]
[4,2,8,1,3,6,5,7,9]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,1,0]
[4,2,6,1,9,3,5,8,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]
[9,7,1,8,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,6,1,7,2,8,3,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,6,1,9,7,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[9,8,6,1,7,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,5,1,9,6,2,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[9,8,5,1,6,2,7,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,5,1,8,6,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,5,1,6,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,4,1,8,5,2,6,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,4,1,5,2,6,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,6,4,1,9,7,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[9,8,6,4,1,7,5,2,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,4,1,5,2,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,2,8,4,3,5,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,9,3,2,4,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[9,8,2,1,3,5,6,4,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,9,2,4,5,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[1,4,3,6,5,8,7,9,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[1,4,2,6,5,8,7,9,3]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[1,5,2,6,4,8,7,9,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[1,5,2,7,4,8,6,9,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[1,5,2,7,4,9,6,8,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[1,5,2,7,4,6,9,8,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[1,5,2,4,7,6,9,8,3]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,2,5,4,7,6,9,8,3]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,5,2,6,3,8,7,9,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[1,6,2,7,4,8,5,9,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[1,5,2,8,4,9,6,7,3]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[1,5,2,7,4,6,8,9,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[1,5,2,4,7,9,6,8,3]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[1,2,5,7,4,6,9,8,3]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[3,4,5,6,8,9,7,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,5,7,8,9,6,1,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[3,5,6,7,8,9,4,1,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,8,9,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,4,5,8,1,9,7,6,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[3,4,7,1,8,9,6,5,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,6,1,7,8,9,4,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[5,1,6,7,8,9,4,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]
[1,5,6,7,8,9,3,2,4]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,4,5,8,9,6,7,1,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[3,4,7,8,5,9,6,1,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[3,4,5,9,1,6,7,8,2]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,8,1,5,9,7,6,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[5,6,3,7,8,9,4,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]
[3,7,1,4,8,9,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,2,6,7,8,9,3,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]
[6,1,3,7,8,9,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]
[1,2,6,7,8,9,4,3,5]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[9,3,4,5,6,8,7,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,4,3,5,6,7,8,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,3,4,5,7,6,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,4,3,5,6,7,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,4,5,6,2,8,7,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,2,4,5,6,8,7,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,4,3,5,6,7,2,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,2,5,6,7,8,4,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,6,3,5,7,2,8,1,9]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]
[5,6,3,4,7,2,8,1,9]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]
[1,5,7,4,6,8,3,9,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[1,6,7,4,5,8,3,9,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[1,2,3,4,8,5,9,6,7]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,2,3,7,4,5,8,6,9]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,2,3,4,8,6,5,7,9]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,3,4,9,7,5,6,8]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[9,7,6,5,4,3,8,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,4,3,2,1,9,7,8,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,4,3,6,5,8,7,10,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,4,1,2,6,5,8,7,10,9]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,3,2,1,6,5,8,7,10,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[6,3,2,5,4,1,8,7,10,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,3,2,5,4,7,6,1,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,3,2,5,4,7,6,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,5,6,1,2,3,8,7,10,9]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0]
[3,5,1,6,2,4,8,7,10,9]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,5,6,3,4,8,7,10,9]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,6,5,4,3,8,7,10,9]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[6,5,4,3,2,1,8,7,10,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,5,4,3,2,7,6,1,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,5,4,3,2,7,6,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,8,5,4,7,6,3,10,9]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,7,4,3,6,5,2,1,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,7,4,3,6,5,2,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,5,4,7,6,9,8,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,9,4,3,6,5,8,7,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,9,5,6,3,4,10,1,2,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]
[5,6,7,8,1,2,3,4,10,9]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,1,0,0]
[4,6,7,1,8,2,3,5,10,9]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0]
[3,6,1,7,8,2,4,5,10,9]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]
[2,1,6,7,8,3,4,5,10,9]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[2,1,5,7,3,8,4,6,10,9]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[3,5,1,7,2,8,4,6,10,9]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0]
[4,5,7,1,2,8,3,6,10,9]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]
[3,4,1,2,7,8,5,6,10,9]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[2,1,4,3,7,8,5,6,10,9]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[2,1,4,3,8,7,6,5,10,9]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[4,3,2,1,8,7,6,5,10,9]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[8,3,2,7,6,5,4,1,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,3,2,7,6,5,4,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,8,7,6,5,4,3,10,9]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,7,6,5,4,3,2,1,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[9,7,6,5,4,3,2,10,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[10,7,6,5,4,3,2,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,7,6,5,4,9,8,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,9,6,5,4,3,8,7,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,10,7,6,9,8,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,1,10,7,6,9,8,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[10,3,2,9,6,5,8,7,4,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,9,6,5,8,7,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,9,8,5,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,9,10,1,7,8,5,6,2,3]=>[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[10,8,9,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,7,8,9,10,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[3,7,1,8,9,10,2,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]
[4,7,8,1,9,10,2,3,5,6]=>[1,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]
[5,7,8,9,1,10,2,3,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[6,7,8,9,10,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[5,6,8,9,1,2,10,3,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0,0,0]
[4,6,8,1,9,2,10,3,5,7]=>[1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0]
[3,6,1,8,9,2,10,4,5,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]
[2,1,6,8,9,3,10,4,5,7]=>[1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[2,1,5,8,3,9,10,4,6,7]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,5,1,8,2,9,10,4,6,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0]
[4,5,8,1,2,9,10,3,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]
[7,3,2,8,9,10,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0]
[3,4,1,2,8,9,10,5,6,7]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,4,3,8,9,10,5,6,7]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,4,3,7,9,5,10,6,8]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[3,4,1,2,7,9,5,10,6,8]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[4,5,7,1,2,9,3,10,6,8]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[3,5,1,7,2,9,4,10,6,8]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[2,1,5,7,3,9,4,10,6,8]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[2,1,6,7,9,3,4,10,5,8]=>[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[3,6,1,7,9,2,4,10,5,8]=>[1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]
[4,6,7,1,9,2,3,10,5,8]=>[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]
[5,6,7,9,1,2,3,10,4,8]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0,0]
[8,5,4,3,2,9,10,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0,0]
[2,1,5,6,3,4,9,10,7,8]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[3,5,1,6,2,4,9,10,7,8]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0]
[4,5,6,1,2,3,9,10,7,8]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]
[3,4,1,2,6,5,9,10,7,8]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,4,3,6,5,9,10,7,8]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,4,3,6,5,10,9,8,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[4,3,2,1,6,5,10,9,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[6,3,2,5,4,1,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,3,2,5,4,9,8,7,6,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,6,5,4,3,10,9,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[6,5,4,3,2,1,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,5,4,3,2,9,8,7,6,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,5,4,9,8,7,6,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,9,4,3,8,7,6,5,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,10,5,9,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[9,7,5,10,3,8,2,6,1,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[5,6,7,10,1,2,3,9,8,4]=>[1,1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,10,9,8,7,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,1,10,9,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[10,3,2,9,8,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,5,10,1,2,9,8,7,6,3]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,10,9,8,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,10,1,9,8,7,6,5,4,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,10,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,2,1,6,5,8,7,10,9]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,5,2,6,4,1,8,7,10,9]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]
[3,5,2,7,4,8,6,1,10,9]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0]
[3,5,2,7,4,9,6,10,8,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[2,1,5,6,4,3,8,7,10,9]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[4,5,6,3,2,1,8,7,10,9]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0]
[4,5,7,3,2,8,6,1,10,9]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]
[4,5,7,3,2,9,6,10,8,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[2,1,5,7,4,8,6,3,10,9]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[4,6,7,3,8,5,2,1,10,9]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0]
[4,6,7,3,9,5,2,10,8,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]
[2,1,5,7,4,9,6,10,8,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[4,6,8,3,9,5,10,7,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0]
[2,1,4,3,7,8,6,5,10,9]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[3,4,2,1,7,8,6,5,10,9]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[3,6,2,7,8,5,4,1,10,9]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]
[3,6,2,7,9,5,4,10,8,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]
[2,1,6,7,8,5,4,3,10,9]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[5,6,7,8,4,3,2,1,10,9]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,1,0,0]
[5,6,7,9,4,3,2,10,8,1]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0,0]
[2,1,6,7,9,5,4,10,8,3]=>[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[5,6,8,9,4,3,10,7,2,1]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0,0,0]
[2,1,4,3,7,9,6,10,8,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[3,4,2,1,7,9,6,10,8,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[3,6,2,8,9,5,10,7,4,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]
[2,1,6,8,9,5,10,7,4,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[5,7,8,9,4,10,6,3,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[6,7,8,9,10,4,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,1,4,5,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,1,4,5,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,4,5,2,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,3,4,5,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,3,4,5,1,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,1,3,4,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,3,4,1,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,3,4,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,2,3,4,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,2,3,4,5,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[2,1,4,3,6,5,9,10,8,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[3,4,2,1,6,5,9,10,8,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[3,5,2,6,4,1,9,10,8,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0]
[3,5,2,8,4,9,10,7,6,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0]
[2,1,5,6,4,3,9,10,8,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[4,5,6,3,2,1,9,10,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]
[4,5,8,3,2,9,10,7,6,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]
[2,1,5,8,4,9,10,7,6,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[4,7,8,3,9,10,6,5,2,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]
[2,1,4,3,8,9,10,7,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,4,2,1,8,9,10,7,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,7,2,8,9,10,6,5,4,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]
[2,1,7,8,9,10,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[6,7,8,9,10,1,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,10,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,5,6,7,8,9,1,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[2,3,4,5,6,7,8,10,1,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[2,3,4,5,6,7,9,10,1,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[2,3,4,5,6,8,9,10,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[2,3,4,5,7,8,9,10,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[2,3,4,6,7,8,9,10,1,5]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[2,3,5,6,7,8,9,10,1,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[2,4,5,6,7,8,9,10,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[3,4,5,6,7,8,9,10,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[10,8,9,5,6,7,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,9,4,5,6,1,2,3,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,8,5,6,9,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,8,4,5,9,1,2,3,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,6,7,4,5,8,1,2,3,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,8,3,4,9,1,2,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,6,7,3,4,8,1,2,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,8,10,5,6,7,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,8,10,4,5,6,1,2,3,7]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,5,6,8,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,4,5,8,1,2,3,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,6,10,4,5,7,1,2,3,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,3,4,8,1,2,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,6,10,3,4,7,1,2,5,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,7,9,5,6,10,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,7,9,4,5,10,1,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,6,9,4,5,10,1,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[7,6,8,4,5,9,1,2,3,10]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]
[8,7,9,3,4,10,1,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,6,9,3,4,10,1,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[7,6,8,3,4,9,1,2,5,10]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]
[9,6,10,5,7,8,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,6,10,4,7,8,1,2,3,5]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,5,10,4,6,7,1,2,3,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,6,10,3,7,8,1,2,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,5,10,3,6,7,1,2,4,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,6,9,5,7,10,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,6,9,4,7,10,1,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,5,9,4,6,10,1,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[7,5,8,4,6,9,1,2,3,10]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]
[8,6,9,3,7,10,1,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,5,9,3,6,10,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[7,5,8,3,6,9,1,2,4,10]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]
[8,4,9,3,5,10,1,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[7,4,8,3,5,9,1,2,6,10]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]
[9,6,10,2,7,8,1,3,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,5,10,2,6,7,1,3,4,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,6,9,2,7,10,1,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,5,9,2,6,10,1,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[7,5,8,2,6,9,1,3,4,10]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]
[8,4,9,2,5,10,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[7,4,8,2,5,9,1,3,6,10]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]
[1,2,3,4,5,6,7,8,10,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,3,4,5,6,7,8,9,10]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[9,1,2,3,4,5,6,7,10,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[2,10,1,3,4,5,6,7,8,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,9,10]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,3,4,5,6,7,9,10,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,3,4,5,6,8,9,10,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,3,4,5,7,8,9,10,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,4,6,7,8,9,10,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,3,5,6,7,8,9,10,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,2,4,5,6,7,8,9,10,3]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,3,4,5,6,7,8,9,10,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[9,10,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,8,10,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,8,7,10,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[9,8,7,6,10,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[9,8,7,6,5,10,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[9,8,7,6,5,4,10,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[9,8,7,6,5,4,3,10,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[9,8,7,6,5,4,3,2,10,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[9,8,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[10,1,2,3,4,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,4,5,6,9,7,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,4,5,9,6,7,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,2,3,4,10,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[10,1,2,3,9,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,9,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,10,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[10,9,1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,6,9,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]
[7,1,2,3,4,5,10,9,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]
[6,1,2,3,4,10,9,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[5,1,2,3,9,10,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]
[4,1,2,10,9,3,5,6,7,8]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,10,9,2,4,5,6,7,8]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,9,10,1,3,4,5,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,10,9,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,5,6,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,10,9,8,6,7,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10,2,1,3,4,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,4,5,6,7,8,9,10,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,4,6,8,10,1,3,5,7,9]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[2,4,6,9,10,1,3,5,7,8]=>[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[2,4,7,8,10,1,3,5,6,9]=>[1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[2,4,7,9,10,1,3,5,6,8]=>[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[2,4,8,9,10,1,3,5,6,7]=>[1,1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[2,5,6,8,10,1,3,4,7,9]=>[1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0]
[2,5,6,9,10,1,3,4,7,8]=>[1,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]
[2,5,7,8,10,1,3,4,6,9]=>[1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]
[2,5,7,9,10,1,3,4,6,8]=>[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]
[2,5,8,9,10,1,3,4,6,7]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]
[2,6,7,8,10,1,3,4,5,9]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]
[2,6,7,9,10,1,3,4,5,8]=>[1,1,0,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]
[2,6,8,9,10,1,3,4,5,7]=>[1,1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]
[2,7,8,9,10,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[3,4,6,8,10,1,2,5,7,9]=>[1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[3,4,6,9,10,1,2,5,7,8]=>[1,1,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,4,7,8,10,1,2,5,6,9]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[3,4,7,9,10,1,2,5,6,8]=>[1,1,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[3,4,8,9,10,1,2,5,6,7]=>[1,1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[3,5,6,8,10,1,2,4,7,9]=>[1,1,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0]
[3,5,6,9,10,1,2,4,7,8]=>[1,1,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,5,7,8,10,1,2,4,6,9]=>[1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]
[3,5,7,9,10,1,2,4,6,8]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]
[3,5,8,9,10,1,2,4,6,7]=>[1,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]
[3,6,7,8,10,1,2,4,5,9]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]
[3,6,7,9,10,1,2,4,5,8]=>[1,1,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]
[3,6,8,9,10,1,2,4,5,7]=>[1,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]
[3,7,8,9,10,1,2,4,5,6]=>[1,1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[4,5,6,8,10,1,2,3,7,9]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,5,6,9,10,1,2,3,7,8]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]
[4,5,7,8,10,1,2,3,6,9]=>[1,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]
[4,5,7,9,10,1,2,3,6,8]=>[1,1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]
[4,5,8,9,10,1,2,3,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]
[4,6,7,8,10,1,2,3,5,9]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]
[4,6,7,9,10,1,2,3,5,8]=>[1,1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]
[4,6,8,9,10,1,2,3,5,7]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]
[4,7,8,9,10,1,2,3,5,6]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[5,6,7,8,10,1,2,3,4,9]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]
[5,6,7,9,10,1,2,3,4,8]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]
[5,6,8,9,10,1,2,3,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0]
[5,7,8,9,10,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[3,1,4,5,6,7,8,9,10,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[10,3,4,5,6,7,8,1,2,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,4,5,6,7,8,9,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,10,4,5,6,7,8,1,3,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,3,4,5,6,7,1,10,2,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[3,1,10,5,6,7,8,9,2,4]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,1,4,5,6,7,8,2,10,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[9,10,1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,9,10,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[10,8,9,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,8,9,10,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[10,7,8,9,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,10,7,8,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,7,8,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,6,7,8,9,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,10,6,7,8,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,6,7,8,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,9,6,7,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,6,7,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,10,5,6,7,8,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,5,6,7,8,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,9,10,5,6,7,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[10,9,8,5,6,7,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,10,7,8,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,7,8,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,8,9,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,10,7,8,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,7,8,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,9,6,7,4,5,1,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,6,7,4,5,1,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,4,5,1,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,10,7,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,7,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,9,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[9,1,2,3,4,5,6,7,8,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,10,2,3,4,5,6,7,8,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,4,1,3,6,5,8,7,10,9]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,4,1,6,3,5,8,7,10,9]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[2,4,1,6,3,8,5,7,10,9]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[2,4,1,6,3,8,5,10,7,9]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,4,1,6,3,8,5,9,7,10]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[2,4,1,6,3,7,5,9,8,10]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[2,4,1,5,3,7,6,9,8,10]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[2,3,1,5,4,7,6,9,8,10]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,3,2,5,4,7,6,9,8,10]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[3,4,1,2,5,6,7,8,9,10]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,1,4,5,6,7,8,9,10]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,6,1,2,3,7,8,9,10]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]
[4,2,5,1,3,6,7,8,9,10]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[4,3,2,1,5,6,7,8,9,10]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[5,6,7,8,1,2,3,4,9,10]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0]
[5,2,6,7,1,3,4,8,9,10]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,1,0,1,0]
[5,6,3,4,1,2,7,8,9,10]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[5,3,2,6,1,4,7,8,9,10]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0]
[5,4,3,2,1,6,7,8,9,10]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[6,2,7,8,9,1,3,4,5,10]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,1,0]
[6,7,3,4,8,1,2,5,9,10]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0,1,0]
[6,3,2,7,8,1,4,5,9,10]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0,1,0]
[6,4,7,2,5,1,3,8,9,10]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0,1,0]
[6,4,3,2,7,1,5,8,9,10]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0]
[6,5,4,3,2,1,7,8,9,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[7,8,3,4,9,10,1,2,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[7,8,9,4,5,6,1,2,3,10]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[7,4,3,2,8,9,1,5,6,10]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,1,0]
[7,8,5,6,3,4,1,2,9,10]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]
[7,5,3,8,2,6,1,4,9,10]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,1,0]
[7,5,4,3,2,8,1,6,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0,1,0]
[7,6,5,4,3,2,1,8,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[8,5,9,10,2,6,7,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,5,3,9,2,6,10,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0]
[8,6,9,4,7,2,5,1,3,10]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[8,6,4,3,9,2,7,1,5,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]
[8,6,5,4,3,2,9,1,7,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]
[8,7,6,5,4,3,2,1,9,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[9,7,5,4,3,10,2,8,1,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[2,3,1,4,5,6,7,8,9,10]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,4,1,5,6,7,8,9,10]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,4,5,1,6,7,8,9,10]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[2,3,4,5,6,1,7,8,9,10]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[2,3,4,5,6,7,1,8,9,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[2,3,4,5,6,7,8,1,9,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[3,4,1,5,6,7,8,9,10,2]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,4,5,1,6,7,8,9,10,2]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,4,5,6,1,7,8,9,10,2]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[3,4,5,6,7,1,8,9,10,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[3,4,5,6,7,8,1,9,10,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[3,4,5,6,7,8,9,1,10,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[9,8,7,6,5,4,3,1,10,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[8,10,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[1,8,7,6,5,4,3,10,9,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[1,10,7,6,5,4,3,2,9,8]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,7,6,5,4,3,10,8,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[3,8,7,6,5,4,10,1,9,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]
[8,10,1,6,5,4,3,2,9,7]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[2,10,7,6,5,4,3,9,1,8]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,10,9,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[7,10,9,8,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[6,10,9,8,7,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,9,8,7,6,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,10,9,8,7,6,5,3,2,1]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,10,9,8,7,6,5,4,2,1]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,10,9,8,7,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,10,8,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,3,4,5,6,10,7,8,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,4,5,10,6,7,8,9]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,4,10,5,6,7,8,9]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,10,4,5,6,7,8,9]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,10,3,4,5,6,7,8,9]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[8,7,10,9,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[8,9,10,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[7,6,5,10,9,8,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]
[7,9,6,10,8,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]
[7,8,9,10,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[6,5,4,3,10,9,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[6,9,5,4,10,8,7,3,2,1]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]
[6,5,8,7,10,9,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,0]
[6,8,9,5,10,7,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0,0]
[5,4,3,2,1,10,9,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,9,4,3,2,10,8,7,6,1]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[5,4,8,7,3,10,9,6,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0,0]
[5,8,9,4,3,10,7,6,2,1]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0]
[5,7,4,9,6,10,8,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0,0]
[5,6,7,8,9,10,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[4,3,8,7,2,1,10,9,6,5]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[4,8,9,3,2,1,10,7,6,5]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]
[4,3,2,7,6,5,10,9,8,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,7,3,9,6,2,10,8,5,1]=>[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0]
[4,7,8,9,3,2,10,6,5,1]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]
[4,3,6,5,8,7,10,9,2,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,6,7,8,9,3,10,5,2,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]
[4,5,6,7,8,9,10,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,6,2,1,9,5,4,10,8,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]
[3,2,6,5,8,7,1,10,9,4]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[3,6,8,2,9,5,1,10,7,4]=>[1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0]
[3,6,7,8,9,2,1,10,5,4]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]
[3,5,7,8,2,9,4,10,6,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0,0]
[3,5,6,7,8,9,2,10,4,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[3,4,5,6,7,8,9,10,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[2,4,6,1,8,3,9,5,10,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[2,4,6,7,8,1,9,3,10,5]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[2,4,5,6,7,8,9,1,10,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[7,8,10,9,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]
[9,10,5,6,8,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[5,8,10,6,9,7,3,4,1,2]=>[1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[5,6,7,10,9,8,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[9,10,7,8,3,4,6,5,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[7,8,10,9,3,4,6,5,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]
[9,10,3,6,8,4,7,5,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[3,8,10,6,9,4,7,5,1,2]=>[1,1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[3,6,7,10,9,4,8,5,1,2]=>[1,1,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[9,10,3,4,5,8,7,6,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[3,8,10,4,5,9,7,6,1,2]=>[1,1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[3,4,7,10,5,9,8,6,1,2]=>[1,1,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,4,5,6,10,9,8,7,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[9,10,7,8,5,6,1,2,4,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[7,8,10,9,5,6,1,2,4,3]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]
[9,10,5,6,8,7,1,2,4,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[5,8,10,6,9,7,1,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[5,6,7,10,9,8,1,2,4,3]=>[1,1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[9,10,7,8,1,4,6,2,5,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[7,8,10,9,1,4,6,2,5,3]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]
[9,10,1,6,8,4,7,2,5,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,8,10,6,9,4,7,2,5,3]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,6,7,10,9,4,8,2,5,3]=>[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[9,10,1,4,5,8,7,2,6,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,8,10,4,5,9,7,2,6,3]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,4,7,10,5,9,8,2,6,3]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,4,5,6,10,9,8,2,7,3]=>[1,0,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[9,10,7,8,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[7,8,10,9,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]
[9,10,1,6,8,2,3,7,5,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,8,10,6,9,2,3,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,6,7,10,9,2,3,8,5,4]=>[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[9,10,1,2,5,8,3,7,6,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,8,10,2,5,9,3,7,6,4]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,2,7,10,5,9,3,8,6,4]=>[1,0,1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,2,5,6,10,9,3,8,7,4]=>[1,0,1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[9,10,1,2,3,4,8,7,6,5]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,8,10,2,3,4,9,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,2,7,10,3,4,9,8,6,5]=>[1,0,1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,2,3,6,10,4,9,8,7,5]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,2,3,4,5,10,9,8,7,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[4,3,2,1,7,6,5,9,8,10]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[7,3,2,1,6,5,4,9,8,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]
[4,3,2,1,9,6,5,8,7,10]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[6,3,2,1,9,5,4,8,7,10]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,1,0]
[9,3,2,1,8,5,4,7,6,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[6,5,2,1,9,4,3,8,7,10]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,1,0]
[9,5,2,1,8,4,3,7,6,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[4,3,2,1,7,6,5,10,8,9]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[7,3,2,1,6,5,4,10,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[4,3,2,1,8,6,5,10,7,9]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[6,3,2,1,8,5,4,10,7,9]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,0]
[8,3,2,1,7,5,4,10,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[6,5,2,1,8,4,3,10,7,9]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,0]
[8,5,2,1,7,4,3,10,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[4,3,2,1,10,6,5,9,7,8]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,1,10,5,4,9,7,8]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[7,3,2,1,10,5,4,9,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[10,3,2,1,9,5,4,8,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,2,1,10,4,3,9,7,8]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[7,5,2,1,10,4,3,9,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[10,5,2,1,9,4,3,8,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,3,2,1,8,7,5,10,6,9]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[5,3,2,1,8,7,4,10,6,9]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,0]
[8,3,2,1,7,6,4,10,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[5,4,2,1,8,7,3,10,6,9]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,0]
[8,4,2,1,7,6,3,10,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[4,3,2,1,10,7,5,9,6,8]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,2,1,10,7,4,9,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,3,2,1,10,6,4,9,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[10,3,2,1,9,6,4,8,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,4,2,1,10,7,3,9,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,4,2,1,10,6,3,9,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[10,4,2,1,9,6,3,8,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,6,2,1,10,5,3,9,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[10,6,2,1,9,5,3,8,4,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,4,3,1,8,7,2,10,6,9]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,0]
[8,4,3,1,7,6,2,10,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[5,4,3,1,10,7,2,9,6,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,4,3,1,10,6,2,9,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[10,4,3,1,9,6,2,8,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,6,3,1,10,5,2,9,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[10,6,3,1,9,5,2,8,4,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,3,1,2,6,5,8,7,10,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[10,3,1,5,2,7,4,9,6,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,4,1,6,2,8,3,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,5,1,7,2,3,4,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,2,10,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[7,6,5,4,3,10,2,9,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[7,6,5,4,3,2,9,1,8,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,1,0]
[6,5,4,10,3,9,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,9,2,8,1,7,10]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,1,0]
[6,5,4,3,2,8,10,1,7,9]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0,0]
[6,5,4,3,2,8,1,7,9,10]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0,1,0]
[5,10,4,9,3,8,2,7,1,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,4,9,3,8,2,7,1,6,10]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,4,3,8,2,7,10,1,6,9]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0,0]
[5,4,3,8,2,7,1,6,9,10]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0,1,0]
[5,4,3,2,7,9,1,6,8,10]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0,1,0]
[5,4,3,2,7,1,6,8,9,10]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,1,0,1,0]
[4,8,3,7,2,6,10,1,5,9]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]
[4,8,3,7,2,6,1,5,9,10]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[4,3,7,10,2,6,9,1,5,8]=>[1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[4,3,7,2,6,9,1,5,8,10]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,3,7,2,6,1,5,8,9,10]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[4,3,2,6,8,10,1,5,7,9]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[4,3,2,6,8,1,5,7,9,10]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[4,3,2,6,1,5,7,8,9,10]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[3,6,9,2,5,8,1,4,7,10]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]
[3,6,2,5,8,10,1,4,7,9]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0]
[3,6,2,5,8,1,4,7,9,10]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0]
[3,6,2,5,1,4,7,8,9,10]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[3,2,5,7,9,1,4,6,8,10]=>[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[3,2,5,7,1,4,6,8,9,10]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[3,2,5,1,4,6,7,8,9,10]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[2,4,6,8,1,3,5,7,9,10]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[2,4,6,1,3,5,7,8,9,10]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[2,4,1,3,5,6,7,8,9,10]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[9,8,7,6,5,4,2,1,10,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[9,8,7,6,5,3,2,1,10,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[9,8,7,6,4,3,2,1,10,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[9,8,7,5,4,3,2,1,10,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[9,8,6,5,4,3,2,1,10,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[9,7,6,5,4,3,2,1,10,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[7,8,9,10,4,5,6,2,3,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,4,5,6,10,2,3,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[7,8,9,10,4,5,2,3,6,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,4,5,10,2,3,6,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[7,8,9,4,5,2,3,6,10,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]
[7,8,4,5,9,10,2,3,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[7,8,4,5,9,2,3,6,10,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0,0]
[7,8,9,10,4,5,6,2,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,4,5,6,10,2,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[7,8,9,10,4,5,2,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,4,5,10,2,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[7,8,9,4,5,2,6,10,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]
[7,8,4,5,9,10,2,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[7,8,4,5,9,2,6,10,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,0]
[7,8,9,10,4,5,2,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,4,5,10,2,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[7,8,9,4,5,2,10,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[7,8,9,4,5,2,1,3,6,10]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[7,8,4,5,9,10,2,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[7,8,4,5,9,2,10,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,0]
[7,8,4,5,9,2,1,3,6,10]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,1,0]
[7,8,9,10,4,2,5,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,4,10,2,5,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[7,8,9,4,2,5,6,10,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]
[7,8,4,9,10,2,5,6,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[7,8,4,9,2,5,6,10,1,3]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,0]
[7,8,9,10,4,2,5,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,4,10,2,5,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[7,8,9,4,2,5,10,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[7,8,9,4,2,5,1,3,6,10]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[7,8,4,9,10,2,5,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[7,8,4,9,2,5,10,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,0]
[7,8,4,9,2,5,1,3,6,10]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0]
[7,8,4,2,5,9,10,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0]
[7,8,4,2,5,9,1,3,6,10]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,1,0]
[7,4,8,9,10,2,5,6,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[7,4,8,9,2,5,6,10,1,3]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,0,0]
[7,4,8,9,10,2,5,1,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[7,4,8,9,2,5,10,1,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0]
[7,4,8,9,2,5,1,3,6,10]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]
[7,4,8,2,5,9,10,1,3,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0,0,0]
[8,10,7,9,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[9,10,6,8,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,10,6,9,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[7,10,6,9,5,8,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[9,10,7,8,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,10,7,9,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[9,10,6,8,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,10,6,9,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[7,10,6,9,4,8,3,5,1,2]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[9,10,5,8,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,10,5,9,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[7,10,5,9,4,8,3,6,1,2]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[6,10,5,9,4,8,3,7,1,2]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,10,7,8,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,10,7,9,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[9,10,6,8,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,10,6,9,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[7,10,6,9,5,8,2,4,1,3]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[9,10,7,8,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,10,7,9,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[9,10,6,8,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,10,6,9,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[7,10,6,9,4,8,2,5,1,3]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[9,10,5,8,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,10,5,9,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[7,10,5,9,4,8,2,6,1,3]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[6,10,5,9,4,8,2,7,1,3]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,10,7,8,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,10,7,9,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[9,10,6,8,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,10,6,9,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[7,10,6,9,3,8,2,5,1,4]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[9,10,5,8,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,10,5,9,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[7,10,5,9,3,8,2,6,1,4]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[6,10,5,9,3,8,2,7,1,4]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,10,4,8,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,10,4,9,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[7,10,4,9,3,8,2,6,1,5]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[6,10,4,9,3,8,2,7,1,5]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,9,1,2,10]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,4,5,6,7,8,9,10,2,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[9,10,7,8,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,8,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,5,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,7,10,5,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[10,7,9,5,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,9,5,7,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,9,6,7,3,5,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,9,6,7,4,5,1,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,6,5,4,3,2,1,10,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[7,6,5,4,3,2,1,9,8,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]
[6,5,4,3,2,1,9,8,7,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]
[6,5,4,3,2,1,8,7,9,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0,1,0]
[5,4,3,2,1,9,8,7,6,10]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[5,4,3,2,1,8,7,6,10,9]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[5,4,3,2,1,8,7,6,9,10]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0,1,0]
[5,4,3,2,1,7,6,9,8,10]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[5,4,3,2,1,7,6,8,9,10]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0,1,0]
[4,3,2,1,8,7,6,5,9,10]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[4,3,2,1,7,6,5,10,9,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[4,3,2,1,7,6,5,8,9,10]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[4,3,2,1,6,5,8,7,9,10]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[4,3,2,1,6,5,7,8,9,10]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,1,6,5,4,9,8,7,10]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[3,2,1,6,5,4,8,7,10,9]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,2,1,6,5,4,8,7,9,10]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[3,2,1,6,5,4,7,8,9,10]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[3,2,1,5,4,7,6,9,8,10]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[3,2,1,5,4,7,6,8,9,10]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[3,2,1,5,4,6,7,8,9,10]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,3,6,5,8,7,9,10]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[2,1,4,3,6,5,7,8,9,10]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,4,3,5,6,7,8,9,10]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,4,2,6,5,8,7,10,9]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,5,2,6,4,8,7,10,9]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[3,1,5,2,7,4,8,6,10,9]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[3,1,5,2,7,4,9,6,10,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[3,1,5,2,7,4,9,6,8,10]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[3,1,5,2,7,4,6,9,8,10]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[3,1,5,2,4,7,6,9,8,10]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[3,1,2,5,4,7,6,9,8,10]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[4,5,6,7,8,9,10,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,8,9,10,2,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[5,6,7,8,9,10,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[5,6,7,8,9,10,2,3,4,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[5,6,7,8,9,10,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[5,6,7,8,9,10,3,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[7,8,9,10,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,10,5,6,7,2,3,4,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,7,3,4,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,6,7,4,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[9,10,7,8,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,8,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,8,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,7,5,3,1,10,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,7,5,3,1,10,9,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[9,6,5,3,1,10,8,7,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,6,5,3,1,10,9,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[7,6,5,3,1,10,9,8,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[9,7,4,3,1,10,8,6,5,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,7,4,3,1,10,9,6,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[9,6,4,3,1,10,8,7,5,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,6,4,3,1,10,9,7,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[7,6,4,3,1,10,9,8,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[9,5,4,3,1,10,8,7,6,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,5,4,3,1,10,9,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[7,5,4,3,1,10,9,8,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[6,5,4,3,1,10,9,8,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[9,7,5,2,1,10,8,6,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,7,5,2,1,10,9,6,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[9,6,5,2,1,10,8,7,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,6,5,2,1,10,9,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[7,6,5,2,1,10,9,8,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[9,7,4,2,1,10,8,6,5,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,7,4,2,1,10,9,6,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[9,6,4,2,1,10,8,7,5,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,6,4,2,1,10,9,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[7,6,4,2,1,10,9,8,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[9,5,4,2,1,10,8,7,6,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,5,4,2,1,10,9,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[7,5,4,2,1,10,9,8,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[6,5,4,2,1,10,9,8,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[9,7,3,2,1,10,8,6,5,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,7,3,2,1,10,9,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[9,6,3,2,1,10,8,7,5,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,6,3,2,1,10,9,7,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[7,6,3,2,1,10,9,8,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[9,5,3,2,1,10,8,7,6,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,5,3,2,1,10,9,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[7,5,3,2,1,10,9,8,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[6,5,3,2,1,10,9,8,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[9,4,3,2,1,10,8,7,6,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,4,3,2,1,10,9,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[7,4,3,2,1,10,9,8,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[6,4,3,2,1,10,9,8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[6,1,7,2,8,3,9,4,10,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[6,1,7,2,8,3,9,10,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0]
[6,1,7,2,8,9,3,4,10,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0]
[6,1,7,2,8,9,3,10,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0,0,0]
[6,1,7,2,8,9,10,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0]
[6,1,7,8,2,3,9,4,10,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0]
[6,1,7,8,2,3,9,10,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0]
[6,1,7,8,2,9,3,4,10,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,0]
[6,1,7,8,2,9,3,10,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,0]
[6,1,7,8,2,9,10,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,0]
[6,1,7,8,9,2,3,4,10,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0,0]
[6,1,7,8,9,2,3,10,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,0,0]
[6,1,7,8,9,2,10,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0]
[6,1,7,8,9,10,2,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]
[6,7,1,2,8,3,9,4,10,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]
[6,7,1,2,8,3,9,10,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0]
[6,7,1,2,8,9,3,4,10,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0]
[6,7,1,2,8,9,3,10,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,0,0]
[6,7,1,2,8,9,10,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0]
[6,7,1,8,2,3,9,4,10,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]
[6,7,1,8,2,3,9,10,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0,0]
[6,7,1,8,2,9,3,4,10,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]
[6,7,1,8,2,9,3,10,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]
[6,7,1,8,2,9,10,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0]
[6,7,1,8,9,2,3,4,10,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,1,0,0]
[6,7,1,8,9,2,3,10,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0,0]
[6,7,1,8,9,2,10,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0,0]
[6,7,1,8,9,10,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0]
[6,7,8,1,2,3,9,4,10,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0,0]
[6,7,8,1,2,3,9,10,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,0,0]
[6,7,8,1,2,9,3,4,10,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0]
[6,7,8,1,2,9,3,10,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,0]
[6,7,8,1,2,9,10,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,0]
[6,7,8,1,9,2,3,4,10,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0,0]
[6,7,8,1,9,2,3,10,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0]
[6,7,8,1,9,2,10,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,0]
[6,7,8,1,9,10,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]
[6,7,8,9,1,2,3,4,10,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0]
[6,7,8,9,1,2,3,10,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0]
[6,7,8,9,1,2,10,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]
[6,7,8,9,1,10,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]
[10,9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,3,1,2,4,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,4,1,2,3,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,10,1,2,3,4,6,7,8,9]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10,6,1,2,3,4,5,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,1,2,3,4,5,6,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,10,1,2,3,4,5,6,7,9]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[2,3,10,1,4,5,6,7,8,9]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,1,10,2,5,6,7,8,9]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,1,2,10,3,6,7,8,9]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[5,6,1,2,3,10,4,7,8,9]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[7,6,1,2,3,4,10,5,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]
[8,7,1,2,3,4,5,10,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[8,9,1,2,3,4,5,6,10,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]
[10,9,8,7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,4,8,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,4,7,3,6,1,2,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,2,4,6,1,3,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,4,6,1,2,3,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,5,9,4,8,3,7,1,2,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,5,8,2,4,7,1,3,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,5,8,4,7,1,2,3,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,3,5,7,1,2,4,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,5,7,1,2,3,4,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,10,5,9,2,4,8,1,3,7]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,10,5,9,4,8,1,2,3,7]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10,3,6,9,2,5,8,1,4,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,6,9,3,5,8,1,2,4,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,6,9,5,8,1,2,3,4,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,2,4,6,8,1,3,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,4,6,8,1,2,3,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,6,8,1,2,3,4,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,7,10,3,6,9,1,2,5,8]=>[1,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[7,10,2,4,6,9,1,3,5,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[7,10,4,6,9,1,2,3,5,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[7,10,6,9,1,2,3,4,5,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[10,3,5,7,9,1,2,4,6,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,5,7,9,1,2,3,4,6,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,9,1,2,3,4,5,6,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,6,8,10,1,2,3,5,7,9]=>[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,10,1,2,3,4,5,7,9]=>[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]
[10,7,6,5,4,3,2,1,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,2,10,9,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[10,1,2,3,4,6,5,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,7,6,8,9,10,1]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[9,10,5,6,7,8,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[5,8,9,6,7,10,3,4,1,2]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0]
[9,10,7,8,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,3,6,7,4,5,8,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[3,8,9,6,7,4,5,10,1,2]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]
[3,6,7,8,9,4,5,10,1,2]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]
[9,10,3,4,5,6,7,8,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[3,8,9,4,5,6,7,10,1,2]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]
[3,4,7,8,5,6,9,10,1,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[7,8,9,10,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[5,8,9,6,7,10,1,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0]
[9,10,7,8,1,4,5,2,3,6]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[7,8,9,10,1,4,5,2,3,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[9,10,1,6,7,4,5,2,3,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,8,9,6,7,4,5,2,3,10]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,6,7,8,9,4,5,2,3,10]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]
[9,10,1,4,5,6,7,2,3,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,8,9,4,5,6,7,2,3,10]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,4,7,8,5,6,9,2,3,10]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[1,4,5,6,7,8,9,2,3,10]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[9,10,1,6,7,2,3,4,5,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,8,9,6,7,2,3,4,5,10]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,6,7,8,9,2,3,4,5,10]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]
[9,10,1,2,5,6,3,4,7,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,8,9,2,5,6,3,4,7,10]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,2,7,8,5,6,3,4,9,10]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,2,5,6,7,8,3,4,9,10]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,8,9,2,3,4,5,6,7,10]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,2,7,8,3,4,5,6,9,10]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,2,3,6,7,4,5,8,9,10]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[9,8,7,6,4,5,3,2,1,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,10,9,8,7,5,6,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,9,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[8,7,6,9,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]
[8,7,6,5,10,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]
[8,7,6,5,4,9,3,2,1,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]
[8,7,6,5,4,3,9,2,1,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]
[7,10,9,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[8,6,9,10,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,7,5,9,10,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0]
[8,7,6,4,10,9,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]
[8,7,6,5,3,9,10,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0,0]
[8,7,6,5,4,2,9,10,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,0]
[8,7,6,5,4,3,1,10,9,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[2,3,4,5,6,7,10,1,8,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,10,9,8,7,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,1,10,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,1,2,3,4,5,6,10,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[9,2,1,8,7,6,5,4,3,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[3,2,9,8,7,6,5,4,1,10]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[9,3,1,8,7,6,5,4,10,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[9,2,10,1,7,6,5,4,3,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[4,2,9,8,7,6,5,10,1,3]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[3,10,2,8,7,6,5,4,1,9]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,4,3,1,2,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,10,9,8,7,6,5,4,2,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,10,9,8,7,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,1,10,9,8,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,10,9,8,7,6,5,4]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,10,9,8,7,6,5,4]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,2,10,9,8,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,3,10,9,8,7,6,5]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,4,10,9,8,7,6,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,5,4,3,2,10,9,8,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,5,4,3,10,9,8,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,2,5,4,3,10,9,8,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,3,2,5,4,10,9,8,7,6]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,5,4,10,9,8,7,6]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,2,6,5,4,3,10,9,8,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[3,2,1,6,5,4,10,9,8,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,3,2,6,5,4,10,9,8,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,2,3,6,5,4,10,9,8,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,2,4,3,6,5,10,9,8,7]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,3,4,6,5,10,9,8,7]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,3,4,5,6,10,9,8,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,4,3,2,7,6,5,10,9,8]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,1,4,3,7,6,5,10,9,8]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,4,3,7,6,5,10,9,8]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,3,4,7,6,5,10,9,8]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,3,2,5,4,7,6,10,9,8]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,3,5,4,7,6,10,9,8]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,3,4,5,7,6,10,9,8]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,3,4,5,6,7,10,9,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,4,3,6,5,8,7,10,9]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,3,4,6,5,8,7,10,9]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,3,4,5,6,8,7,10,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[10,9,8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,4,3,2,1,8,7,6,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,4,3,1,7,6,2,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,4,1,6,2,3,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,5,4,3,1,9,8,7,2,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,5,2,1,8,4,3,7,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,5,4,1,8,7,2,3,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,3,1,5,2,7,4,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,2,1,10,9,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[6,5,4,1,10,9,8,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[10,3,2,1,6,5,4,9,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,6,5,1,9,8,2,3,4,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,2,1,4,3,6,5,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,6,1,8,2,3,4,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,3,1,7,6,2,10,9,5,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[7,2,1,10,4,3,6,5,9,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]
[7,4,1,10,6,2,9,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]
[7,6,1,10,9,2,3,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]
[10,5,1,7,2,9,3,4,6,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,1,9,2,3,4,5,6,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,1,6,2,8,3,10,5,7,9]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[6,1,8,2,10,3,4,5,7,9]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,0]
[8,1,10,2,3,4,5,6,7,9]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[10,1,9,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,1,10,9,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[7,1,10,9,8,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[6,1,10,9,8,7,5,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,10,9,8,7,6,4,3,2]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,10,9,8,7,6,5,3,2]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,10,9,8,7,6,5,4,2]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,10,7,8,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,8,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,8,4,2,5,1,3,6]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,8,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,6,5,7,8,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,6,5,7,8,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,6,4,7,3,5,8,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,6,4,7,2,5,1,3,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,6,3,7,2,1,4,5,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,5,4,3,6,7,8,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,5,4,2,6,7,1,3,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,5,3,2,6,1,4,7,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,4,3,2,1,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,7,9,10,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,7,9,10,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,7,9,10,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,7,9,10,4,2,5,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,7,9,10,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,6,9,5,7,10,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,6,9,5,7,10,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,6,9,4,7,3,5,10,1,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]
[8,6,9,3,7,2,1,4,5,10]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[8,5,9,4,3,6,7,10,1,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]
[8,5,9,4,2,6,7,1,3,10]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[8,5,9,3,2,6,1,4,7,10]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[8,4,9,3,2,1,5,6,7,10]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[7,6,5,8,9,10,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0]
[7,6,5,8,9,10,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0]
[7,6,4,8,9,3,5,10,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0,0]
[7,6,4,8,9,2,5,1,3,10]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,0]
[7,6,3,8,9,2,1,4,5,10]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,0]
[7,5,4,8,3,6,9,10,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0,0]
[7,5,4,8,2,6,9,1,3,10]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0]
[7,4,3,8,2,1,5,6,9,10]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,1,0]
[6,5,4,3,7,8,9,10,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0,0]
[6,5,4,2,7,8,9,1,3,10]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,1,0]
[6,5,3,2,7,8,1,4,9,10]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0,1,0]
[1,3,2,7,6,5,10,9,8,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,4,3,6,5,2,10,9,8,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,4,3,7,6,2,10,9,8,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,5,4,7,6,3,10,9,8,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0]
[1,4,3,8,7,2,10,9,6,5]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,5,4,8,7,3,10,9,6,2]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0]
[2,3,1,6,5,4,10,9,8,7]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,3,1,7,6,5,10,9,8,4]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,4,1,6,5,3,10,9,8,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,4,1,7,6,3,10,9,8,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,5,1,7,6,4,10,9,8,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0]
[2,4,1,8,7,3,10,9,6,5]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[2,5,1,8,7,4,10,9,6,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,4,2,6,5,1,10,9,8,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,4,2,7,6,1,10,9,8,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[3,5,2,7,6,1,10,9,8,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0]
[4,5,3,7,6,2,10,9,8,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0]
[3,4,2,8,7,1,10,9,6,5]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[3,5,2,8,7,1,10,9,6,4]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0]
[4,5,3,8,7,2,10,9,6,1]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0]
[2,5,1,6,4,3,10,9,8,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,1,1,0,0,0,0]
[2,5,1,7,4,3,10,9,8,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0]
[2,6,1,7,5,4,10,9,8,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]
[2,5,1,8,4,3,10,9,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0]
[2,6,1,8,5,4,10,9,7,3]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0]
[3,5,2,6,4,1,10,9,8,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,1,0,0,0,0]
[3,5,2,7,4,1,10,9,8,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0]
[3,6,2,7,5,1,10,9,8,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]
[4,6,3,7,5,2,10,9,8,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]
[3,5,2,8,4,1,10,9,7,6]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0]
[3,6,2,8,5,1,10,9,7,4]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0]
[4,6,3,8,5,2,10,9,7,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0]
[3,7,2,8,6,1,10,9,5,4]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0]
[4,7,3,8,6,2,10,9,5,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0]
[2,5,1,9,4,3,10,8,7,6]=>[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0,0]
[2,6,1,9,5,4,10,8,7,3]=>[1,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]
[3,5,2,9,4,1,10,8,7,6]=>[1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0,0]
[3,6,2,9,5,1,10,8,7,4]=>[1,1,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]
[4,6,3,9,5,2,10,8,7,1]=>[1,1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]
[3,7,2,9,6,1,10,8,5,4]=>[1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0]
[10,1,2,3,4,5,6,7,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,10,9,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[3,2,10,9,8,7,6,5,4,1]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,2,1,9,8,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,6,5,7,8,9,10,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[10,1,2,3,5,4,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,7,10,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,5,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,5,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,5,8,3,6,2,4,1]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,5,8,4,6,2,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,6,8,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,8,10,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[1,10,9,8,7,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,9,8,7,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,10,9,8,7,1,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,9,8,2,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,9,2,8,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,10,1,9,8,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,10,9,8,7,6,5,2,1,4]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,10,9,8,7,6,1,2,5,3]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,9,8,7,1,2,6,4,3]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,10,9,8,2,1,7,5,4,3]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,10,9,1,2,8,6,5,4,3]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[8,10,1,2,9,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[9,2,1,10,8,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[10,2,1,4,3,6,5,8,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,4,3,6,5,7,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,4,3,5,7,8,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,4,3,5,7,6,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,4,3,5,6,8,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,3,5,6,4,8,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,3,5,6,4,7,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,3,5,4,7,8,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,3,5,4,7,6,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,3,5,4,6,8,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,3,4,6,7,8,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,3,4,6,7,5,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,3,4,6,5,8,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,3,4,5,7,8,9,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,4,2,6,5,8,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,4,2,6,5,7,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,4,2,5,7,8,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,4,2,5,7,6,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,4,2,5,6,8,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,2,5,6,4,8,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,2,5,6,4,7,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,2,5,4,7,8,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,2,5,4,7,6,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,2,5,4,6,8,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,2,4,6,7,8,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,2,4,6,7,5,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,2,4,6,5,8,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,3,2,4,5,7,8,9,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,4,5,6,3,8,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,4,5,6,3,7,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,4,5,3,7,8,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,4,5,3,7,6,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,4,5,3,6,8,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,4,3,6,7,8,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,4,3,6,7,5,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,4,3,6,5,8,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,4,3,5,7,8,9,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,5,6,7,8,4,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,5,6,7,4,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,5,6,4,8,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,5,4,7,8,9,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,4,6,7,8,9,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,8,9,1,2,3,4,5,10]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]
[1,7,8,9,10,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[5,6,7,8,9,1,2,3,4,10]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]
[1,6,7,8,9,10,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[1,2,4,3,5,6,7,8,9,10]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,6,8,10,9,7,5,3]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[2,4,1,5,6,7,8,9,10,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,5,6,7,9,1,10,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[2,3,5,1,6,7,8,9,10,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,5,6,8,1,9,10,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[2,3,4,6,1,7,8,9,10,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[2,3,4,5,7,1,8,9,10,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[4,1,2,5,6,7,8,9,10,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,1,5,6,7,8,10,2,9]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[2,6,1,5,3,7,8,9,10,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[5,3,4,1,6,7,9,2,10,8]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,0,0]
[2,3,8,1,6,7,4,9,10,5]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,3,4,5,1,8,2,9,10,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0,0]
[2,3,4,10,1,7,8,9,5,6]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[9,2,1,3,4,5,6,7,8,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[8,7,2,4,6,10,1,3,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[2,10,7,9,4,6,8,1,3,5]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,2,4,8,10,1,3,7,9]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0,0]
[2,8,5,7,4,6,10,1,3,9]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]
[10,5,2,4,7,9,6,8,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,2,8,5,7,4,6,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,7,6,5,2,4,10,1,3,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]
[10,7,2,6,5,9,4,8,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,10,5,9,8,7,2,4,1,3]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,10,3,9,2,6,8,1,5,7]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,3,10,7,9,2,6,8,1,5]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6,2,5,4,8,10,1,7,9]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0]
[3,6,10,2,5,9,4,8,1,7]=>[1,1,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[3,5,8,2,4,7,6,10,1,9]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]
[3,5,7,10,2,4,6,9,8,1]=>[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]
[10,9,3,5,8,2,4,7,6,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,7,3,6,2,5,4,10,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[7,6,3,5,10,2,4,9,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[3,6,10,9,8,2,5,7,4,1]=>[1,1,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[10,9,8,7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,4,3,8,2,7,6,10,1,9]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,3,7,10,2,6,9,8,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0,0]
[5,10,4,9,3,8,2,7,6,1]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,8,3,7,6,5,2,10,1,9]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[4,7,3,6,5,10,2,9,8,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]
[4,6,10,3,5,9,8,7,2,1]=>[1,1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[10,9,4,8,3,7,6,5,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,6,5,4,3,10,2,9,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[6,5,4,10,3,9,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[5,10,4,9,8,7,6,3,2,1]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,2,3,4,5,6,7,8,1,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,10,3,4,5,6,7,8,9,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,9,4,5,6,7,8,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,6,7,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,3,4,5,6,7,9,8,1,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,3,4,5,6,7,8,10,9,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,2,3,4,5,6,10,8,9,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,4,5,10,7,8,9,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,4,10,6,7,8,9,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,10,5,6,7,8,9,4]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,10,4,5,6,7,8,9,3]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,2,3,4,5,6,7,8,9,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,8,5,7,10,9]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,2,3,4,7,5,8,6,10,9]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,2,3,5,7,4,6,9,8,10]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,2,3,6,4,7,5,9,8,10]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,9,8,6,7,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,9,8,7,6,5,4,3,2,10]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[2,8,9,10,1,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[8,1,9,2,10,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]
[7,1,8,2,9,3,10,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0]
[5,1,6,2,7,3,8,4,10,9]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,1,5,2,6,3,8,7,10,9]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,3,4,5,6,7,9,10,8]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,3,4,5,6,7,8,10,9]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[7,1,2,3,4,5,8,9,10,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]
[6,1,2,3,4,7,8,9,10,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]
[5,1,2,3,6,7,8,9,10,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[9,7,5,4,3,2,1,10,8,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[8,6,5,4,3,2,1,9,7,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]
[9,7,5,3,2,1,10,8,6,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[8,6,4,3,2,1,9,7,5,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]
[8,5,4,3,2,1,9,6,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]
[7,5,4,3,2,1,8,6,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,1,0]
[8,6,4,2,1,9,7,5,3,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]
[8,5,3,2,1,9,6,4,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0,0]
[7,5,3,2,1,8,6,4,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0,1,0]
[7,4,3,2,1,8,5,9,6,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0,1,0]
[6,4,3,2,1,7,5,8,9,10]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0,1,0]
[8,5,3,1,9,6,4,2,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0,0]
[7,5,3,1,8,6,4,2,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0,1,0]
[8,5,2,1,9,6,3,10,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0,0]
[7,4,2,1,8,5,3,9,6,10]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0,1,0]
[6,4,2,1,7,5,3,8,9,10]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0]
[7,3,2,1,8,4,9,5,10,6]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0]
[6,3,2,1,7,4,8,5,9,10]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,1,0]
[5,3,2,1,6,4,7,8,9,10]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0,1,0]
[7,4,1,8,5,2,9,6,3,10]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0]
[7,3,1,8,4,2,9,5,10,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0]
[6,3,1,7,4,2,8,5,9,10]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,1,0,1,0]
[5,3,1,6,4,2,7,8,9,10]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0]
[6,2,1,7,3,8,4,9,5,10]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]
[5,2,1,6,3,7,4,8,9,10]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0,1,0]
[4,2,1,5,3,6,7,8,9,10]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[5,1,6,2,7,3,8,4,9,10]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0]
[4,1,5,2,6,3,7,8,9,10]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[3,1,4,2,5,6,7,8,9,10]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,9,2,3,4,5,6,7,8,10]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,2,3,4,5,6,7,9,8,10]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[10,3,4,5,6,7,8,9,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,3,4,5,6,7,8,1,10,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[8,3,4,5,6,7,1,9,10,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]
[7,3,4,5,6,1,8,9,10,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]
[6,3,4,5,1,7,8,9,10,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]
[5,3,4,1,6,7,8,9,10,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,1,5,6,7,8,9,10,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[10,9,4,5,6,7,8,1,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,3,8,5,6,7,1,9,2,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,3,4,7,6,1,8,9,2,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,3,4,5,1,7,8,9,2,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,3,4,1,6,10,8,9,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0]
[4,3,1,5,6,7,10,9,2,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[3,1,4,5,6,7,8,10,2,9]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[9,2,3,4,5,6,7,10,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[9,2,10,4,5,6,7,8,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[2,10,4,5,6,7,8,9,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,8,4,5,6,7,1,2,10,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[2,10,9,5,6,7,8,1,3,4]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,8,5,6,7,1,2,10,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[9,7,4,5,6,1,8,2,10,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[2,10,4,9,6,7,8,1,3,5]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,10,8,5,6,7,1,9,3,4]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,2,4,5,6,7,8,9,10]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[9,2,3,4,5,6,7,8,10,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[8,2,3,4,5,6,7,10,9,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[7,2,3,4,5,6,10,8,9,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]
[6,2,3,4,5,10,7,8,9,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[5,2,3,4,10,6,7,8,9,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,2,3,10,5,6,7,8,9,1]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,10,4,5,6,7,8,9,1]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,10,3,4,5,6,7,8,9,1]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,6,7,5,8,9,1,10]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,3,4,5,7,8,6,9,10,2]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[9,7,5,3,1,8,6,4,2,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,10,8,6,4,2,9,7,5,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,2,4,5,6,7,8,9,10]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,5,1,2,4,7,8,9,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[9,7,6,5,4,3,2,1,8,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[10,3,2,4,5,6,7,8,9,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,2,3,4,5,6,8,7,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,10,2,3,4,5,6,7,9,8]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,4,5,6,7,8,10,2,9]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,3,4,5,6,7,8,9,2,10]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,8,10,9,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[1,7,10,9,8,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[1,5,10,9,8,7,6,4,3,2]=>[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,10,9,8,7,6,5,3,2]=>[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,8,1,10,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[7,8,10,1,9,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]
[6,7,10,9,1,8,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]
[6,5,10,9,8,1,7,4,3,2]=>[1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,10,9,8,7,1,6,3,2]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,10,9,8,7,6,1,5,2]=>[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,10,9,8,7,6,5,1,4]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,8,10,9,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,3,4,5,7,8,10,9,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,3,4,5,7,9,10,8,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,3,4,5,7,10,9,8,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,3,4,6,7,8,10,9,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,2,3,4,6,7,9,10,8,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,3,4,6,7,10,9,8,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,2,3,4,6,8,10,9,7,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,3,4,6,10,9,8,7,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,3,5,6,7,9,10,8,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,2,3,5,6,7,10,9,8,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,2,3,5,6,8,9,10,7,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,2,3,5,6,8,10,9,7,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,2,3,5,6,10,9,8,7,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,2,3,5,7,9,10,8,6,4]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,2,3,5,7,10,9,8,6,4]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,2,3,5,10,9,8,7,6,4]=>[1,0,1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,5,7,8,10,9,6,3]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,2,4,5,7,9,10,8,6,3]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,2,4,5,7,10,9,8,6,3]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,2,4,5,10,9,8,7,6,3]=>[1,0,1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,4,6,10,9,8,7,5,3]=>[1,0,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,2,4,10,9,8,7,6,5,3]=>[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,5,7,9,10,8,6,4,2]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[1,3,5,7,10,9,8,6,4,2]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,3,5,10,9,8,7,6,4,2]=>[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,10,9,8,7,6,5,4,2]=>[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,1,8,2,3,4,5,6,10,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[9,7,1,2,3,4,5,6,10,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[2,10,1,9,3,4,5,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,10,8,1,3,4,5,6,7,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,1,3,2,5,6,7,8,9,10]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,2,4,5,3,7,8,9,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[5,4,1,2,3,6,7,8,9,10]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[8,1,2,3,5,6,7,4,9,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[4,1,6,3,5,2,7,8,9,10]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[8,1,7,3,2,6,4,5,9,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[5,7,1,6,2,4,3,8,9,10]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[7,3,4,6,1,2,5,8,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[6,1,2,9,4,5,7,8,3,10]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,1,0]
[4,1,6,3,8,5,7,2,9,10]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[6,8,5,1,7,2,3,4,9,10]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,1,0]
[8,3,4,5,7,1,2,6,9,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[10,1,6,3,9,5,2,8,4,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,7,1,9,2,8,4,6,3,10]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0,1,0]
[7,9,4,6,1,8,2,3,5,10]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]
[9,3,4,5,6,8,1,2,7,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[4,1,6,3,8,5,10,7,9,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[6,8,10,1,7,2,9,3,5,4]=>[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]
[8,10,4,5,7,1,9,2,3,6]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[10,3,4,5,6,7,9,1,2,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,5,7,9,1,2,4,6,8,10]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]
[4,1,2,3,5,6,7,8,9,10]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,2,3,4,6,7,8,9,10]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[8,1,2,3,4,5,6,7,9,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[7,1,2,3,4,5,6,8,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[6,1,2,3,4,5,7,8,9,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[3,4,1,6,2,5,8,7,10,9]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[10,8,6,4,2,1,3,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,6,2,1,4,3,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,4,2,1,6,3,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,6,4,2,1,8,3,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,6,4,2,1,10,3,5,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[8,6,4,2,9,1,3,5,7,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]
[9,6,4,2,7,1,3,5,8,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,7,4,2,5,1,3,6,8,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,7,5,2,3,1,4,6,8,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,7,5,3,1,2,4,6,8,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,2,10,3,4,5,6,7,9,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,9,4,5,6,10,7,8]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,2,3,4,10,5,6,7,9,8]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,4,5,10,6,7,9,8]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,4,5,6,9,10,7,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[8,1,2,3,4,5,9,6,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]
[7,10,1,2,3,4,5,9,6,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[6,1,10,2,3,4,5,9,7,8]=>[1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
[5,1,2,3,4,6,9,7,10,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,1,0,0]
[4,1,2,3,10,5,6,9,7,8]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,2,4,5,10,6,9,7,8]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[9,1,2,3,4,5,7,10,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[9,1,2,3,5,7,10,4,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[9,1,3,5,7,10,2,4,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[7,8,9,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[7,6,8,9,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]
[7,6,5,8,9,4,3,2,1,10]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,0]
[7,6,5,4,8,9,3,2,1,10]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,1,0]
[7,6,5,4,3,8,9,2,1,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0,1,0]
[7,6,5,4,3,2,8,9,1,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,1,0]
[9,8,7,6,5,4,2,1,3,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,8,7,6,5,3,2,1,4,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,8,7,6,4,3,2,1,5,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,8,7,5,4,3,2,1,6,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,8,6,5,4,3,2,1,7,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[10,1,3,4,5,6,7,8,9,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,9,3,4,5,6,7,10,2,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[9,2,3,4,5,6,1,10,8,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[9,1,10,4,5,6,7,8,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,10,3,4,5,6,7,1,9,2]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[10,6,1,2,3,4,9,5,7,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,1,2,3,4,9,5,6,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,10,1,2,3,4,8,5,6,7]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,1,5,2,3,4,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,5,3,4,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,1,2,3,10,4,6,7,8,9]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,6,1,2,3,4,10,9,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]
[9,7,1,2,3,4,8,5,10,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[5,9,1,2,3,4,6,7,10,8]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[10,8,4,9,1,2,3,5,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,10,1,5,3,4,6,7,8,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,5,2,10,4,6,7,8,9]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,10,3,5,6,7,8,9]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[9,10,1,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,1,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,1,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,5,4,7,6,9,8,1,10]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[2,4,3,6,5,8,7,10,9,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,4,2,6,3,8,5,10,7,9]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,2,5,4,7,6,1,10,9,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[3,2,5,4,9,8,7,6,1,10]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,2,5,4,1,8,7,10,9,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[3,2,5,4,1,10,9,8,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,7,6,5,4,9,8,1,10]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[3,2,7,6,5,4,1,10,9,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[3,2,9,6,5,8,7,4,1,10]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,2,1,6,5,8,7,10,9,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,2,1,6,5,10,9,8,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,1,8,7,6,5,10,9,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[3,2,1,10,7,6,9,8,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,7,6,9,8,1,10]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,1,0]
[5,4,3,2,7,6,1,10,9,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0]
[5,4,3,2,9,8,7,6,1,10]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,1,0]
[5,4,3,2,1,8,7,10,9,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,1,0,0,0]
[7,4,3,6,5,2,9,8,1,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,1,0]
[7,4,3,6,5,2,1,10,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[9,4,3,6,5,8,7,2,1,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,4,3,6,5,8,7,10,9,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,4,3,6,5,10,9,8,7,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[9,4,3,8,7,6,5,2,1,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,4,3,8,7,6,5,10,9,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,4,3,10,7,6,9,8,5,2]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,10,9,8,7,6,5,2]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,3,2,9,8,1,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,1,0]
[9,6,5,4,3,8,7,2,1,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,6,5,4,3,8,7,10,9,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[1,6,5,4,3,10,9,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[9,8,5,4,7,6,3,2,1,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,8,5,4,7,6,3,10,9,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[1,10,5,4,7,6,9,8,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,5,4,9,8,7,6,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,7,6,5,4,9,8,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,9,6,5,8,7,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,7,4,8,3,9,2,10,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[6,5,7,4,8,3,10,2,9,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,0,0]
[5,6,4,7,3,8,2,9,1,10]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[8,10,1,2,3,4,5,9,6,7]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[10,8,1,9,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,7,1,2,3,4,5,9,10,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]
[2,10,1,5,6,7,8,9,3,4]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10,9,2,3,4,5,6,7,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,4,3,1,6,5,8,7,10,9]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[7,8,4,9,5,2,10,6,3,1]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,0]
[2,1,4,3,6,5,8,10,9,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,4,3,6,8,7,5,10,9]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[2,1,4,3,8,10,7,9,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,4,3,6,7,10,8,9,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[2,1,4,6,5,3,8,7,10,9]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,4,6,5,3,8,10,9,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[2,1,6,8,5,7,3,4,10,9]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[2,1,8,7,5,10,4,9,3,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,1,6,7,5,10,8,4,9,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[2,1,4,5,8,6,7,3,10,9]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,1,8,5,10,6,7,9,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,1,4,7,10,6,9,8,3,5]=>[1,1,0,0,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,1,4,5,6,10,7,8,9,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,4,3,1,6,5,8,10,9,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[2,4,3,1,6,8,7,5,10,9]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[2,4,3,1,8,10,7,9,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,4,3,1,6,7,10,8,9,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[4,6,3,5,1,2,8,7,10,9]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[4,6,3,5,1,2,8,10,9,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0]
[6,5,3,8,2,7,1,4,10,9]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,1,0,0]
[8,5,3,7,2,10,4,9,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[6,5,3,7,2,10,8,4,9,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0,0,0]
[4,5,3,8,6,2,7,1,10,9]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,1,1,0,0]
[8,6,3,5,10,2,7,9,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]
[4,7,3,6,10,1,9,8,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]
[4,5,3,6,10,7,1,8,9,2]=>[1,1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0,0]
[2,3,6,4,5,1,8,7,10,9]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,3,6,4,5,1,8,10,9,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[6,3,8,4,5,7,1,2,10,9]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,1,0,0]
[8,3,7,4,5,10,2,9,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[6,3,7,4,5,10,8,2,9,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0,0]
[2,5,8,4,7,6,1,3,10,9]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]
[8,5,10,4,7,6,2,9,1,3]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[2,7,10,4,8,6,9,5,1,3]=>[1,1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,10,8,7,3,9,1]=>[1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,3,4,8,5,6,7,1,10,9]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[8,3,4,10,5,6,7,9,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
[2,7,4,10,5,6,9,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[2,3,6,10,5,9,7,8,1,4]=>[1,1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,10,6,7,8,9,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,5,6,1,8,9,10,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[2,3,4,5,6,8,9,1,10,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[4,5,6,1,7,8,9,10,2,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]
[3,5,6,1,7,8,9,10,2,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]
[3,4,6,1,7,8,9,10,2,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[3,4,5,1,7,8,9,10,2,6]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[2,1,4,3,6,5,8,9,10,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,4,3,6,7,8,5,10,9]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,4,3,8,7,9,10,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[2,1,4,3,6,7,8,9,10,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,4,5,6,3,8,7,10,9]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,4,5,6,3,8,9,10,7]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[2,1,6,5,7,8,3,4,10,9]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[2,1,8,5,9,7,3,10,6,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[2,1,6,5,7,8,9,10,3,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[2,1,4,5,6,7,8,3,10,9]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[2,1,8,5,6,7,9,10,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[2,1,4,7,6,8,9,3,10,5]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[2,1,4,5,6,7,8,9,10,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,1,6,5,8,7,10,9]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,3,4,1,6,5,8,9,10,7]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[2,3,4,1,6,7,8,5,10,9]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[2,3,4,1,8,7,9,10,5,6]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[2,3,4,1,6,7,8,9,10,5]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,5,6,1,2,8,7,10,9]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[4,3,5,6,1,2,8,9,10,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[6,3,7,5,1,8,4,2,10,9]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,1,0,0]
[8,3,9,5,1,7,4,10,6,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]
[6,3,7,5,1,8,9,10,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0]
[4,3,5,6,7,8,1,2,10,9]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[8,3,9,5,6,7,1,10,4,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]
[4,3,7,8,6,10,9,2,5,1]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,3,5,6,7,8,9,10,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[2,3,4,5,6,1,8,7,10,9]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[6,3,4,5,7,8,1,2,10,9]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,1,0,0]
[8,3,4,5,9,7,1,10,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0,0]
[6,3,4,5,7,8,9,10,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0,0]
[2,5,4,6,7,1,8,3,10,9]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0]
[8,5,4,6,7,1,9,10,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,0]
[2,7,4,8,6,1,9,5,10,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]
[2,5,4,6,7,8,9,1,10,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]
[2,3,4,5,6,7,8,1,10,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[8,3,4,5,6,7,9,10,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,0]
[2,7,4,5,6,8,9,1,10,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0]
[2,3,6,5,7,8,1,9,10,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[4,5,2,3,6,7,8,9,10,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,2,5,6,7,8,9,10,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,6,7,2,3,4,8,9,10,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,0]
[5,3,6,2,4,7,8,9,10,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[5,4,3,2,6,7,8,9,10,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[6,7,8,9,2,3,4,5,10,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0]
[6,3,7,8,2,4,5,9,10,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,1,0,0]
[6,7,4,5,2,3,8,9,10,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,0]
[6,4,3,7,2,5,8,9,10,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0,0]
[6,5,4,3,2,7,8,9,10,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]
[7,8,9,10,1,3,4,5,6,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,3,8,9,10,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[7,4,3,8,9,2,5,6,10,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0]
[7,5,8,3,6,2,4,9,10,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0,0]
[7,5,4,3,8,2,6,9,10,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,0]
[7,6,5,4,3,2,8,9,10,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]
[8,5,9,3,6,10,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,5,4,3,9,10,2,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,0]
[8,9,6,7,4,5,2,3,10,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]
[8,6,4,9,3,7,2,5,10,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,0]
[8,6,5,4,3,9,2,7,10,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0,0]
[8,7,6,5,4,3,2,9,10,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]
[9,7,5,4,10,3,8,2,6,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[9,7,6,5,4,3,10,2,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[10,1,9,2,8,3,7,4,6,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,2,3,4,5,6,10,8,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[9,1,2,3,4,5,10,7,8,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[10,1,2,3,4,9,6,7,8,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,9,3,4,5,6,7,8,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,4,5,6,8,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,4,2,3,6,5,8,7,10,9]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,4,2,6,5,8,7,10,9]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,3,4,5,6,7,10,8,9]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[10,2,3,4,5,6,7,8,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,10,1,4,5,6,7,8,9,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,1,10,3,4,5,6,7,2,9]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[8,2,1,10,4,5,6,7,3,9]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
[7,10,8,3,4,5,6,1,2,9]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[3,9,1,2,10,5,6,7,8,4]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[1,2,3,4,8,9,10,5,6,7]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,3,4,5,8,10,6,9,7]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,7,8,9,10,3,4,5,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,2,3,7,8,10,4,5,9,6]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,2,3,4,9,10,7,8,5,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,2,3,4,7,10,5,9,8,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,6,7,8,10,2,3,4,9,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]
[1,2,6,9,10,3,7,8,4,5]=>[1,0,1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[1,2,6,7,10,3,4,9,8,5]=>[1,0,1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,2,3,8,10,6,9,4,7,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,6,9,10,1,2,7,8,3,4]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[1,8,9,10,5,6,7,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,5,8,10,2,6,9,3,7,4]=>[1,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,5,6,10,2,3,9,8,7,4]=>[1,0,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,2,9,10,7,8,5,6,3,4]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,2,5,10,3,9,8,7,6,4]=>[1,0,1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[7,8,10,4,5,9,1,2,6,3]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]
[4,7,10,1,5,9,2,8,6,3]=>[1,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[1,6,10,4,9,2,8,7,5,3]=>[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,10,2,9,8,7,6,5,3]=>[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,10,3,9,1,8,7,6,4,2]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,10,9,8,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,5,6,9,8,10,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[10,5,9,4,8,3,7,2,6,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,5,2,4,7,6,9,8,10]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,4,2,5,3,7,6,9,8,10]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[10,3,1,5,6,7,8,9,2,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,4,1,5,6,7,8,9,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,2,6,8,10,1,3,5,7,9]=>[1,1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,2,8,10,1,3,5,7,9]=>[1,1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]
[4,6,8,2,10,1,3,5,7,9]=>[1,1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]
[4,6,8,10,2,1,3,5,7,9]=>[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[4,6,8,2,9,1,3,5,7,10]=>[1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]
[4,6,2,7,9,1,3,5,8,10]=>[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0]
[4,2,5,7,9,1,3,6,8,10]=>[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[2,3,5,7,9,1,4,6,8,10]=>[1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[9,7,10,8,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,5,10,8,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[8,9,6,10,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[9,7,5,3,10,8,6,4,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[8,9,6,4,10,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,5,9,6,10,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]
[7,8,9,5,10,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[8,9,6,4,2,10,7,5,3,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]
[8,5,9,6,3,10,7,4,2,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[7,8,9,5,3,10,6,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[7,8,4,9,5,10,6,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[6,7,8,9,4,10,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]
[8,5,9,6,3,1,10,7,4,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0]
[7,8,9,5,3,1,10,6,4,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[8,5,2,9,6,3,10,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0]
[6,7,8,9,4,2,10,5,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]
[7,3,8,4,9,5,10,6,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0]
[6,7,8,3,9,4,10,5,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,0]
[5,6,7,8,9,3,10,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]
[7,8,4,1,9,5,2,10,6,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,0]
[7,3,8,4,9,5,1,10,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0]
[6,7,8,3,9,4,1,10,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0]
[5,6,7,8,9,3,1,10,4,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]
[6,7,2,8,3,9,4,10,5,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]
[5,6,7,8,2,9,3,10,4,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0,0]
[4,5,6,7,8,9,2,10,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[5,6,7,1,8,2,9,3,10,4]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]
[4,5,6,7,8,1,9,2,10,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]
[2,1,4,3,6,5,8,10,7,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,4,3,6,8,5,10,7,9]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[2,1,4,6,3,8,5,10,7,9]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,3,4,5,6,7,10,8,9,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,5,6,10,7,8,9,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,10,5,6,7,8,9,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,10,4,5,6,7,8,9,1]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,9,8,10,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[2,1,4,3,7,6,8,5,10,9]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[2,1,4,3,7,6,9,8,10,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[2,1,4,3,8,7,9,6,10,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[2,1,5,4,6,3,8,7,10,9]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,5,4,6,3,9,8,10,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[2,1,5,4,7,6,8,3,10,9]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[2,1,5,4,7,6,9,8,10,3]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,1,5,4,8,7,9,6,10,3]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[2,1,6,5,7,4,8,3,10,9]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[2,1,6,5,7,4,9,8,10,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[2,1,6,5,8,7,9,4,10,3]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[2,1,7,6,8,5,9,4,10,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[3,2,4,1,6,5,8,7,10,9]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,2,4,1,6,5,9,8,10,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[3,2,4,1,7,6,8,5,10,9]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[3,2,4,1,7,6,9,8,10,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[3,2,4,1,8,7,9,6,10,5]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[3,2,5,4,6,1,8,7,10,9]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[3,2,5,4,6,1,9,8,10,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[3,2,5,4,7,6,8,1,10,9]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[3,2,5,4,7,6,9,8,10,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[3,2,5,4,8,7,9,6,10,1]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,2,6,5,7,4,8,1,10,9]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[3,2,6,5,7,4,9,8,10,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[3,2,6,5,8,7,9,4,10,1]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,2,7,6,8,5,9,4,10,1]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,3,5,2,6,1,8,7,10,9]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[4,3,5,2,6,1,9,8,10,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[4,3,5,2,7,6,8,1,10,9]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[4,3,5,2,7,6,9,8,10,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[4,3,5,2,8,7,9,6,10,1]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[4,3,6,5,7,2,8,1,10,9]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,3,6,5,7,2,9,8,10,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,3,6,5,8,7,9,2,10,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,3,7,6,8,5,9,2,10,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,4,6,3,7,2,8,1,10,9]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]
[5,4,6,3,7,2,9,8,10,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[5,4,6,3,8,7,9,2,10,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[5,4,7,6,8,3,9,2,10,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[1,2,3,4,5,6,9,7,10,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,2,3,4,5,7,6,8,9,10]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,3,5,4,6,7,8,9,10]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,2,3,5,4,7,6,9,8,10]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,5,6,7,8,9,10,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,4,2,1,5,6,7,8,9,10]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,2,5,6,7,8,9,10]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[6,5,4,3,1,2,7,8,9,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[7,6,5,4,3,1,2,8,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[9,6,5,4,3,10,1,2,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[2,3,4,5,6,7,10,9,1,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,5,6,10,8,9,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,5,6,10,8,1,9,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,5,6,10,8,1,7,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,5,6,10,1,7,8,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,5,10,7,8,9,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,5,10,7,8,1,9,6]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,5,10,7,8,1,6,9]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,5,10,7,1,9,6,8]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,5,10,7,1,6,8,9]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,5,10,1,6,7,8,9]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,10,6,7,8,1,9,5]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,10,6,7,8,1,5,9]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,10,6,7,1,8,9,5]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,10,6,7,1,9,5,8]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,10,6,7,1,5,8,9]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,10,6,1,8,5,9,7]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,10,6,1,8,5,7,9]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,10,6,1,5,7,8,9]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,10,1,5,6,7,8,9]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,10,5,6,1,8,9,4,7]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,10,5,6,1,8,4,9,7]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,10,5,6,1,8,4,7,9]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,10,5,6,1,4,7,8,9]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,10,5,1,7,4,9,6,8]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,10,5,1,7,4,6,8,9]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,10,5,1,4,6,7,8,9]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,10,4,1,6,3,8,5,9,7]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,10,4,1,6,3,8,5,7,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,10,4,1,6,3,5,7,8,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,10,4,1,3,5,6,7,8,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,2,9,1,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]
[3,4,5,6,8,9,10,1,2,7]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[3,5,6,7,8,9,10,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,4,5,6,7,8,1,2,9,10]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[8,9,10,1,5,6,7,3,4,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,7,1,3,4,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,1,5,6,3,4,7,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,1,3,4,7,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,3,4,7,1,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,5,6,10,1,3,4,7,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,5,6,10,3,4,7,1,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,10,1,5,6,7,3,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,7,1,3,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,1,5,6,3,7,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,1,3,7,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,3,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,5,6,10,1,3,7,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,5,6,10,3,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,10,1,5,6,3,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,1,3,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,3,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,5,6,10,1,3,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,5,6,10,3,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,5,6,10,3,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,10,1,5,3,6,7,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,1,3,6,7,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,3,6,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,5,10,1,3,6,7,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,5,10,3,6,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,10,1,5,3,6,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,1,3,6,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,3,6,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,5,10,1,3,6,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,5,10,3,6,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,5,10,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,5,3,6,10,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]
[8,9,5,3,6,10,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]
[8,5,9,10,1,3,6,7,2,4]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,5,9,10,3,6,7,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,5,9,10,1,3,6,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,5,9,10,3,6,1,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,5,9,10,3,6,2,4,7,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[10,1,9,5,6,7,8,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,10,8,6,7,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,1,9,10,7,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[10,1,8,9,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,1,10,9,6,7,8,2,4,5]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,9,10,8,7,2,4,5,6]=>[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,1,8,9,10,2,4,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[4,2,5,1,6,3,8,7,10,9]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[4,2,6,1,7,3,8,5,10,9]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,2,6,1,8,3,9,5,10,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,2,6,1,8,3,9,5,7,10]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[4,2,6,1,7,3,5,9,8,10]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[4,2,5,1,3,7,6,9,8,10]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[8,7,6,5,4,3,1,2,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,9,8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,9,7,8,10,6,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,3,4,9,6,7,8,10,1,5]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,3,9,5,6,7,8,10,4,1]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,9,4,5,6,7,8,10,3,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[9,3,4,5,6,7,8,10,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[2,3,4,5,6,8,10,1,9,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[2,3,4,5,7,8,1,10,6,9]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[2,3,4,6,7,1,8,10,5,9]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[2,3,5,6,1,7,8,10,9,4]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[2,4,5,1,6,7,8,10,3,9]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[3,4,1,5,6,7,8,10,2,9]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[3,2,4,5,6,7,8,10,9,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[8,10,6,9,4,7,2,5,3,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[8,10,6,9,4,7,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[8,10,6,9,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[8,10,9,6,7,4,5,2,3,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[1,3,5,7,2,4,6,9,8,10]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[2,4,1,5,3,6,7,8,9,10]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[5,6,2,1,3,7,4,8,9,10]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,1,0]
[3,2,5,1,6,4,7,8,9,10]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[6,7,2,1,8,3,4,9,5,10]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]
[3,6,4,1,7,2,8,5,9,10]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]
[3,6,7,2,1,4,8,5,9,10]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]
[4,2,6,1,7,5,3,8,9,10]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[4,3,2,6,1,7,5,8,9,10]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[3,4,7,1,8,2,9,5,10,6]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[7,8,9,3,2,1,4,5,10,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]
[4,7,2,5,1,8,3,9,6,10]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0]
[4,3,7,8,2,1,5,9,6,10]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[3,5,2,7,1,8,6,4,9,10]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0,1,0]
[5,4,3,2,7,1,8,6,9,10]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,0,1,0]
[5,8,9,2,1,6,3,10,7,4]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0,0]
[5,3,8,6,4,1,9,2,10,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0,1,0,0]
[3,5,8,2,6,1,9,4,10,7]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0,0]
[5,4,3,8,9,2,1,6,10,7]=>[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,1,0,0]
[6,4,2,8,1,9,7,5,3,10]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,1,0]
[4,3,6,2,8,1,9,7,5,10]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[6,5,4,3,2,8,1,9,7,10]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0,1,0]
[5,3,7,2,9,1,10,8,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,4,3,7,2,9,1,10,8,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[7,6,5,4,3,2,9,1,10,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0,0]
[2,1,10,3,4,5,6,7,8,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,10,5,6,7,8,9]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,3,4,5,10,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,8,6,4,2,9,7,5,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,4,1,8,5,2,9,6,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,6,3,8,5,2,10,7,4,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[9,5,1,7,3,10,6,2,8,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[10,6,2,7,3,8,4,9,5,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,3,8,4,10,6,2,9,5,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0,0]
[8,4,7,3,10,6,2,9,5,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]
[10,5,8,3,6,1,9,4,7,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,4,7,2,10,5,8,3,6,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[10,5,7,2,8,3,9,4,6,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,3,10,5,7,2,9,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[8,3,9,4,7,2,10,5,6,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0]
[9,3,5,7,1,10,4,6,8,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[10,4,6,8,2,9,3,5,7,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,4,5,6,7,1,8,2,9,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,2,9,3,10,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]
[9,3,8,2,10,4,5,6,7,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[5,6,9,3,7,1,10,4,8,2]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0]
[5,6,10,4,8,2,9,3,7,1]=>[1,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[5,6,9,3,8,2,10,4,7,1]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0]
[6,5,9,3,8,2,10,4,7,1]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0,0,0]
[9,2,7,6,5,4,10,3,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[10,3,7,6,5,4,8,1,9,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,2,10,3,7,6,5,4,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[7,6,5,4,9,2,10,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,0]
[6,4,7,5,10,3,9,2,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0,0]
[6,4,7,5,9,2,10,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,0,0]
[7,5,6,4,9,2,10,3,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,0]
[6,5,7,4,9,2,10,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,0,0]
[5,6,7,3,8,4,9,1,10,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]
[5,6,7,3,8,4,10,2,9,1]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,0]
[5,6,8,4,7,3,10,2,9,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,0]
[6,5,8,4,7,3,10,2,9,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0]
[4,2,5,6,7,8,9,10,1,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[7,1,2,3,9,5,6,10,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,0]
[6,1,2,9,4,5,3,10,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0,0]
[9,1,2,3,8,5,10,7,6,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[9,1,2,8,4,3,10,7,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[8,1,2,7,4,10,6,5,3,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[9,1,8,3,2,5,10,7,4,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[8,1,7,3,2,10,6,4,5,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[7,1,2,3,10,5,6,9,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[6,1,2,10,4,5,3,9,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[8,1,2,3,10,5,9,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]
[8,1,2,10,4,3,9,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
[7,1,2,10,4,9,5,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]
[8,1,10,3,2,5,9,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[7,1,10,3,2,9,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[10,1,2,3,9,5,8,7,6,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,9,4,3,8,7,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,9,4,8,3,6,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,2,8,4,7,6,5,3,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[10,1,9,3,2,5,8,7,4,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,9,3,2,8,5,6,4,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,8,3,2,7,6,4,5,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[8,1,2,3,10,9,5,7,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]
[8,1,2,10,3,9,4,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
[7,1,2,10,9,4,6,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]
[8,1,10,2,4,9,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[7,1,10,2,9,3,6,4,5,8]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[10,1,2,3,9,8,5,6,7,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,9,3,8,4,6,7,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,9,8,4,3,5,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,2,8,7,4,5,6,3,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[10,1,9,2,4,8,3,6,7,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,9,2,8,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,8,2,7,3,5,6,4,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[10,1,9,8,3,2,6,4,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,8,7,3,2,4,5,6,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[8,10,1,3,4,9,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[7,10,1,3,9,2,6,4,5,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[10,9,1,3,4,8,2,6,7,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,1,3,8,2,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,8,1,3,7,2,5,6,4,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[10,9,1,8,2,3,6,4,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,8,1,7,2,3,4,5,6,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,6,7,5,8,4,9,3,10,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]
[1,2,3,4,5,6,8,10,7,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[8,9,10,4,5,6,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,4,5,6,10,2,3,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]
[8,9,10,4,5,2,3,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,4,5,10,2,3,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,4,5,2,3,6,10,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]
[8,4,5,9,10,2,3,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0]
[8,4,5,9,2,3,6,10,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0,0]
[8,9,10,4,5,6,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,4,5,6,10,2,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]
[8,9,10,4,5,2,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,4,5,10,2,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,4,5,2,6,10,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]
[8,4,5,9,10,2,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0]
[8,4,5,9,2,6,10,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0]
[8,9,10,4,5,2,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,4,5,10,2,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,4,5,2,10,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]
[8,9,4,5,2,1,3,6,10,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]
[8,4,5,9,10,2,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0]
[8,4,5,9,2,10,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0]
[8,4,5,9,2,1,3,6,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,0]
[8,9,10,4,2,5,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,4,10,2,5,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,4,2,5,6,10,1,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]
[8,4,9,10,2,5,6,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,4,9,2,5,6,10,1,3,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0]
[8,9,10,4,2,5,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,4,10,2,5,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,4,2,5,10,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]
[8,9,4,2,5,1,3,6,10,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]
[8,4,9,10,2,5,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,4,9,2,5,1,3,6,10,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]
[8,4,2,5,9,10,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,0]
[8,4,2,5,9,1,3,6,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0,0]
[4,8,9,10,2,5,6,1,3,7]=>[1,1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[4,8,9,2,5,6,10,1,3,7]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]
[4,8,9,10,2,5,1,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[4,8,9,2,5,10,1,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]
[4,8,9,2,5,1,3,6,10,7]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[4,8,2,5,9,10,1,3,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]
[4,8,2,5,9,1,3,6,10,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]
[4,8,9,10,5,6,7,2,3,1]=>[1,1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[5,8,9,10,2,6,7,3,4,1]=>[1,1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[2,8,9,10,3,6,7,4,5,1]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[5,6,9,10,2,7,8,3,4,1]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[2,6,9,10,3,7,8,4,5,1]=>[1,1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,4,5,6,1,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[4,8,9,10,5,6,7,1,3,2]=>[1,1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,3,5,6,1,4,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[5,8,9,10,3,6,7,1,4,2]=>[1,1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[3,8,9,10,4,6,7,1,5,2]=>[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[5,6,9,10,3,7,8,1,4,2]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[3,6,9,10,4,7,8,1,5,2]=>[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,1,5,6,2,4,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[5,8,9,10,1,6,7,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[4,8,9,10,1,6,7,2,5,3]=>[1,1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,8,9,10,2,6,7,3,5,4]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[5,6,9,10,1,7,8,2,4,3]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[4,6,9,10,1,7,8,2,5,3]=>[1,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[1,6,9,10,2,7,8,3,5,4]=>[1,0,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,3,4,6,1,5,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[6,8,9,10,3,4,7,1,5,2]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[3,8,9,10,4,5,7,1,6,2]=>[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[6,7,9,10,3,4,8,1,5,2]=>[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[3,7,9,10,4,5,8,1,6,2]=>[1,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,1,4,6,2,5,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[6,8,9,10,1,4,7,2,5,3]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[4,8,9,10,1,5,7,2,6,3]=>[1,1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[1,8,9,10,2,5,7,3,6,4]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[6,7,9,10,1,4,8,2,5,3]=>[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[4,7,9,10,1,5,8,2,6,3]=>[1,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[1,7,9,10,2,5,8,3,6,4]=>[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[4,5,9,10,1,6,8,2,7,3]=>[1,1,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,5,9,10,2,6,8,3,7,4]=>[1,0,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]
[6,7,8,10,3,4,9,1,5,2]=>[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[3,7,8,10,4,5,9,1,6,2]=>[1,1,1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[6,7,8,10,1,4,9,2,5,3]=>[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[4,7,8,10,1,5,9,2,6,3]=>[1,1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[1,7,8,10,2,5,9,3,6,4]=>[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[4,5,8,10,1,6,9,2,7,3]=>[1,1,1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]
[6,5,3,1,2,4,8,7,10,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,7,5,3,1,2,4,6,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,9,7,5,3,1,2,4,6,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,5,3,1,2,4,6,9,8,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]
[5,3,1,2,4,7,6,9,8,10]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[2,1,4,3,6,5,9,7,10,8]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[2,1,4,3,7,5,8,6,10,9]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[2,1,4,3,7,5,9,6,10,8]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[2,1,4,3,8,5,9,6,10,7]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[2,1,5,3,6,4,8,7,10,9]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,5,3,6,4,9,7,10,8]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[2,1,5,3,7,4,8,6,10,9]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[2,1,5,3,7,4,9,6,10,8]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,1,5,3,8,4,9,6,10,7]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[2,1,6,3,7,4,8,5,10,9]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[2,1,6,3,7,4,9,5,10,8]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[2,1,6,3,8,4,9,5,10,7]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[2,1,7,3,8,4,9,5,10,6]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[3,1,4,2,6,5,9,7,10,8]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[3,1,4,2,7,5,8,6,10,9]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[3,1,4,2,7,5,9,6,10,8]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,4,2,8,5,9,6,10,7]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[3,1,5,2,6,4,9,7,10,8]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[3,1,5,2,8,4,9,6,10,7]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,1,6,2,7,4,8,5,10,9]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[3,1,6,2,7,4,9,5,10,8]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[3,1,6,2,8,4,9,5,10,7]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,1,7,2,8,4,9,5,10,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,1,5,2,6,3,9,7,10,8]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[4,1,5,2,7,3,8,6,10,9]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[4,1,5,2,7,3,9,6,10,8]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[4,1,5,2,8,3,9,6,10,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[4,1,6,2,7,3,8,5,10,9]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,1,6,2,7,3,9,5,10,8]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,1,6,2,8,3,9,5,10,7]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,1,7,2,8,3,9,5,10,6]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,1,6,2,7,3,9,4,10,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[5,1,6,2,8,3,9,4,10,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[5,1,7,2,8,3,9,4,10,6]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[2,10,9,8,7,6,5,1,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,3,4,5,6,7,1,2,10,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[1,7,2,8,3,9,4,10,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]
[1,7,2,8,3,9,10,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]
[1,7,2,8,9,3,4,10,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,0]
[1,7,2,8,9,3,10,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]
[1,7,2,8,9,10,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]
[1,7,8,2,3,9,4,10,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0]
[1,7,8,2,3,9,10,4,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]
[1,7,8,2,9,3,4,10,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]
[1,7,8,2,9,3,10,4,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]
[1,7,8,2,9,10,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]
[1,7,8,9,2,3,4,10,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]
[1,7,8,9,2,3,10,4,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]
[1,7,8,9,2,10,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[7,1,2,8,3,9,4,10,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0]
[7,1,2,8,3,9,10,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,0,0]
[7,1,2,8,9,3,4,10,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0,0]
[7,1,2,8,9,3,10,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,0,0]
[7,1,2,8,9,10,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0]
[7,1,8,2,3,9,4,10,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0]
[7,1,8,2,3,9,10,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0,0,0]
[7,1,8,2,9,3,4,10,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0]
[7,1,8,2,9,10,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0,0]
[7,1,8,9,2,3,4,10,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,0,0]
[7,1,8,9,2,3,10,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0]
[7,1,8,9,2,10,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0,0]
[7,1,8,9,10,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[7,8,1,2,3,9,4,10,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,0]
[7,8,1,2,3,9,10,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0]
[7,8,1,2,9,3,4,10,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,0]
[7,8,1,2,9,3,10,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,0]
[7,8,1,2,9,10,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[7,8,1,9,2,3,4,10,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,0]
[7,8,1,9,2,3,10,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,0]
[7,8,1,9,2,10,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[7,8,1,9,10,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[7,8,9,1,2,3,4,10,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]
[7,8,9,1,2,3,10,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[7,8,9,1,2,10,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[7,8,9,1,10,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[7,2,8,9,10,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[9,10,6,4,2,1,3,5,8,7]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,7,8,4,2,1,3,6,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,7,10,4,2,1,3,6,8,5]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,9,10,4,2,1,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[10,8,5,6,2,1,4,3,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,10,5,6,2,1,4,3,8,7]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,7,5,8,2,1,4,6,3,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,7,5,10,2,1,4,6,8,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[8,9,5,10,2,1,4,7,6,3]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[10,6,7,8,2,1,5,4,3,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,6,7,10,2,1,5,4,8,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[8,6,9,10,2,1,5,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[10,8,6,3,4,2,1,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,10,6,3,4,2,1,5,8,7]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,7,8,3,4,2,1,6,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,7,10,3,4,2,1,6,8,5]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,9,10,3,4,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[10,8,5,3,6,2,4,1,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,10,5,3,6,2,4,1,8,7]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,7,5,3,8,2,4,6,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,7,5,3,10,2,4,6,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[8,9,5,3,10,2,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[10,6,7,3,8,2,5,4,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,6,7,3,10,2,5,4,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[8,6,9,3,10,2,5,7,4,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]
[7,8,9,3,10,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[10,8,4,5,6,3,2,1,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,10,4,5,6,3,2,1,8,7]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,7,4,5,8,3,2,6,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,7,4,5,10,3,2,6,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[8,9,4,5,10,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[10,6,4,7,8,3,5,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,6,4,7,10,3,5,2,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[8,6,4,9,10,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0]
[7,8,4,9,10,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[10,5,6,7,8,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,5,6,7,10,4,3,2,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[8,5,6,9,10,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0]
[7,5,8,9,10,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[2,10,4,5,6,7,9,1,3,8]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10,3,4,5,6,7,1,9,2,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,7,6,4,2,1,3,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,9,6,4,2,1,3,8,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,6,5,4,2,1,3,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,5,7,4,2,1,6,3,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,5,9,7,4,2,1,6,8,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,5,7,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,7,6,5,4,2,1,3,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,9,6,5,4,2,1,8,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,6,9,8,5,7,2,1,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,6,4,3,2,1,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,7,6,4,3,2,1,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,9,6,4,3,2,1,8,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,6,3,5,2,4,1,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,6,3,5,2,4,1,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,3,7,5,2,4,6,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,3,9,7,5,2,4,6,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,3,7,5,2,4,6,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,7,6,3,5,2,4,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,9,6,3,5,2,4,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,3,8,6,5,2,7,4,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,6,5,4,3,2,1,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,5,7,4,3,2,6,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,5,9,7,4,3,2,6,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,4,7,6,3,5,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,4,9,7,6,3,5,2,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,4,9,6,8,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,4,7,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,9,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,6,9,8,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,5,9,8,7,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,8,9,10,1,4,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[2,5,6,7,8,9,10,1,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,2,7,3,8,4,9,5,10,6]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,1,2,3,6,5,8,7,10,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[7,1,2,3,4,5,9,6,10,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0,0]
[3,4,5,6,7,1,8,2,10,9]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[1,4,5,6,10,7,8,2,9,3]=>[1,0,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[2,4,5,6,10,7,1,8,3,9]=>[1,1,0,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,4,5,6,8,7,1,10,2,9]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[3,5,6,7,10,8,1,9,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,4,5,9,6,7,2,8,10,3]=>[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[10,2,3,4,5,6,7,1,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,3,4,5,6,1,8,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,3,4,5,1,7,8,9,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,3,4,1,6,7,8,9,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,3,1,5,6,7,8,9,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,4,5,6,7,8,9,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,1,9,8,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[2,3,4,5,1,7,6,9,8,10]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[3,4,5,6,7,8,10,1,9,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[7,8,9,6,1,2,3,4,10,5]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]
[2,8,9,10,7,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,7,5,6,1,2,3,10,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]
[2,9,10,8,6,7,1,3,4,5]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[7,8,9,5,1,2,3,4,10,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]
[7,8,9,1,6,2,3,4,10,5]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]
[2,8,9,10,6,1,3,4,5,7]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[2,8,9,10,1,7,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[4,2,3,5,6,7,8,9,10,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[9,10,6,7,4,5,2,3,1,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,9,4,5,10,1,2,3,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,4,3,9,10,1,2,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0]
[9,6,10,1,3,7,8,2,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,10,6,7,4,5,1,2,3,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,6,4,10,3,7,1,2,5,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[10,1,8,9,6,7,4,5,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,6,1,4,9,3,7,2,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,6,5,4,1,3,9,2,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,7,6,5,4,3,1,2,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,6,5,7,8,9,10]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,3,4,5,6,8,7,9,10]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[10,7,6,5,4,3,2,1,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,4,5,6,9,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,4,5,9,7,8,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,9,5,6,7,8,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,9,4,5,6,7,8,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,9,10,1,8,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,5,7,8,9,10,1,6,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[3,4,6,7,8,9,10,1,5,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,8,9,10,1,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[6,4,5,7,3,8,2,9,1,10]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]
[7,5,1,3,2,6,4,8,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[9,6,1,3,4,2,7,8,5,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[8,3,6,1,4,2,7,5,9,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[10,1,8,3,2,5,7,4,9,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,3,7,1,4,5,2,8,9,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,3,4,7,1,5,2,8,6,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[7,10,1,3,8,2,6,5,9,4]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[10,9,5,1,8,2,4,3,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,3,4,5,8,1,6,2,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,8,7,5,6,4,3,2,10,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[9,10,2,4,6,8,1,3,5,7]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[7,8,2,4,6,10,1,3,5,9]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0,0,0]
[9,7,10,2,4,6,8,1,3,5]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,9,10,7,2,4,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[5,6,2,4,8,10,1,3,7,9]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,0]
[5,6,9,10,2,4,8,1,3,7]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[7,5,8,2,4,6,10,1,3,9]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0,0]
[7,9,5,10,2,4,6,8,1,3]=>[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]
[5,8,9,10,7,2,4,6,1,3]=>[1,1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[6,7,8,5,2,4,10,1,3,9]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0,0]
[9,6,7,5,10,2,4,8,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[8,9,6,10,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[7,8,9,10,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[3,4,2,6,8,10,1,5,7,9]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,4,9,10,2,6,8,1,5,7]=>[1,1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,4,7,8,2,6,10,1,5,9]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[9,3,4,7,10,2,6,8,1,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[8,9,10,3,4,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[5,3,6,2,4,8,10,1,7,9]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,0]
[5,3,6,9,10,2,4,8,1,7]=>[1,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0,0]
[5,7,3,8,2,4,6,10,1,9]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,1,0,0,0]
[5,7,9,3,10,2,4,6,8,1]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,0]
[8,5,9,10,3,7,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[3,6,7,8,5,2,4,10,1,9]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0]
[9,3,6,7,5,10,2,4,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[6,8,3,9,10,5,7,2,4,1]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0,0]
[7,8,9,10,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[4,5,6,3,2,8,10,1,7,9]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0]
[4,5,6,3,9,10,2,8,1,7]=>[1,1,1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,0,0]
[7,4,5,3,8,2,6,10,1,9]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,1,0,0,0]
[7,4,5,9,3,10,2,6,8,1]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0]
[4,8,5,9,10,3,7,2,6,1]=>[1,1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]
[6,7,4,8,3,5,2,10,1,9]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0,0]
[6,7,9,4,3,5,10,2,8,1]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0,0]
[8,6,9,4,10,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]
[7,4,8,9,10,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[5,6,7,8,4,3,2,10,1,9]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0,0]
[9,5,6,7,4,3,10,2,8,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[8,9,5,6,4,10,3,7,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]
[7,8,9,5,10,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[1,2,4,5,6,8,10,9,3,7]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,2,3,5,7,8,10,6,9,4]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,2,4,5,7,8,10,3,9,6]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,2,4,6,7,5,10,8,3,9]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,3,4,2,7,8,10,5,9,6]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,3,4,6,7,2,10,8,5,9]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,2,3,5,6,9,8,10,7,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,2,4,5,6,9,8,10,3,7]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,2,3,5,7,9,6,10,8,4]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,2,4,5,7,9,3,10,8,6]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,2,4,6,5,9,7,10,3,8]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,3,4,2,7,9,5,10,8,6]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,3,4,6,2,9,7,10,5,8]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,2,3,5,8,7,9,6,10,4]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,2,4,5,8,7,9,3,10,6]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,2,4,6,8,5,9,3,10,7]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,2,4,7,6,8,5,9,3,10]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,3,4,2,8,7,9,5,10,6]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,3,4,6,8,2,9,5,10,7]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,3,4,7,6,8,2,9,5,10]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,2,3,6,5,9,7,10,8,4]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,2,4,6,3,9,7,10,8,5]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,2,5,4,6,9,7,10,3,8]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[1,3,2,6,4,9,7,10,8,5]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,3,5,2,6,9,7,10,4,8]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[1,2,3,6,8,5,9,7,10,4]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,2,4,6,8,3,9,7,10,5]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,2,5,4,8,6,9,3,10,7]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[1,2,5,7,4,8,6,9,3,10]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[1,3,2,6,8,4,9,7,10,5]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,3,5,2,8,6,9,4,10,7]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[1,3,5,7,2,8,6,9,4,10]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[1,4,3,5,8,2,9,6,10,7]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,4,3,7,5,8,2,9,6,10]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[2,1,3,6,4,9,7,10,8,5]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[2,1,5,3,6,9,7,10,4,8]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[2,1,3,6,8,4,9,7,10,5]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[2,1,5,3,8,6,9,4,10,7]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[2,1,5,7,3,8,6,9,4,10]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[2,4,1,5,8,3,9,6,10,7]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[2,4,1,7,5,8,3,9,6,10]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[5,6,1,2,3,7,8,9,10,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[2,5,1,3,6,7,8,9,10,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,1,5,6,7,8,9,10,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,7,8,1,2,3,4,9,10,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,1,0,0]
[2,6,7,1,3,4,8,9,10,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]
[6,3,4,1,2,7,8,9,10,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]
[3,2,6,1,4,7,8,9,10,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[4,3,2,1,6,7,8,9,10,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[2,7,8,9,1,3,4,5,10,6]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]
[7,3,4,8,1,2,5,9,10,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0,0]
[3,2,7,8,1,4,5,9,10,6]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[4,7,2,5,1,3,8,9,10,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[4,3,2,7,1,5,8,9,10,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[5,4,3,2,1,7,8,9,10,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]
[8,3,4,9,10,1,2,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0]
[8,9,4,5,6,1,2,3,10,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]
[4,3,2,8,9,1,5,6,10,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[8,5,6,3,4,1,2,9,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]
[5,3,8,2,6,1,4,9,10,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,4,3,2,8,1,6,9,10,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0,0]
[6,5,4,3,2,1,8,9,10,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]
[5,9,10,2,6,7,1,3,4,8]=>[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[9,5,6,3,4,10,1,2,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[5,3,9,2,6,10,1,4,7,8]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,4,3,2,9,10,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]
[6,9,4,7,2,5,1,3,10,8]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0]
[6,4,3,9,2,7,1,5,10,8]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0,0]
[6,5,4,3,2,9,1,7,10,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0,0]
[7,6,5,4,3,2,1,9,10,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]
[10,7,8,5,6,3,4,1,2,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,5,10,3,8,2,6,1,4,9]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[7,5,4,3,10,2,8,1,6,9]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[7,6,5,4,3,2,10,1,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]
[2,1,8,7,4,3,6,5,10,9]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,4,3,6,5,7,9,10,8]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,4,3,5,7,8,6,10,9]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,4,3,5,7,6,9,10,8]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,4,3,5,6,8,9,10,7]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,5,6,4,8,7,10,9]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,3,5,6,4,7,9,10,8]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[2,1,3,5,4,7,8,6,10,9]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[2,1,3,5,4,7,6,9,10,8]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[2,1,3,5,4,6,8,9,10,7]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,4,6,7,8,5,10,9]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,3,4,6,7,5,9,10,8]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,3,4,6,5,8,9,10,7]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,3,4,5,7,8,9,10,6]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,4,2,6,5,7,9,10,8]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,3,4,2,5,7,8,6,10,9]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,3,4,2,5,7,6,9,10,8]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,3,4,2,5,6,8,9,10,7]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,2,5,6,4,8,7,10,9]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,3,2,5,6,4,7,9,10,8]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,3,2,5,4,7,8,6,10,9]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,3,2,5,4,7,6,9,10,8]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,3,2,5,4,6,8,9,10,7]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,3,2,4,6,7,8,5,10,9]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,2,4,6,7,5,9,10,8]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,3,2,4,6,5,8,9,10,7]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,2,4,5,7,8,9,10,6]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,4,5,6,3,8,7,10,9]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,2,4,5,6,3,7,9,10,8]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,2,4,5,3,7,8,6,10,9]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,2,4,5,3,7,6,9,10,8]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,2,4,5,3,6,8,9,10,7]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,2,4,3,6,7,8,5,10,9]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,4,3,6,7,5,9,10,8]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,2,4,3,6,5,8,9,10,7]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,2,4,3,5,7,8,9,10,6]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,5,6,7,8,4,10,9]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,2,3,5,6,7,4,9,10,8]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,2,3,5,6,4,8,9,10,7]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,2,3,5,4,7,8,9,10,6]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[2,3,4,5,6,10,8,9,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,5,10,7,8,9,6,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,10,6,7,8,9,5,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,10,5,6,7,8,9,4,1]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,10,4,5,6,7,8,9,3,1]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10,3,4,5,6,7,8,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,7,4,8,3,10,1,9,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,0,0]
[6,5,7,4,10,1,9,2,8,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0,0]
[6,5,10,1,9,2,8,3,7,4]=>[1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
[5,10,1,9,2,8,3,7,4,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,6,4,10,1,9,2,8,3,7]=>[1,1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[5,6,4,7,3,10,1,9,2,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,0,0]
[5,6,4,7,3,8,2,10,1,9]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]
[2,10,1,3,4,5,6,9,7,8]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,9,1,3,4,5,6,7,10,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[10,3,1,2,4,5,6,9,7,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,1,10,2,4,5,6,9,7,8]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9,3,1,2,4,5,6,7,10,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[3,1,9,2,4,5,6,7,10,8]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[10,9,3,4,5,6,7,8,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,2,3,4,5,6,7,1,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,4,5,6,7,8,9,2,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,3,4,5,6,7,8,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,5,2,9,6,3,10,7,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]
[10,9,3,8,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,7,6,4,5,3,2,1,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,9,8,6,5,4,7,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,10,4,9,3,8,2,1,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,4,9,3,2,8,7,1,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,4,9,3,2,8,1,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,4,9,3,2,1,8,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,4,3,9,8,2,7,1,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,4,3,9,8,2,1,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,4,3,9,2,8,7,1,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,4,3,9,2,8,1,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,4,3,9,2,1,8,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,4,3,2,9,8,7,1,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,4,3,2,9,8,1,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,4,3,2,9,1,8,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,10,4,3,2,1,9,8,7,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,4,10,9,3,8,2,7,1,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,10,9,3,8,2,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,10,9,3,2,8,7,1,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,10,9,3,2,8,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,10,9,3,2,1,8,7,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,10,3,9,8,2,7,1,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,10,3,9,8,2,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,10,3,9,2,8,7,1,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,10,3,9,2,8,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,10,3,9,2,1,8,7,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,10,3,2,9,8,7,1,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,10,3,2,9,8,1,7,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,10,3,2,9,1,8,7,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,10,3,2,1,9,8,7,6]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,10,9,8,2,7,1,6]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,10,9,8,2,1,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,10,9,2,8,7,1,6]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,10,9,2,8,1,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,10,9,2,1,8,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,10,2,9,8,7,1,6]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,10,2,9,8,1,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,10,2,9,1,8,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,10,2,1,9,8,7,6]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,10,9,8,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,2,10,9,8,1,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,2,10,9,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[5,4,3,2,10,1,9,8,7,6]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[3,4,5,6,7,10,1,2,8,9]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,5,6,9,10,1,2,7,8]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[3,4,5,8,9,10,1,2,6,7]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[3,4,7,8,9,10,1,2,5,6]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[3,6,7,8,9,10,1,2,4,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[2,1,4,3,6,5,10,7,9,8]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,4,3,8,5,7,6,10,9]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,4,3,10,9,7,5,6,8]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,10,5,6,8,9,7]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,3,5,4,8,7,10,9]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,6,3,5,4,10,7,9,8]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,8,7,5,3,4,6,10,9]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,10,7,5,9,4,3,6,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,10,8,5,3,6,4,9,7]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,4,6,7,5,10,9]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,10,9,4,6,7,3,5,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,10,3,9,6,4,8,5,7]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,10,3,4,5,7,8,9,6]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,6,5,8,7,10,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,1,3,2,6,5,10,7,9,8]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[4,1,3,2,8,5,7,6,10,9]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[4,1,3,2,10,9,7,5,6,8]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,2,10,5,6,8,9,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,1,2,4,10,7,9,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[8,5,3,7,2,1,4,6,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,5,3,7,2,9,4,1,6,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,5,3,8,2,1,6,4,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,6,3,1,4,2,7,5,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,6,3,9,4,2,7,1,5,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,6,3,1,9,2,4,8,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,3,1,4,5,2,8,9,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,1,2,4,5,3,8,7,10,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[6,1,2,4,5,3,10,7,9,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[8,7,2,4,5,1,3,6,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,7,2,4,5,9,3,1,6,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,2,4,5,1,6,3,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,1,7,4,2,6,3,5,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,9,7,4,2,6,3,1,5,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,8,4,9,6,2,3,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,8,4,2,5,7,3,9,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,1,2,3,5,6,7,4,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,9,2,3,5,6,7,1,4,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,9,3,5,6,2,8,4,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,9,5,3,7,8,4,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,7,6,5,4,3,8,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,4,1,5,6,7,8,9,10]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,2,5,1,6,7,8,9,10]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[4,3,5,2,6,1,7,8,9,10]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[4,5,3,6,2,7,1,8,9,10]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,1,0]
[5,4,6,3,7,2,8,1,9,10]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0]
[2,1,4,3,6,5,10,7,8,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,4,3,8,5,6,7,10,9]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,4,3,10,9,6,5,8,7]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,10,5,6,7,8,9]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,3,4,5,8,7,10,9]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,6,3,4,5,10,7,8,9]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,10,7,4,9,6,3,8,5]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,10,9,4,3,6,7,8,5]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,8,3,4,5,6,7,10,9]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,10,9,4,5,6,3,8,7]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,10,3,8,5,4,7,6,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,6,5,10,7,8,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[4,1,2,3,8,5,6,7,10,9]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[4,1,2,3,10,9,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,2,1,4,3,8,7,10,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[6,5,2,1,4,3,10,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[8,5,2,7,4,1,6,3,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,5,2,7,4,9,6,1,8,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,5,2,9,4,1,6,7,8,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,7,2,1,4,5,6,3,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,7,2,9,4,5,6,1,8,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,2,1,8,5,4,7,6,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,2,1,4,5,6,7,8,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,1,2,3,4,5,8,7,10,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,7,2,3,4,1,6,5,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,7,2,3,4,9,6,1,8,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,2,3,4,1,6,7,8,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,1,6,3,2,5,4,7,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,9,6,3,2,5,4,1,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,6,3,8,5,2,7,4,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,8,3,2,5,6,7,4,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,2,3,4,5,6,1,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,8,3,4,5,2,7,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,7,4,3,6,5,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,9,7,5,3,10,8,6,4]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,4,1,5,6,7,8,10,3,9]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,3,5,7,2,9,4,6,8,10]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[1,3,5,7,2,9,4,10,6,8]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[1,3,5,7,2,8,4,9,6,10]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[1,3,5,6,2,7,4,9,8,10]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[1,3,4,5,2,7,6,9,8,10]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[10,1,2,3,4,5,7,8,9,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,10,7,9,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]
[8,1,2,3,4,5,9,7,10,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]
[9,1,2,3,4,10,6,7,8,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,1,2,3,4,10,6,7,9,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[8,1,2,3,4,9,6,7,10,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0,0]
[7,1,2,3,4,9,6,10,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0,0]
[7,1,2,3,4,8,6,9,10,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0,0]
[8,1,2,3,10,5,6,7,9,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]
[8,1,2,3,9,5,6,7,10,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0,0]
[7,1,2,3,10,5,6,8,9,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[7,1,2,3,8,5,6,9,10,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,0]
[6,1,2,3,8,5,10,7,9,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,0]
[6,1,2,3,8,5,9,7,10,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,0,0]
[6,1,2,3,7,5,8,9,10,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0,0]
[6,1,2,9,4,5,10,7,8,3]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0,0]
[6,1,2,8,4,5,10,7,9,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,0]
[6,1,2,8,4,5,9,7,10,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,1,0,0]
[6,1,2,7,4,5,8,9,10,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0,0]
[5,1,2,7,4,9,6,10,8,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[5,1,2,7,4,8,6,9,10,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,0,0]
[5,1,2,6,4,7,8,9,10,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0]
[4,1,6,3,8,5,9,7,10,2]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,1,6,3,7,5,8,9,10,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[4,1,5,3,6,7,8,9,10,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,10,9,8,7,6,5,3,2,4]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,9,8,7,6,4,3,2,5]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,9,8,7,5,4,3,2,6]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,9,8,6,5,4,3,2,7]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,9,7,6,5,4,3,2,8]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,8,7,6,5,4,3,2,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,10,2,3,4,5,6,7,1,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[8,9,10,2,3,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[7,8,9,10,2,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[5,6,7,8,9,10,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[4,5,6,7,8,9,10,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[8,10,3,4,5,6,7,2,1,9]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[3,10,2,1,5,6,7,8,9,4]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,9,1,4,5,6,7,8,2,10]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[2,10,9,8,7,6,1,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,10,9,8,1,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,10,9,1,8,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,4,3,10,5,7,6,9,8]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,9,6,10,5,8,7]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[2,1,8,3,5,4,7,6,10,9]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,10,3,5,4,7,6,9,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,9,6,10,3,5,4,8,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,1,7,4,8,3,6,5,10,9]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[2,1,7,4,10,3,6,5,9,8]=>[1,1,0,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,1,10,3,6,5,9,4,8,7]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,9,4,8,5,10,3,7,6]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,1,3,2,10,5,7,6,9,8]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,2,9,6,10,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[6,1,3,2,5,4,8,7,10,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[6,1,3,2,5,4,10,7,9,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[8,1,3,2,5,4,7,6,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[9,6,10,1,3,2,5,4,8,7]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[7,4,8,1,3,2,6,5,10,9]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]
[7,4,10,1,3,2,6,5,9,8]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[10,1,3,2,6,5,9,4,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,4,8,5,10,1,3,2,7,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[5,2,6,1,4,3,8,7,10,9]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,1,0,0]
[5,2,6,1,4,3,10,7,9,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,1,0,0,0,0]
[5,2,8,1,4,3,7,6,10,9]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,2,10,1,4,3,7,6,9,8]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[5,2,9,6,10,1,4,3,8,7]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0,0]
[8,1,4,3,7,2,6,5,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,1,4,3,7,2,6,5,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,2,6,5,10,1,4,3,8,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[10,1,4,3,8,5,9,2,7,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,2,6,3,8,1,5,4,10,9]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,1,0,0]
[7,2,6,3,10,1,5,4,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[10,1,5,4,9,2,6,3,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,3,10,1,5,4,9,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[8,3,9,2,7,4,10,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0]
[1,2,3,4,5,6,8,9,7,10]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[10,1,2,3,4,5,9,7,6,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,4,9,6,7,5,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,2,3,10,5,6,7,4,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[10,1,2,9,4,5,6,7,3,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,9,3,4,5,6,7,2,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,10,6,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]
[7,1,2,3,4,9,5,6,10,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0,0]
[6,1,2,3,9,4,5,7,10,8]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,0]
[5,1,2,10,3,4,6,7,9,8]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,9,2,3,5,6,7,10,8]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,9,1,2,4,5,6,7,10,8]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[10,2,1,3,4,5,6,7,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,7,8,6,9,10]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,3,4,5,7,8,9,6,10]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[9,8,10,1,4,5,6,7,2,3]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[7,1,10,9,2,3,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[6,7,9,1,2,3,4,5,10,8]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0,0]
[2,8,1,9,10,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]
[8,7,1,10,2,3,4,5,6,9]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
[1,5,2,8,6,3,10,9,7,4]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0]
[4,1,5,2,8,6,3,10,9,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[1,7,5,2,8,6,3,10,9,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,0]
[4,1,7,5,2,8,3,10,9,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[6,4,1,7,5,2,8,3,10,9]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,1,1,0,0]
[3,4,1,7,2,8,5,10,9,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[3,6,4,1,7,2,8,5,10,9]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0]
[1,5,2,9,8,6,3,10,7,4]=>[1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]
[4,1,5,2,9,8,6,3,10,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,7,5,2,9,6,3,10,8,4]=>[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]
[4,1,7,5,2,9,3,10,8,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[4,1,9,6,5,2,7,3,10,8]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[3,4,1,7,2,9,5,10,8,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[3,6,1,9,4,2,7,5,10,8]=>[1,1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0]
[1,8,7,5,2,9,6,3,10,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]
[4,1,8,7,5,2,9,3,10,6]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[6,4,1,8,5,2,9,3,10,7]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,1,0,0]
[7,6,4,1,8,5,2,9,3,10]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0,1,0]
[3,4,1,8,7,2,9,5,10,6]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[3,6,4,1,8,2,9,5,10,7]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0]
[3,7,6,4,1,8,2,9,5,10]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0]
[1,9,6,5,2,7,3,10,8,4]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[6,1,9,4,2,7,3,10,8,5]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0,0]
[5,4,1,9,6,2,7,3,10,8]=>[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,1,0,0]
[9,3,1,6,2,7,4,10,8,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[9,5,3,1,6,2,7,4,10,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[6,1,8,5,2,9,7,3,10,4]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0]
[6,4,1,8,2,9,7,3,10,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0,0]
[8,5,4,1,6,2,9,3,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]
[5,7,4,1,8,6,2,9,3,10]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0]
[3,6,1,8,2,9,7,4,10,5]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0]
[5,8,3,1,6,2,9,4,10,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,1,0,0]
[5,3,7,1,8,6,2,9,4,10]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,1,0]
[4,3,8,1,9,5,2,6,10,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[7,4,3,5,1,8,2,9,6,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0,1,0]
[9,6,2,1,3,7,4,10,8,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[5,9,2,1,6,3,7,4,10,8]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[6,8,2,1,3,9,7,4,10,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0]
[8,2,5,1,6,3,9,4,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]
[2,5,7,1,8,6,3,9,4,10]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]
[2,4,8,1,9,5,3,6,10,7]=>[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[5,6,4,3,2,1,7,8,9,10]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[6,7,5,4,3,2,1,8,9,10]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]
[7,8,9,10,1,5,6,3,4,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[10,9,8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,4,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,4,8,7,6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,3,9,8,7,6,5,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,9,8,7,6,5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,10,2,1,6,4,3,5,7,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[7,10,2,1,8,4,3,5,6,9]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[2,9,1,10,7,4,3,5,6,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[2,8,1,9,4,3,10,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]
[10,8,5,2,1,6,3,4,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,5,2,1,10,6,3,4,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[10,7,2,1,8,5,3,4,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,2,1,10,7,5,3,4,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[2,8,1,9,3,10,5,4,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]
[10,6,2,1,7,3,8,4,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,2,1,10,6,3,7,4,5,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[8,2,1,9,3,10,6,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0]
[7,2,1,8,3,9,4,10,5,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0]
[10,8,6,3,1,4,2,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,9,1,10,6,4,2,5,7,8]=>[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[10,7,3,1,8,4,2,5,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,3,1,10,7,4,2,5,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[8,3,1,9,4,2,10,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0]
[10,8,5,1,6,3,2,4,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,5,1,10,6,3,2,4,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[10,7,1,8,5,3,2,4,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,10,7,5,3,2,4,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,3,1,9,2,10,5,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0]
[10,6,1,7,3,2,8,4,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,10,6,3,2,7,4,5,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,1,9,3,2,10,6,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[7,1,8,3,2,9,4,10,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0]
[10,8,4,1,5,2,6,3,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,4,1,10,5,2,6,3,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[10,7,1,8,4,2,5,3,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,10,7,4,2,5,3,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,1,9,4,2,10,5,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[10,6,1,7,2,8,4,3,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,10,6,2,7,4,3,5,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,1,9,2,10,6,4,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]
[7,1,8,2,9,4,3,10,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0]
[10,5,1,6,2,7,3,8,4,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,10,5,2,6,3,7,4,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,1,9,2,10,5,3,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]
[7,1,8,2,9,3,10,5,4,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0]
[4,2,1,3,6,5,8,7,10,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[10,2,3,1,4,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,4,5,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,5,4,6,7,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,3,4,2,5,6,7,8,9,10]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,5,6,3,7,8,9,10]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,2,3,5,6,7,8,4,9,10]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[2,1,5,3,6,7,4,8,9,10]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[1,3,5,6,4,2,7,8,9,10]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[3,5,2,1,6,4,7,8,9,10]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]
[2,1,3,6,4,7,8,9,5,10]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,3,4,6,7,2,8,5,9,10]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[3,2,6,1,4,7,8,5,9,10]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[2,4,6,1,7,5,3,8,9,10]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[4,6,3,2,1,7,5,8,9,10]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]
[1,3,4,2,7,8,5,9,10,6]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[3,2,1,7,4,5,8,9,10,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,2,4,5,7,8,9,6,3,10]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[4,3,7,2,1,5,8,9,6,10]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[1,3,5,7,8,6,4,2,9,10]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[3,5,7,2,1,8,6,4,9,10]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0]
[5,7,4,3,2,1,8,6,9,10]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0,1,0]
[2,1,5,3,8,6,9,10,7,4]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[1,3,5,6,8,9,4,2,10,7]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[3,5,2,8,1,6,9,4,10,7]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,0]
[5,4,8,3,2,1,6,9,10,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0,1,0,0]
[2,4,6,8,1,9,7,5,3,10]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[4,6,8,3,2,1,9,7,5,10]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0]
[6,8,5,4,3,2,1,9,7,10]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,1,0]
[3,5,7,9,2,1,10,8,6,4]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,7,9,4,3,2,1,10,8,6]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,0,0]
[7,9,6,5,4,3,2,1,10,8]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]
[2,3,7,5,6,1,10,9,4,8]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[2,3,4,10,6,9,8,5,1,7]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,9,10,8,4,1,7]=>[1,1,0,1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[2,3,9,5,8,7,4,1,10,6]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,5,4,9,6,10,8,3,1,7]=>[1,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,5,4,8,9,7,3,1,10,6]=>[1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0]
[2,3,4,10,6,7,1,9,8,5]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,7,5,6,1,10,9,8,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[2,3,4,10,6,8,9,1,7,5]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,8,10,9,1,7,4]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[2,3,8,5,7,9,1,10,6,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[2,5,4,8,6,10,9,1,7,3]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0]
[2,5,4,7,8,9,1,10,6,3]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0,0]
[2,3,4,10,6,9,8,7,5,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,5,9,10,8,7,4,1]=>[1,1,0,1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[2,3,7,5,9,8,10,6,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[2,3,9,5,8,7,6,4,1,10]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,5,4,9,6,10,8,7,3,1]=>[1,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]
[2,5,4,9,7,8,10,6,3,1]=>[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0,0]
[2,5,4,8,9,7,6,3,1,10]=>[1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,1,0]
[2,3,4,10,7,9,8,1,6,5]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,10,9,8,1,6,4]=>[1,1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,3,8,6,9,7,1,10,5,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[2,4,7,5,10,9,8,1,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,4,6,8,9,7,1,10,5,3]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[2,3,4,10,7,8,9,6,5,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,5,7,10,8,9,6,4,1]=>[1,1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[2,3,7,6,8,9,10,5,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[2,3,9,6,7,8,5,4,1,10]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,4,7,5,10,8,9,6,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,4,6,7,8,9,10,5,3,1]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[2,4,6,9,7,8,5,3,1,10]=>[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[2,6,5,8,9,7,10,4,3,1]=>[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]
[2,6,5,7,8,9,4,3,1,10]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]
[3,7,4,5,10,9,8,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]
[3,6,4,8,9,7,1,10,5,2]=>[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0]
[3,7,4,5,10,8,9,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]
[3,6,4,7,8,9,10,5,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]
[3,6,4,9,7,8,5,2,1,10]=>[1,1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0]
[3,5,6,8,9,7,10,4,2,1]=>[1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0]
[3,5,6,7,8,9,4,2,1,10]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]
[4,3,2,7,6,5,1,9,8,10]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[4,3,2,1,7,6,9,8,5,10]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[4,3,2,7,6,1,9,8,5,10]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[4,3,2,7,6,9,8,5,1,10]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[4,3,7,6,2,1,9,8,5,10]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[4,3,7,6,2,9,8,5,1,10]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[4,3,2,1,7,6,5,9,10,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[4,3,2,7,6,5,1,9,10,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[4,3,2,1,7,6,9,5,10,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[4,3,2,7,6,1,9,5,10,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[4,3,2,7,6,9,5,1,10,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,3,7,6,2,1,9,5,10,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[4,3,7,6,2,9,5,1,10,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[4,3,2,1,7,6,9,10,8,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[4,3,2,7,6,1,9,10,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[4,3,2,7,6,9,1,10,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,3,2,7,6,9,10,8,5,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,3,7,6,2,1,9,10,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[4,3,7,6,2,9,1,10,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[4,3,7,6,2,9,10,8,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[4,3,2,1,7,9,6,5,10,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[4,3,2,7,1,9,6,5,10,8]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[4,3,2,7,9,6,5,1,10,8]=>[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[4,3,7,2,1,9,6,5,10,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[4,3,7,2,9,6,5,1,10,8]=>[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[4,3,2,1,7,9,6,10,8,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[4,3,2,7,1,9,6,10,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[4,3,2,7,9,6,1,10,8,5]=>[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[4,3,2,7,9,6,10,8,5,1]=>[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,3,7,2,1,9,6,10,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[4,3,7,2,9,6,1,10,8,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[4,3,7,2,9,6,10,8,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[4,3,7,9,6,2,1,10,8,5]=>[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[4,3,7,9,6,2,10,8,5,1]=>[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[4,7,3,2,1,9,6,5,10,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]
[4,7,3,2,9,6,5,1,10,8]=>[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,0]
[4,7,3,2,1,9,6,10,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0]
[4,7,3,2,9,6,1,10,8,5]=>[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]
[4,7,3,2,9,6,10,8,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0]
[4,7,3,9,6,2,1,10,8,5]=>[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0,0,0]
[5,6,4,7,3,9,1,8,2,10]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,0,1,0]
[1,6,7,5,8,4,10,2,9,3]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,0]
[4,5,6,7,8,9,1,10,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[3,2,5,4,7,6,8,10,9,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[3,2,5,4,6,9,7,8,10,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[3,2,5,4,6,8,7,10,9,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[3,2,5,4,6,7,10,8,9,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[3,2,4,7,5,6,9,8,10,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[3,2,4,7,5,6,8,10,9,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[3,2,4,6,5,9,7,8,10,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,2,4,6,5,8,7,10,9,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,2,4,6,5,7,10,8,9,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,2,4,5,9,6,7,8,10,1]=>[1,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[3,2,4,5,8,6,7,10,9,1]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[3,2,4,5,7,6,10,8,9,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[3,2,4,5,6,10,7,8,9,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,5,3,4,7,6,9,8,10,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,5,3,4,7,6,8,10,9,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0]
[2,5,3,4,6,9,7,8,10,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]
[2,5,3,4,6,8,7,10,9,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,0]
[2,5,3,4,6,7,10,8,9,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0]
[2,4,3,7,5,6,9,8,10,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[2,4,3,7,5,6,8,10,9,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[2,4,3,6,5,9,7,8,10,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[2,4,3,6,5,7,10,8,9,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[2,4,3,5,9,6,7,8,10,1]=>[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,4,3,5,8,6,7,10,9,1]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,4,3,5,7,6,10,8,9,1]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,3,5,6,10,7,8,9,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,7,4,5,6,9,8,10,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[2,3,7,4,5,6,8,10,9,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[2,3,6,4,5,9,7,8,10,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[2,3,6,4,5,8,7,10,9,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[2,3,6,4,5,7,10,8,9,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[2,3,5,4,9,6,7,8,10,1]=>[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[2,3,5,4,8,6,7,10,9,1]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[2,3,5,4,7,6,10,8,9,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[2,3,5,4,6,10,7,8,9,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,9,5,6,7,8,10,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,3,4,8,5,6,7,10,9,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,3,4,7,5,6,10,8,9,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,3,4,6,5,10,7,8,9,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[9,3,10,1,2,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[10,3,1,9,2,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,1,4,10,2,5,6,7,8,9]=>[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[9,8,10,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[10,7,1,2,3,4,8,9,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,2,3,4,5,7,8,9,10,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]
[2,6,3,4,5,7,8,9,10,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[2,3,6,4,5,7,8,9,10,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[10,2,3,4,5,6,7,1,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,3,4,5,6,1,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,3,4,5,1,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,3,4,1,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,8,1,3,4,5,6,10,7,9]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[10,7,1,2,3,4,5,9,6,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,5,6,8,2,9,3,10,7,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,0,0]
[10,4,5,6,9,3,8,2,7,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,5,10,6,9,3,8,2,7,1]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,8,2,6,10,9,3,7,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]
[10,6,9,5,4,3,8,2,7,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,2,6,10,9,5,4,3,7,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
[8,2,10,4,5,6,7,1,9,3]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[4,5,6,8,2,10,7,1,9,3]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0]
[10,4,5,6,8,2,7,1,9,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,5,10,6,8,2,7,1,9,3]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,5,10,8,2,6,7,1,9,3]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,6,8,2,7,1,9,5,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,2,6,7,1,9,5,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,2,7,1,9,3,10,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,0,0]
[4,5,8,2,7,1,9,3,10,6]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0,1,0,0]
[4,5,9,3,10,7,1,8,2,6]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,5,7,1,9,3,8,2,6,10]=>[1,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0]
[8,2,7,1,9,5,4,3,10,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0,0]
[9,5,4,3,10,7,1,8,2,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[7,1,9,5,4,3,8,2,6,10]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,1,0]
[8,2,6,10,4,5,7,1,9,3]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
[4,8,2,6,10,5,7,1,9,3]=>[1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]
[4,10,8,2,5,6,7,1,9,3]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,2,6,10,5,7,1,9,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
[10,8,2,5,6,7,1,9,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,3,10,4,5,7,1,8,2,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[4,9,3,10,5,7,1,8,2,6]=>[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[4,9,3,10,7,1,8,2,5,6]=>[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[4,7,1,9,3,8,2,5,6,10]=>[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]
[9,4,3,10,5,7,1,8,2,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[9,4,3,10,7,1,8,2,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[7,1,9,4,3,8,2,5,6,10]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,1,0]
[5,10,7,1,8,2,4,3,9,6]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,7,1,8,2,4,3,9,6,10]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0]
[10,5,7,1,9,4,2,6,8,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,4,2,5,6,7,1,10,8,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[10,5,7,1,8,3,9,4,2,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,1,8,3,9,4,2,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,1,8,3,9,4,2,5,6,10]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,1,0]
[4,2,5,10,7,1,8,3,9,6]=>[1,1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[4,2,5,7,1,8,3,9,6,10]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[4,5,6,7,8,9,1,2,10,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[2,1,10,9,8,7,6,5,3,4]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[10,9,7,3,6,1,2,4,8,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,7,3,6,1,2,4,10,8,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[7,3,10,9,6,1,2,4,8,5]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[7,3,9,6,1,2,4,10,8,5]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0,0]
[9,6,1,2,4,10,7,3,8,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[8,4,10,9,7,3,6,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[10,8,4,9,7,3,6,1,2,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,3,8,4,10,9,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0,0]
[7,3,10,8,4,9,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[10,7,3,8,4,9,6,1,2,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,1,2,7,3,8,4,10,9,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,0]
[6,1,2,7,3,10,8,4,9,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0,0,0]
[6,1,2,10,7,3,8,4,9,5]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[10,6,1,2,7,3,8,4,9,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,1,3,10,9,7,2,4,8,5]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[6,1,3,9,7,2,4,10,8,5]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0,0]
[10,9,6,1,3,7,2,4,8,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,6,1,3,7,2,4,10,8,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[10,7,2,4,9,6,1,3,8,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,1,3,8,4,10,9,7,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0,0]
[6,1,3,10,8,4,9,7,2,5]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[8,4,10,9,6,1,3,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[10,8,4,9,6,1,3,7,2,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,6,1,3,8,4,10,7,2,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[7,2,6,1,3,8,4,10,9,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0,0]
[7,2,6,1,3,10,8,4,9,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[10,7,2,6,1,3,8,4,9,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,2,10,6,1,3,8,4,9,5]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[8,3,6,1,4,10,9,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[10,8,3,6,1,4,9,7,2,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,6,1,4,8,3,7,2,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,6,1,4,10,8,3,7,2,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[8,3,9,6,1,4,10,7,2,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0]
[8,3,7,2,6,1,4,10,9,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[10,8,3,7,2,6,1,4,9,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,3,10,7,2,6,1,4,9,5]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[7,2,8,3,10,6,1,4,9,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0,0]
[9,4,10,8,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[8,3,9,4,10,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]
[7,2,8,3,9,4,10,6,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0]
[10,3,4,1,2,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,8,5,9,6,10,7]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,2,3,4,5,8,6,10,9,7]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,2,3,7,4,8,5,10,9,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,2,3,4,9,7,5,10,8,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,2,3,4,7,5,10,9,8,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,6,2,7,3,8,4,10,9,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,0]
[1,2,6,3,9,7,4,10,8,5]=>[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[1,2,6,3,7,4,10,9,8,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[1,2,3,8,6,4,10,9,7,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,2,3,6,4,10,9,8,7,5]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[5,1,6,2,9,7,3,10,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0,0]
[5,1,6,2,7,3,10,9,8,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,0,0]
[1,5,2,6,3,10,9,8,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]
[1,2,7,5,3,10,9,8,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,2,5,3,10,9,8,7,6,4]=>[1,0,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,4,1,8,5,2,10,9,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,0,0]
[4,1,9,7,5,2,10,8,6,3]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,1,7,5,2,10,9,8,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,1,5,2,10,9,8,7,6,3]=>[1,1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,8,6,4,2,10,9,7,5,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[1,6,4,2,10,9,8,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]
[1,4,2,10,9,8,7,6,5,3]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,5,3,1,10,9,8,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[5,3,1,10,9,8,7,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,2,6,4,8,5,10,7,9]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,3,2,5,4,8,6,10,7,9]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,3,2,5,4,7,6,10,8,9]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,4,2,5,6,7,8,10,9,3]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[2,1,4,5,6,7,10,8,3,9]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[3,1,5,2,6,10,7,8,9,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[4,5,1,6,7,9,8,10,2,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0,0,0]
[7,2,8,3,9,4,10,5,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0]
[7,2,8,3,9,4,10,1,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0]
[7,2,8,3,9,10,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0,0]
[7,2,8,3,9,10,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0,0]
[7,2,8,3,9,10,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0,0]
[7,2,8,9,3,4,10,5,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0]
[7,2,8,9,3,4,10,1,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0]
[7,2,8,9,3,10,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0,0]
[7,2,8,9,3,10,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0,0]
[7,2,8,9,3,10,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0,0]
[7,2,8,9,10,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[7,2,8,9,10,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[7,2,8,9,10,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[7,8,2,3,9,4,10,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,0]
[7,8,2,3,9,4,10,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,0]
[7,8,2,3,9,10,4,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[7,8,2,3,9,10,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[7,8,2,3,9,10,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[7,8,2,9,3,4,10,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,0]
[7,8,2,9,3,4,10,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,0]
[7,8,2,9,3,10,4,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[7,8,2,9,3,10,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[7,8,2,9,3,10,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[7,8,2,9,10,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[7,8,2,9,10,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[7,8,2,9,10,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[7,8,2,9,10,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[7,8,9,2,3,4,10,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[7,8,9,2,3,4,10,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[7,8,9,2,3,10,4,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[7,8,9,2,3,10,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[7,8,9,2,3,10,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[7,8,9,2,10,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[7,8,9,2,10,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[7,8,9,2,10,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[7,8,9,2,10,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[7,8,9,10,2,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,2,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[5,9,8,7,6,4,3,2,1,10]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[10,9,8,6,1,7,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,9,3,4,5,6,7,10,8]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,2,3,4,5,9,6,7,10,8]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,10,6,2,3,4,9,5,7,8]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,5,2,9,3,10,4,6,7,8]=>[1,0,1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,2,4,3,10,9,5,6,7,8]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,2,4,5,10,9,6,7,8]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,4,5,9,6,10,7,8]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[9,8,7,6,5,4,1,10,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[9,8,7,6,5,2,10,1,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[9,8,7,6,3,10,2,1,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[9,8,7,4,10,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[9,8,5,10,4,3,2,1,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[9,6,10,5,4,3,2,1,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[7,10,6,5,4,3,2,1,9,8]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[10,7,8,1,2,3,4,5,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,7,10,1,2,3,4,5,8,9]=>[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]
[10,9,8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,7,6,8,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,7,6,9,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,8,7,6,4,3,2,5,1,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,8,7,6,4,3,5,2,1,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[1,10,9,8,6,5,7,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,9,2,10,8]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[2,4,3,1,5,6,7,8,9,10]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,6,4,5,1,7,8,9,10]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[3,4,5,2,1,6,7,8,9,10]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[2,3,4,8,5,6,7,1,9,10]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[3,5,4,7,2,6,1,8,9,10]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0]
[2,6,4,1,5,3,7,8,9,10]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[4,5,2,6,3,1,7,8,9,10]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0]
[3,6,4,5,9,2,7,8,1,10]=>[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]
[2,5,4,7,8,6,3,1,9,10]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0]
[4,6,2,5,8,3,7,1,9,10]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0]
[3,5,7,6,1,4,2,8,9,10]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0]
[5,6,2,3,7,4,1,8,9,10]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,1,0]
[2,5,4,8,6,10,7,3,9,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,7,2,5,6,10,3,8,9,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]
[2,3,9,5,6,1,7,8,4,10]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,7,2,3,6,9,4,8,1,10]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0,1,0]
[2,8,4,1,6,3,7,5,9,10]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[4,6,7,8,3,1,5,2,9,10]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0,1,0]
[6,7,2,3,4,8,5,1,9,10]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,1,0,1,0]
[3,6,4,10,8,7,1,5,9,2]=>[1,1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[2,7,4,9,6,3,10,8,5,1]=>[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0]
[4,6,8,7,3,9,10,5,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0,0,0]
[6,8,2,3,4,7,10,5,9,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0,0]
[3,5,9,7,1,8,2,6,4,10]=>[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,7,8,3,9,4,1,6,2,10]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0,1,0]
[7,8,2,3,4,5,9,6,1,10]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,1,0]
[4,6,8,10,9,1,5,2,7,3]=>[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[6,8,9,3,4,10,5,1,7,2]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,0]
[8,9,2,3,4,5,6,10,7,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]
[10,1,2,9,6,3,4,5,7,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,1,2,10,3,5,9,6,7,8]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,10,9,8,5,6,7,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,9,5,6,7,8,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,10,4,5,6,7,8,9,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,3,1,2,6,7,8,9,10,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[7,3,4,5,1,2,8,9,10,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]
[8,3,4,5,6,1,2,9,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]
[2,6,7,8,9,10,1,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[10,8,9,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,6,4,9,7,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,6,4,2,1,9,7,5,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,9,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,7,10,8,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,4,3,2,1,5,10,8,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[9,7,5,10,8,6,3,2,1,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[10,8,6,4,9,7,5,2,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,6,4,1,2,9,7,5,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,5,1,6,3,7,4,8,9,10]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,1,0]
[3,4,5,1,6,2,7,8,9,10]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[2,6,1,7,3,8,4,9,5,10]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[3,4,6,1,7,2,8,5,9,10]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[3,2,6,1,7,4,8,5,9,10]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[4,2,5,6,1,7,3,8,9,10]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[3,4,2,6,1,7,5,8,9,10]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[3,2,7,1,8,4,9,5,10,6]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,5,6,7,1,8,2,9,3,10]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0]
[3,4,2,7,1,8,5,9,6,10]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[5,3,6,4,7,1,8,2,9,10]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0]
[3,5,2,6,7,1,8,4,9,10]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0]
[4,3,5,2,7,1,8,6,9,10]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[5,2,6,7,8,1,9,3,10,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0,0]
[5,3,6,4,8,1,9,2,10,7]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,5,2,6,8,1,9,4,10,7]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0]
[4,3,5,2,8,1,9,6,10,7]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[4,6,2,7,5,8,1,9,3,10]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[4,3,6,2,7,8,1,9,5,10]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[4,5,3,6,2,8,1,9,7,10]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[5,3,7,2,8,6,9,1,10,4]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,5,3,7,2,8,9,1,10,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0]
[5,4,6,3,7,2,9,1,10,8]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[8,7,10,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[8,7,6,10,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
[8,7,6,5,4,10,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[8,7,6,5,4,3,10,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]
[5,6,7,8,9,10,1,3,4,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[5,6,7,8,9,10,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[7,8,9,10,1,4,5,6,2,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,1,4,5,6,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,1,5,6,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,10,1,4,5,6,7,2,3]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,1,4,5,6,7,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,1,5,6,7,2,3,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,1,5,6,7,4,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,1,6,7,4,5,2,3]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,1,6,7,4,5,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,1,6,7,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,1,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[9,10,1,6,7,8,3,4,5,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,1,6,7,8,4,5,2,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,1,6,7,8,4,5,3,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,1,6,7,8,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,1,7,8,5,6,3,4,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,1,7,8,5,6,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,1,7,8,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,1,8,9,6,7,4,5,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,8,9,6,7,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,1,8,9,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,10,9,8,7,5,4,3,1,2]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,1,9,10,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[2,3,4,5,1,7,8,9,10,6]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[2,3,1,5,6,7,8,9,10,4]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,5,3,7,6,9,8,1,10]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[4,2,6,3,7,5,9,8,1,10]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[4,2,6,3,8,5,9,7,1,10]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[4,2,6,3,8,5,10,7,1,9]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,2,6,3,8,5,10,7,9,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[4,2,6,3,8,5,7,10,9,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[4,2,6,3,5,8,7,10,9,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[4,2,3,6,5,8,7,10,9,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,4,5,6,7,10,2,1,9,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,5,6,9,2,10,1,8,7]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[3,4,5,8,2,9,10,1,6,7]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,4,7,2,8,9,10,1,6,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[3,6,2,7,8,9,10,1,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]
[5,2,6,7,8,9,10,1,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[9,10,8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,8,7,6,5,4,3,2,9,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,9,4,5,6,7,8,1,10,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[4,3,10,5,6,7,8,9,2,1]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,2,9,5,6,7,8,1,10,4]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[8,9,4,5,6,7,1,3,10,2]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]
[3,4,1,10,6,7,8,9,2,5]=>[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,9,10,5,6,7,8,2,1,3]=>[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[5,6,7,8,9,10,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[7,8,9,10,3,4,5,1,2,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,3,4,5,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,4,5,2,3,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,4,5,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,10,3,4,5,6,1,2,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,3,4,5,6,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,4,5,6,1,2,3,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,4,5,6,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,3,4,1,2,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,3,4,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,5,6,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[9,10,5,6,7,2,3,4,1,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,5,6,7,3,4,1,2,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,5,6,7,3,4,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,5,6,7,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,6,7,4,5,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,6,7,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[10,7,8,5,6,3,4,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,8,5,6,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,8,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,1,2,3,7,8,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,1,2,8,7,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,8,1,10,7,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[8,6,1,2,3,4,5,9,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]
[5,7,1,2,3,4,8,9,10,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[10,4,1,2,3,7,8,9,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,3,1,2,9,7,8,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,9,1,10,8,7,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[4,2,6,1,3,5,8,7,10,9]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[4,2,6,1,8,3,5,7,10,9]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[4,2,6,1,8,3,10,5,7,9]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[10,7,1,8,2,9,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,7,1,10,8,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[10,9,7,1,8,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,6,1,7,2,8,3,9,4,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,6,1,10,7,2,8,3,4,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[10,9,6,1,7,2,8,3,4,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,6,1,9,7,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,6,1,7,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,5,1,10,6,2,7,3,8,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[10,9,5,1,6,2,7,3,8,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,5,1,9,6,2,10,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0]
[10,8,5,1,9,6,2,7,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,5,1,6,2,7,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,7,5,1,10,8,6,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[10,9,7,5,1,8,6,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,5,1,6,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,7,4,1,10,8,5,2,6,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[10,9,7,4,1,8,5,2,6,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,4,1,5,2,6,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,8,6,4,1,9,7,5,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,6,4,1,7,5,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,4,1,5,2,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,7,5,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,10,6,7,8,9,1,5]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,10,5,6,7,8,9,1,4]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,10,1,9,7,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,5,10,1,8,9,6,7]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,10,1,6,7,8,9,4,5]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,2,6,5,8,7,10,9,3]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,5,2,6,4,8,7,10,9,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]
[1,5,2,7,4,8,6,10,9,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0]
[1,5,2,7,4,9,6,10,8,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[1,5,2,7,4,9,6,8,10,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]
[1,5,2,7,4,6,9,8,10,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0]
[1,5,2,4,7,6,9,8,10,3]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[1,2,5,4,7,6,9,8,10,3]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[9,10,7,8,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,8,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,5,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,5,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,5,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,5,8,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,5,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,5,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,5,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,7,5,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,7,10,8,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,8,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,8,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,8,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,5,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,5,8,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,5,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,5,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,5,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,10,5,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[9,7,5,10,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[9,7,5,10,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[9,7,5,10,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[9,7,5,10,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[9,7,5,10,8,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[9,7,5,10,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[9,7,5,10,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[9,7,5,10,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[9,7,5,10,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[9,7,5,3,10,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[9,7,5,3,10,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[9,7,5,3,10,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[9,7,5,3,10,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[3,4,5,6,7,9,10,8,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,5,6,8,9,10,7,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[3,4,6,7,8,9,10,5,1,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,5,6,7,8,9,10,4,1,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,4,5,6,7,10,1,8,9,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[3,4,5,6,9,1,10,8,7,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[3,4,5,8,1,9,10,7,6,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,4,7,1,8,9,10,5,6,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[3,6,1,7,8,9,10,5,4,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]
[5,1,6,7,8,9,10,4,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[6,10,5,1,2,3,4,7,8,9]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10,5,4,1,2,3,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,3,4,5,6,8,7,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,4,3,5,6,7,8,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,3,4,5,6,7,9,8,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,4,3,5,6,7,8,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,7,5,6,8,4,9,3,10,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]
[1,2,3,4,5,8,6,9,7,10]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,2,3,4,5,9,6,10,7,8]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[10,8,7,6,5,4,3,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,7,6,5,4,8,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,9,11,10]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,3,4,5,6,7,8,9,10,11]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[11,1,2,3,4,5,6,7,8,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,4,5,6,7,8,11,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
[11,1,2,3,4,5,6,7,10,8,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,1,2,3,4,5,6,10,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,4,5,11,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0]
[11,1,2,3,4,10,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,1,2,3,10,4,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,1,2,11,3,4,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]
[11,1,10,2,3,4,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,10,1,2,3,4,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[1,11,10,9,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,10,11,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,5,6,7,8,9,11,1,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[3,1,4,5,6,7,8,9,10,11,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[11,3,4,5,6,7,8,9,1,2,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,1,4,5,6,7,8,9,10,2,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,4,5,6,7,8,9,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[1,11,2,3,4,5,6,7,8,9,10]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,4,3,1,11,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
[9,11,8,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,9,8,7,6,5,4,3,11,10,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[1,11,8,7,6,5,4,3,2,10,9]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,11,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[11,10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,10,1,11]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,3,4,5,6,7,8,9,10,11,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,11,1,3,4,5,6,7,8,9,10]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[11,3,1,2,4,5,6,7,8,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,4,1,2,3,5,6,7,8,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[5,11,1,2,3,4,6,7,8,9,10]=>[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[11,6,1,2,3,4,5,7,8,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,7,1,2,3,4,5,6,8,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,11,1,2,3,4,5,6,7,9,10]=>[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
[11,9,1,2,3,4,5,6,7,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,9,8,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,4,3,2,11,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
[9,8,10,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]
[9,8,7,10,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,1,0]
[9,8,7,6,11,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0]
[9,8,7,6,5,10,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,1,0]
[9,8,7,6,5,4,10,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0]
[9,8,7,6,5,4,3,11,2,1,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0]
[9,8,7,6,5,4,3,2,10,1,11]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0]
[9,8,7,6,5,4,3,2,1,10,11]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
[3,4,5,6,7,8,9,10,11,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[10,1,11,9,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[2,11,10,9,8,7,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,2,1,9,8,7,6,5,4,3,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[3,2,10,9,8,7,6,5,4,1,11]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[2,11,10,9,8,7,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[11,1,10,9,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,11,10,9,8,7,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,11,10,9,8,7,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,11,10,9,8,7,1,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,11,10,9,8,2,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,11,10,9,2,8,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,11,10,1,9,8,7,6,5,4,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,11,2,10,9,8,7,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,11,10,9,8,7,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,7,8,9,10,1,2,3,4,5,11]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]
[1,7,8,9,10,11,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[2,4,1,5,6,7,8,9,10,11,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,5,6,7,8,10,1,11,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[2,3,5,1,6,7,8,9,10,11,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,5,6,7,9,1,10,11,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[2,3,4,6,1,7,8,9,10,11,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,5,6,8,1,9,10,11,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[2,3,4,5,7,1,8,9,10,11,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,2,3,4,6,8,5,7,10,9,11]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,2,3,4,7,5,8,6,10,9,11]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,1,11,10,9,8,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,10,11,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[2,4,1,3,6,5,8,7,10,9,11]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[11,3,4,5,6,7,8,9,10,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,3,4,5,6,7,8,9,1,11,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
[9,3,4,5,6,7,8,1,10,11,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0]
[8,3,4,5,6,7,1,9,10,11,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,0]
[7,3,4,5,6,1,8,9,10,11,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0]
[6,3,4,5,1,7,8,9,10,11,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,3,4,1,6,7,8,9,10,11,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,1,5,6,7,8,9,10,11,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,11,4,5,6,7,8,9,10,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,9,4,5,6,7,8,1,2,11,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
[2,11,10,5,6,7,8,9,1,3,4]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[11,2,3,4,5,6,7,8,9,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,9,11,10,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[1,8,11,10,9,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,11,10,9,8,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,6,11,10,9,8,7,5,4,3,2]=>[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,5,11,10,9,8,7,6,4,3,2]=>[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[4,1,11,10,9,8,7,6,5,3,2]=>[1,1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,3,11,10,9,8,7,6,5,4,2]=>[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10,9,1,2,3,4,5,6,7,11,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
[2,11,10,1,3,4,5,6,7,8,9]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,4,1,6,3,5,8,7,10,9,11]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[10,1,2,3,4,5,6,7,11,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]
[1,11,2,3,4,5,6,7,8,10,9]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,11,3,4,5,6,7,8,10,9]=>[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,10,4,5,6,7,11,8,9]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,2,3,4,11,5,6,7,8,10,9]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,5,11,6,7,8,10,9]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,3,4,5,6,10,7,11,8,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,2,3,4,5,6,7,11,8,10,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,3,4,5,6,7,8,11,10,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,3,4,5,6,7,8,11,9,10]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[11,1,3,4,5,6,7,8,9,10,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,2,3,4,5,6,7,8,11,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]
[10,11,3,4,5,6,7,8,9,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[7,1,2,3,4,5,11,6,8,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[11,1,2,3,4,5,8,6,7,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,1,2,3,4,5,9,6,7,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,10,5,1,2,3,4,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,10,1,5,2,3,4,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[5,11,1,2,10,3,4,6,7,8,9]=>[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,11,1,2,3,10,4,6,7,8,9]=>[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,10,11,1,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[2,4,5,6,7,8,9,10,11,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[3,4,5,6,7,8,9,10,11,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[10,11,1,9,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,9,10,11]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,4,2,6,5,8,7,10,9,11]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,2,3,4,5,6,7,8,10,9,11]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[11,2,3,4,5,6,7,8,9,1,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,11,1,4,5,6,7,8,9,10,2]=>[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,1,11,3,4,5,6,7,8,2,10]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,11,10,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[3,1,11,5,6,7,8,9,10,2,4]=>[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,1,4,5,6,7,8,9,10,11]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,2,4,5,6,7,8,9,10,11]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,5,6,7,8,9,10,1,2,11]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[3,4,5,6,7,9,10,11,1,2,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[3,4,6,7,8,9,10,11,1,2,5]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[11,1,10,5,6,7,8,9,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,1,11,9,6,7,8,2,3,4,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[9,1,10,11,8,7,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0]
[8,1,9,10,11,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[11,1,10,9,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,4,3,2,1,11,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]
[2,3,4,5,6,7,10,9,11,8,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[2,3,4,5,6,10,8,9,11,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[2,3,4,5,10,7,8,9,11,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[2,3,4,10,6,7,8,9,11,5,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[2,3,10,5,6,7,8,9,11,4,1]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[2,10,4,5,6,7,8,9,11,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[10,3,4,5,6,7,8,9,11,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]
[1,3,2,5,4,7,6,9,8,11,10]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[10,9,11,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,9,10,1,11,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[6,5,7,4,8,3,9,2,10,1,11]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[1,7,6,8,5,9,4,10,3,11,2]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[2,3,4,5,6,7,8,11,10,1,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[11,3,4,5,6,7,8,10,1,2,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,2,4,5,6,7,8,9,10,11,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,4,5,6,7,8,1,9,2,11,10]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[1,4,5,6,7,11,8,9,2,10,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[8,9,10,7,6,1,2,3,4,11,5]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0,0]
[2,9,10,11,8,7,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[7,8,9,10,1,2,3,4,5,11,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0,0]
[2,8,9,10,11,1,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,11,1,9,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,4,5,6,7,11,1,8,9,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,5,6,11,1,7,8,9,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,5,11,1,6,7,8,9,10]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,11,1,5,6,7,8,9,10]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,11,1,4,5,6,7,8,9,10]=>[1,1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,1,4,5,6,7,8,9,11,2,10]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[2,11,1,3,4,5,6,7,10,8,9]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,10,1,3,4,5,6,7,8,11,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[11,2,1,3,4,5,6,7,8,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,10,2,3,4,5,6,7,8,9,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,3,4,5,6,7,8,9,10,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,10,9,8,6,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,1,2,3,4,5,6,10,8,7,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,1,2,3,4,5,10,7,8,6,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,4,11,6,7,8,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]
[11,1,2,3,10,5,6,7,8,4,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,1,2,10,4,5,6,7,8,3,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,1,11,3,4,5,6,7,8,2,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[11,10,2,3,4,5,6,7,8,1,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,10,2,1,4,5,6,7,8,9,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,11,8,1,2,3,4,5,6,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[6,7,5,4,3,2,1,8,9,10,11]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[7,6,5,4,3,1,2,8,9,10,11]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[11,10,9,8,5,7,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,10,9,8,6,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,9,1,2,3,4,5,6,10,11,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0,0]
[2,3,4,5,6,7,8,9,1,11,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[3,4,1,5,6,7,8,9,10,11,2]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,3,4,5,6,7,8,9,11,2,10]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,4,2,5,6,7,8,9,11,10,3]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,2,10,3,4,5,6,7,8,11,9]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[1,2,3,4,5,10,6,7,8,11,9]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[10,9,8,7,6,5,4,2,1,3,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,9,8,7,6,5,3,2,1,4,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,9,8,7,6,4,3,2,1,11,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
[10,9,8,7,5,4,3,2,1,6,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,9,8,6,5,4,3,2,1,7,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,9,7,6,5,4,3,2,1,11,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
[10,8,7,6,5,4,3,2,1,9,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[11,9,10,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,8,11,9,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[10,8,6,5,4,3,2,1,11,9,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]
[10,8,6,11,9,7,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,10,8,6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,9,7,5,3,2,1,10,8,6,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,9,7,5,3,10,8,6,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[10,8,6,4,2,11,9,7,5,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]
[3,4,5,6,7,8,9,11,1,10,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[3,4,5,6,7,8,10,11,1,9,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,5,6,8,9,10,11,1,7,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[3,4,5,7,8,9,10,11,1,6,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,5,6,7,8,9,10,11,1,4,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,8,9,10,11,1,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[10,2,3,4,5,6,7,8,9,11,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
[2,10,4,5,6,7,8,9,1,11,3]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[4,3,11,5,6,7,8,9,10,2,1]=>[1,1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,11,1,2,3,4,5,9,10,6,7]=>[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,11,1,2,3,4,8,9,5,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[10,11,1,2,3,9,8,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[10,9,1,2,11,8,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0]
[9,8,1,10,11,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0]
[11,8,9,10,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,11,9,10,1,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,5,6,11,8,9,10,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,5,11,7,8,9,10,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,11,6,7,8,9,10,1,5]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,11,5,6,7,8,9,10,1,4]=>[1,1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,6,7,8,10,11,9,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[3,4,5,6,7,9,10,11,8,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[3,4,5,7,8,9,10,11,6,1,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,4,6,7,8,9,10,11,5,1,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,8,9,10,11,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[4,5,6,7,8,9,10,11,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[11,10,3,4,5,6,7,9,8,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,10,4,3,5,6,7,8,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,10,9,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,4,3,6,5,8,7,12,11,10,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,4,3,6,5,10,9,8,7,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,4,3,6,5,12,9,8,11,10,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,6,5,12,11,10,9,8,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,8,7,6,5,10,9,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,4,3,8,7,6,5,12,11,10,9]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,4,3,10,7,6,9,8,5,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,4,3,12,7,6,9,8,11,10,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,12,7,6,11,10,9,8,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,10,9,8,7,6,5,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,4,3,12,9,8,7,6,11,10,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,12,11,8,7,10,9,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,12,11,10,9,8,7,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,5,4,3,8,7,10,9,12,11]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,6,5,4,3,8,7,12,11,10,9]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,6,5,4,3,10,9,8,7,12,11]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,6,5,4,3,12,9,8,11,10,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,5,4,3,12,11,10,9,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,5,4,7,6,3,10,9,12,11]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,8,5,4,7,6,3,12,11,10,9]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,10,5,4,7,6,9,8,3,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,5,4,7,6,9,8,11,10,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,5,4,7,6,11,10,9,8,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,5,4,9,8,7,6,3,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,5,4,9,8,7,6,11,10,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,5,4,11,8,7,10,9,6,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,5,4,11,10,9,8,7,6,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,8,7,6,5,4,3,10,9,12,11]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,8,7,6,5,4,3,12,11,10,9]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,10,7,6,5,4,9,8,3,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,7,6,5,4,9,8,11,10,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,7,6,5,4,11,10,9,8,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,9,6,5,8,7,4,3,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,9,6,5,8,7,4,11,10,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,11,6,5,8,7,10,9,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,11,6,5,10,9,8,7,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,9,8,7,6,5,4,3,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,9,8,7,6,5,4,11,10,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,11,8,7,6,5,10,9,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,11,10,7,6,9,8,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,11,10,9,8,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,3,2,1,6,5,8,7,10,9,12,11]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,3,2,1,6,5,8,7,12,11,10,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[4,3,2,1,6,5,10,9,8,7,12,11]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[4,3,2,1,6,5,12,9,8,11,10,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,1,6,5,12,11,10,9,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,2,1,8,7,6,5,10,9,12,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[4,3,2,1,8,7,6,5,12,11,10,9]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,3,2,1,10,7,6,9,8,5,12,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,3,2,1,12,7,6,9,8,11,10,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,12,7,6,11,10,9,8,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,10,9,8,7,6,5,12,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,3,2,1,12,9,8,7,6,11,10,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,12,11,8,7,10,9,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,3,2,1,12,11,10,9,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,3,2,5,4,1,8,7,10,9,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[6,3,2,5,4,1,8,7,12,11,10,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[6,3,2,5,4,1,10,9,8,7,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[6,3,2,5,4,1,12,9,8,11,10,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,2,5,4,1,12,11,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,3,2,5,4,7,6,1,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,3,2,5,4,7,6,1,12,11,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,3,2,5,4,7,6,9,8,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,3,2,5,4,7,6,9,8,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,3,2,5,4,7,6,11,10,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,3,2,5,4,9,8,7,6,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,3,2,5,4,9,8,7,6,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,3,2,5,4,11,8,7,10,9,6,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,3,2,5,4,11,10,9,8,7,6,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,3,2,7,6,5,4,1,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,3,2,7,6,5,4,1,12,11,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,3,2,7,6,5,4,9,8,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,3,2,7,6,5,4,9,8,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,3,2,7,6,5,4,11,10,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,3,2,9,6,5,8,7,4,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,3,2,9,6,5,8,7,4,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,3,2,11,6,5,8,7,10,9,4,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,3,2,11,6,5,10,9,8,7,4,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,3,2,9,8,7,6,5,4,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,3,2,9,8,7,6,5,4,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,3,2,11,8,7,6,5,10,9,4,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,3,2,11,10,7,6,9,8,5,4,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,3,2,11,10,9,8,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[6,5,4,3,2,1,8,7,10,9,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[6,5,4,3,2,1,8,7,12,11,10,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[6,5,4,3,2,1,10,9,8,7,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[6,5,4,3,2,1,12,9,8,11,10,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,4,3,2,1,12,11,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,5,4,3,2,7,6,1,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,5,4,3,2,7,6,1,12,11,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,5,4,3,2,7,6,9,8,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,5,4,3,2,7,6,9,8,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,4,3,2,7,6,11,10,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,5,4,3,2,9,8,7,6,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,5,4,3,2,9,8,7,6,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,4,3,2,11,8,7,10,9,6,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,4,3,2,11,10,9,8,7,6,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,7,4,3,6,5,2,1,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,7,4,3,6,5,2,1,12,11,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,7,4,3,6,5,2,9,8,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,7,4,3,6,5,2,9,8,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,4,3,6,5,2,11,10,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,4,3,6,5,8,7,2,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,9,4,3,6,5,8,7,2,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,4,3,6,5,8,7,10,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,4,3,6,5,10,9,8,7,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,4,3,8,7,6,5,2,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,9,4,3,8,7,6,5,2,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,4,3,8,7,6,5,10,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,4,3,10,7,6,9,8,5,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,4,3,10,9,8,7,6,5,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,2,1,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,7,6,5,4,3,2,1,12,11,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,7,6,5,4,3,2,9,8,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,7,6,5,4,3,2,9,8,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,6,5,4,3,2,11,10,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,6,5,4,3,8,7,2,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,9,6,5,4,3,8,7,2,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,6,5,4,3,8,7,10,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,6,5,4,3,10,9,8,7,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,8,5,4,7,6,3,2,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,9,8,5,4,7,6,3,2,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,8,5,4,7,6,3,10,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,5,4,7,6,9,8,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,5,4,9,8,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,4,3,2,1,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,9,8,7,6,5,4,3,2,11,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,8,7,6,5,4,3,10,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,7,6,5,4,9,8,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,6,5,8,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,4,6,8,10,12,1,3,5,7,9,11]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[2,4,6,8,11,12,1,3,5,7,9,10]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[2,4,6,9,10,12,1,3,5,7,8,11]=>[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[2,4,6,9,11,12,1,3,5,7,8,10]=>[1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[2,4,6,10,11,12,1,3,5,7,8,9]=>[1,1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[2,4,7,8,10,12,1,3,5,6,9,11]=>[1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[2,4,7,8,11,12,1,3,5,6,9,10]=>[1,1,0,1,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[2,4,7,9,10,12,1,3,5,6,8,11]=>[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[2,4,7,9,11,12,1,3,5,6,8,10]=>[1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[2,4,7,10,11,12,1,3,5,6,8,9]=>[1,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[2,4,8,9,10,12,1,3,5,6,7,11]=>[1,1,0,1,1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[2,4,8,9,11,12,1,3,5,6,7,10]=>[1,1,0,1,1,0,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[2,4,8,10,11,12,1,3,5,6,7,9]=>[1,1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[2,4,9,10,11,12,1,3,5,6,7,8]=>[1,1,0,1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[2,5,6,8,10,12,1,3,4,7,9,11]=>[1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[2,5,6,8,11,12,1,3,4,7,9,10]=>[1,1,0,1,1,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[2,5,6,9,10,12,1,3,4,7,8,11]=>[1,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[2,5,6,9,11,12,1,3,4,7,8,10]=>[1,1,0,1,1,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[2,5,6,10,11,12,1,3,4,7,8,9]=>[1,1,0,1,1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[2,5,7,8,10,12,1,3,4,6,9,11]=>[1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[2,5,7,8,11,12,1,3,4,6,9,10]=>[1,1,0,1,1,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[2,5,7,9,10,12,1,3,4,6,8,11]=>[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[2,5,7,9,11,12,1,3,4,6,8,10]=>[1,1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[2,5,7,10,11,12,1,3,4,6,8,9]=>[1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[2,5,8,9,10,12,1,3,4,6,7,11]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[2,5,8,9,11,12,1,3,4,6,7,10]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[2,5,8,10,11,12,1,3,4,6,7,9]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[2,5,9,10,11,12,1,3,4,6,7,8]=>[1,1,0,1,1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[2,6,7,8,10,12,1,3,4,5,9,11]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[2,6,7,8,11,12,1,3,4,5,9,10]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[2,6,7,9,10,12,1,3,4,5,8,11]=>[1,1,0,1,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[2,6,7,9,11,12,1,3,4,5,8,10]=>[1,1,0,1,1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[2,6,7,10,11,12,1,3,4,5,8,9]=>[1,1,0,1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[2,6,8,9,10,12,1,3,4,5,7,11]=>[1,1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[2,6,8,9,11,12,1,3,4,5,7,10]=>[1,1,0,1,1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[2,6,8,10,11,12,1,3,4,5,7,9]=>[1,1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[2,6,9,10,11,12,1,3,4,5,7,8]=>[1,1,0,1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[2,7,8,9,10,12,1,3,4,5,6,11]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[2,7,8,9,11,12,1,3,4,5,6,10]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[2,7,8,10,11,12,1,3,4,5,6,9]=>[1,1,0,1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[2,7,9,10,11,12,1,3,4,5,6,8]=>[1,1,0,1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[2,8,9,10,11,12,1,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[3,4,6,8,10,12,1,2,5,7,9,11]=>[1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[3,4,6,8,11,12,1,2,5,7,9,10]=>[1,1,1,0,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[3,4,6,9,10,12,1,2,5,7,8,11]=>[1,1,1,0,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[3,4,6,9,11,12,1,2,5,7,8,10]=>[1,1,1,0,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[3,4,6,10,11,12,1,2,5,7,8,9]=>[1,1,1,0,1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[3,4,7,8,10,12,1,2,5,6,9,11]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[3,4,7,8,11,12,1,2,5,6,9,10]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[3,4,7,9,10,12,1,2,5,6,8,11]=>[1,1,1,0,1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[3,4,7,9,11,12,1,2,5,6,8,10]=>[1,1,1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[3,4,7,10,11,12,1,2,5,6,8,9]=>[1,1,1,0,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[3,4,8,9,10,12,1,2,5,6,7,11]=>[1,1,1,0,1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[3,4,8,9,11,12,1,2,5,6,7,10]=>[1,1,1,0,1,0,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[3,4,8,10,11,12,1,2,5,6,7,9]=>[1,1,1,0,1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[3,4,9,10,11,12,1,2,5,6,7,8]=>[1,1,1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[3,5,6,8,10,12,1,2,4,7,9,11]=>[1,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[3,5,6,8,11,12,1,2,4,7,9,10]=>[1,1,1,0,1,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[3,5,6,9,10,12,1,2,4,7,8,11]=>[1,1,1,0,1,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[3,5,6,9,11,12,1,2,4,7,8,10]=>[1,1,1,0,1,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[3,5,6,10,11,12,1,2,4,7,8,9]=>[1,1,1,0,1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[3,5,7,8,10,12,1,2,4,6,9,11]=>[1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[3,5,7,8,11,12,1,2,4,6,9,10]=>[1,1,1,0,1,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[3,5,7,9,10,12,1,2,4,6,8,11]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[3,5,7,9,11,12,1,2,4,6,8,10]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[3,5,7,10,11,12,1,2,4,6,8,9]=>[1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[3,5,8,9,10,12,1,2,4,6,7,11]=>[1,1,1,0,1,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[3,5,8,9,11,12,1,2,4,6,7,10]=>[1,1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[3,5,8,10,11,12,1,2,4,6,7,9]=>[1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[3,5,9,10,11,12,1,2,4,6,7,8]=>[1,1,1,0,1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[3,6,7,8,10,12,1,2,4,5,9,11]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[3,6,7,8,11,12,1,2,4,5,9,10]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[3,6,7,9,10,12,1,2,4,5,8,11]=>[1,1,1,0,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[3,6,7,9,11,12,1,2,4,5,8,10]=>[1,1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[3,6,7,10,11,12,1,2,4,5,8,9]=>[1,1,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[3,6,8,9,10,12,1,2,4,5,7,11]=>[1,1,1,0,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[3,6,8,9,11,12,1,2,4,5,7,10]=>[1,1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[3,6,8,10,11,12,1,2,4,5,7,9]=>[1,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[3,6,9,10,11,12,1,2,4,5,7,8]=>[1,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[3,7,8,9,10,12,1,2,4,5,6,11]=>[1,1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[3,7,8,9,11,12,1,2,4,5,6,10]=>[1,1,1,0,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[3,7,8,10,11,12,1,2,4,5,6,9]=>[1,1,1,0,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[3,7,9,10,11,12,1,2,4,5,6,8]=>[1,1,1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[3,8,9,10,11,12,1,2,4,5,6,7]=>[1,1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[4,5,6,8,10,12,1,2,3,7,9,11]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[4,5,6,8,11,12,1,2,3,7,9,10]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[4,5,6,9,10,12,1,2,3,7,8,11]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[4,5,6,9,11,12,1,2,3,7,8,10]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[4,5,6,10,11,12,1,2,3,7,8,9]=>[1,1,1,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[4,5,7,8,10,12,1,2,3,6,9,11]=>[1,1,1,1,0,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[4,5,7,8,11,12,1,2,3,6,9,10]=>[1,1,1,1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[4,5,7,9,10,12,1,2,3,6,8,11]=>[1,1,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[4,5,7,9,11,12,1,2,3,6,8,10]=>[1,1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[4,5,7,10,11,12,1,2,3,6,8,9]=>[1,1,1,1,0,1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[4,5,8,9,10,12,1,2,3,6,7,11]=>[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[4,5,8,9,11,12,1,2,3,6,7,10]=>[1,1,1,1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[4,5,8,10,11,12,1,2,3,6,7,9]=>[1,1,1,1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[4,5,9,10,11,12,1,2,3,6,7,8]=>[1,1,1,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[4,6,7,8,10,12,1,2,3,5,9,11]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[4,6,7,8,11,12,1,2,3,5,9,10]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[4,6,7,9,10,12,1,2,3,5,8,11]=>[1,1,1,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[4,6,7,9,11,12,1,2,3,5,8,10]=>[1,1,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[4,6,7,10,11,12,1,2,3,5,8,9]=>[1,1,1,1,0,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[4,6,8,9,10,12,1,2,3,5,7,11]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[4,6,8,9,11,12,1,2,3,5,7,10]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[4,6,8,10,11,12,1,2,3,5,7,9]=>[1,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[4,6,9,10,11,12,1,2,3,5,7,8]=>[1,1,1,1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[4,7,8,9,10,12,1,2,3,5,6,11]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[4,7,8,9,11,12,1,2,3,5,6,10]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[4,7,8,10,11,12,1,2,3,5,6,9]=>[1,1,1,1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[4,7,9,10,11,12,1,2,3,5,6,8]=>[1,1,1,1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[4,8,9,10,11,12,1,2,3,5,6,7]=>[1,1,1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[5,6,7,8,10,12,1,2,3,4,9,11]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[5,6,7,8,11,12,1,2,3,4,9,10]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[5,6,7,9,10,12,1,2,3,4,8,11]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[5,6,7,9,11,12,1,2,3,4,8,10]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[5,6,7,10,11,12,1,2,3,4,8,9]=>[1,1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[5,6,8,9,10,12,1,2,3,4,7,11]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[5,6,8,9,11,12,1,2,3,4,7,10]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[5,6,8,10,11,12,1,2,3,4,7,9]=>[1,1,1,1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[5,6,9,10,11,12,1,2,3,4,7,8]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[5,7,8,9,10,12,1,2,3,4,6,11]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[5,7,8,9,11,12,1,2,3,4,6,10]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[5,7,8,10,11,12,1,2,3,4,6,9]=>[1,1,1,1,1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[5,7,9,10,11,12,1,2,3,4,6,8]=>[1,1,1,1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[5,8,9,10,11,12,1,2,3,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[6,7,8,9,10,12,1,2,3,4,5,11]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]
[6,7,8,9,11,12,1,2,3,4,5,10]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]
[6,7,8,10,11,12,1,2,3,4,5,9]=>[1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[6,7,9,10,11,12,1,2,3,4,5,8]=>[1,1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[6,8,9,10,11,12,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,10,11,12,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,10,12,1,11]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[3,1,4,5,6,7,8,9,10,11,12,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,4,3,6,5,8,7,11,12,10,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,4,3,6,5,9,10,8,7,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[2,1,4,3,6,5,9,11,8,12,10,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[2,1,4,3,6,5,10,11,12,9,8,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,4,3,7,8,6,5,10,9,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,4,3,7,8,6,5,11,12,10,9]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[2,1,4,3,7,9,6,10,8,5,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[2,1,4,3,7,9,6,11,8,12,10,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[2,1,4,3,7,10,6,11,12,9,8,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[2,1,4,3,8,9,10,7,6,5,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[2,1,4,3,8,9,11,7,6,12,10,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[2,1,4,3,8,10,11,7,12,9,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[2,1,4,3,9,10,11,12,8,7,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[2,1,5,6,4,3,8,7,10,9,12,11]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,5,6,4,3,8,7,11,12,10,9]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,5,6,4,3,9,10,8,7,12,11]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[2,1,5,6,4,3,9,11,8,12,10,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[2,1,5,6,4,3,10,11,12,9,8,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,5,7,4,8,6,3,10,9,12,11]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,5,7,4,8,6,3,11,12,10,9]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0]
[2,1,5,7,4,9,6,10,8,3,12,11]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0]
[2,1,5,7,4,9,6,11,8,12,10,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[2,1,5,7,4,10,6,11,12,9,8,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0]
[2,1,5,8,4,9,10,7,6,3,12,11]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]
[2,1,5,8,4,9,11,7,6,12,10,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]
[2,1,5,8,4,10,11,7,12,9,6,3]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]
[2,1,5,9,4,10,11,12,8,7,6,3]=>[1,1,0,0,1,1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]
[2,1,6,7,8,5,4,3,10,9,12,11]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,6,7,8,5,4,3,11,12,10,9]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]
[2,1,6,7,9,5,4,10,8,3,12,11]=>[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]
[2,1,6,7,9,5,4,11,8,12,10,3]=>[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[2,1,6,7,10,5,4,11,12,9,8,3]=>[1,1,0,0,1,1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]
[2,1,6,8,9,5,10,7,4,3,12,11]=>[1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0]
[2,1,6,8,9,5,11,7,4,12,10,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]
[2,1,6,8,10,5,11,7,12,9,4,3]=>[1,1,0,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0]
[2,1,6,9,10,5,11,12,8,7,4,3]=>[1,1,0,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]
[2,1,7,8,9,10,6,5,4,3,12,11]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,1,0,0]
[2,1,7,8,9,11,6,5,4,12,10,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0,0]
[2,1,7,8,10,11,6,5,12,9,4,3]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0,0,0]
[2,1,7,9,10,11,6,12,8,5,4,3]=>[1,1,0,0,1,1,1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[2,1,8,9,10,11,12,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[3,4,2,1,6,5,8,7,10,9,12,11]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,4,2,1,6,5,8,7,11,12,10,9]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[3,4,2,1,6,5,9,10,8,7,12,11]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[3,4,2,1,6,5,9,11,8,12,10,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[3,4,2,1,6,5,10,11,12,9,8,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,4,2,1,7,8,6,5,10,9,12,11]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[3,4,2,1,7,8,6,5,11,12,10,9]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[3,4,2,1,7,9,6,10,8,5,12,11]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[3,4,2,1,7,9,6,11,8,12,10,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[3,4,2,1,7,10,6,11,12,9,8,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,4,2,1,8,9,10,7,6,5,12,11]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[3,4,2,1,8,9,11,7,6,12,10,5]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[3,4,2,1,8,10,11,7,12,9,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[3,4,2,1,9,10,11,12,8,7,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[3,5,2,6,4,1,8,7,10,9,12,11]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,5,2,6,4,1,8,7,11,12,10,9]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[3,5,2,6,4,1,9,10,8,7,12,11]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[3,5,2,6,4,1,9,11,8,12,10,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[3,5,2,6,4,1,10,11,12,9,8,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,5,2,7,4,8,6,1,10,9,12,11]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]
[3,5,2,7,4,8,6,1,11,12,10,9]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0]
[3,5,2,7,4,9,6,10,8,1,12,11]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0]
[3,5,2,7,4,9,6,11,8,12,10,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[3,5,2,7,4,10,6,11,12,9,8,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,5,2,8,4,9,10,7,6,1,12,11]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]
[3,5,2,8,4,9,11,7,6,12,10,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]
[3,5,2,8,4,10,11,7,12,9,6,1]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]
[3,5,2,9,4,10,11,12,8,7,6,1]=>[1,1,1,0,1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]
[3,6,2,7,8,5,4,1,10,9,12,11]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0]
[3,6,2,7,8,5,4,1,11,12,10,9]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]
[3,6,2,7,9,5,4,10,8,1,12,11]=>[1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]
[3,6,2,7,9,5,4,11,8,12,10,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[3,6,2,7,10,5,4,11,12,9,8,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]
[3,6,2,8,9,5,10,7,4,1,12,11]=>[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0]
[3,6,2,8,9,5,11,7,4,12,10,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]
[3,6,2,8,10,5,11,7,12,9,4,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0]
[3,6,2,9,10,5,11,12,8,7,4,1]=>[1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]
[3,7,2,8,9,10,6,5,4,1,12,11]=>[1,1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,1,1,0,0]
[3,7,2,8,9,11,6,5,4,12,10,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,1,0,0,0]
[3,7,2,8,10,11,6,5,12,9,4,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,0,0,0]
[3,7,2,9,10,11,6,12,8,5,4,1]=>[1,1,1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[3,8,2,9,10,11,12,7,6,5,4,1]=>[1,1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[4,5,6,3,2,1,8,7,10,9,12,11]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,5,6,3,2,1,8,7,11,12,10,9]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[4,5,6,3,2,1,9,10,8,7,12,11]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[4,5,6,3,2,1,9,11,8,12,10,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[4,5,6,3,2,1,10,11,12,9,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[4,5,7,3,2,8,6,1,10,9,12,11]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0]
[4,5,7,3,2,8,6,1,11,12,10,9]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,1,0,1,0,0,0]
[4,5,7,3,2,9,6,10,8,1,12,11]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,1,0,0]
[4,5,7,3,2,9,6,11,8,12,10,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[4,5,7,3,2,10,6,11,12,9,8,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,0]
[4,5,8,3,2,9,10,7,6,1,12,11]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0,1,1,0,0]
[4,5,8,3,2,9,11,7,6,12,10,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,0]
[4,5,8,3,2,10,11,7,12,9,6,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0,0]
[4,5,9,3,2,10,11,12,8,7,6,1]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0]
[4,6,7,3,8,5,2,1,10,9,12,11]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0,1,1,0,0]
[4,6,7,3,8,5,2,1,11,12,10,9]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,1,1,0,1,0,0,0]
[4,6,7,3,9,5,2,10,8,1,12,11]=>[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0,1,1,0,0]
[4,6,7,3,9,5,2,11,8,12,10,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[4,6,7,3,10,5,2,11,12,9,8,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,0]
[4,6,8,3,9,5,10,7,2,1,12,11]=>[1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0,1,1,0,0]
[4,6,8,3,9,5,11,7,2,12,10,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]
[4,6,8,3,10,5,11,7,12,9,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,0,0]
[4,6,9,3,10,5,11,12,8,7,2,1]=>[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0,0]
[4,7,8,3,9,10,6,5,2,1,12,11]=>[1,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,1,1,0,0]
[4,7,8,3,9,11,6,5,2,12,10,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0,1,0,0,0]
[4,7,8,3,10,11,6,5,12,9,2,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,0]
[4,7,9,3,10,11,6,12,8,5,2,1]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0,0,0,0]
[4,8,9,3,10,11,12,7,6,5,2,1]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[5,6,7,8,4,3,2,1,10,9,12,11]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[5,6,7,8,4,3,2,1,11,12,10,9]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,1,1,0,1,0,0,0]
[5,6,7,9,4,3,2,10,8,1,12,11]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0,0,1,1,0,0]
[5,6,7,9,4,3,2,11,8,12,10,1]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,1,0,0,1,0,0,0]
[5,6,7,10,4,3,2,11,12,9,8,1]=>[1,1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0,0]
[5,6,8,9,4,3,10,7,2,1,12,11]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,1,0,0]
[5,6,8,9,4,3,11,7,2,12,10,1]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0,0,0]
[5,6,8,10,4,3,11,7,12,9,2,1]=>[1,1,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0]
[5,6,9,10,4,3,11,12,8,7,2,1]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[5,7,8,9,4,10,6,3,2,1,12,11]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0,0,1,1,0,0]
[5,7,8,9,4,11,6,3,2,12,10,1]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0,0,0]
[5,7,8,10,4,11,6,3,12,9,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0,0,0,0]
[5,7,9,10,4,11,6,12,8,3,2,1]=>[1,1,1,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[5,8,9,10,4,11,12,7,6,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,5,4,3,2,1,12,11]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,1,0,0]
[6,7,8,9,11,5,4,3,2,12,10,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0]
[6,7,8,10,11,5,4,3,12,9,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0,0,0]
[6,7,9,10,11,5,4,12,8,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[6,8,9,10,11,5,12,7,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[7,8,9,10,11,12,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[11,10,9,8,7,6,5,4,3,1,12,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]
[10,12,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,7,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,7,8,10,9,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[7,10,12,8,11,9,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[7,8,9,12,11,10,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,9,10,5,6,8,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,5,6,8,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,5,8,10,6,9,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[5,10,12,8,11,6,9,7,3,4,1,2]=>[1,1,1,1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[5,8,9,12,11,6,10,7,3,4,1,2]=>[1,1,1,1,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,5,6,7,10,9,8,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[5,10,12,6,7,11,9,8,3,4,1,2]=>[1,1,1,1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[5,6,9,12,7,11,10,8,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[5,6,7,8,12,11,10,9,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,3,4,6,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,7,8,3,4,6,5,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,7,8,10,9,3,4,6,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[7,10,12,8,11,9,3,4,6,5,1,2]=>[1,1,1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[7,8,9,12,11,10,3,4,6,5,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,9,10,3,6,8,4,7,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,3,6,8,4,7,5,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,3,8,10,6,9,4,7,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,10,12,8,11,6,9,4,7,5,1,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[3,8,9,12,11,6,10,4,7,5,1,2]=>[1,1,1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,3,6,7,10,9,4,8,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,10,12,6,7,11,9,4,8,5,1,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[3,6,9,12,7,11,10,4,8,5,1,2]=>[1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[3,6,7,8,12,11,10,4,9,5,1,2]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[11,12,9,10,3,4,5,8,7,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,3,4,5,8,7,6,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,3,8,10,4,5,9,7,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,10,12,8,11,4,5,9,7,6,1,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[3,8,9,12,11,4,5,10,7,6,1,2]=>[1,1,1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,3,4,7,10,5,9,8,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,10,12,4,7,11,5,9,8,6,1,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,9,12,7,11,5,10,8,6,1,2]=>[1,1,1,0,1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,7,8,12,11,5,10,9,6,1,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[11,12,3,4,5,6,10,9,8,7,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,10,12,4,5,6,11,9,8,7,1,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[3,4,9,12,5,6,11,10,8,7,1,2]=>[1,1,1,0,1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[3,4,5,8,12,6,11,10,9,7,1,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[3,4,5,6,7,12,11,10,9,8,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[11,12,9,10,7,8,5,6,1,2,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,7,8,5,6,1,2,4,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,7,8,10,9,5,6,1,2,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[7,10,12,8,11,9,5,6,1,2,4,3]=>[1,1,1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[7,8,9,12,11,10,5,6,1,2,4,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,9,10,5,6,8,7,1,2,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,5,6,8,7,1,2,4,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,5,8,10,6,9,7,1,2,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[5,10,12,8,11,6,9,7,1,2,4,3]=>[1,1,1,1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[5,8,9,12,11,6,10,7,1,2,4,3]=>[1,1,1,1,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,5,6,7,10,9,8,1,2,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[5,10,12,6,7,11,9,8,1,2,4,3]=>[1,1,1,1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[5,6,9,12,7,11,10,8,1,2,4,3]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[5,6,7,8,12,11,10,9,1,2,4,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,1,4,6,2,5,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,7,8,1,4,6,2,5,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,7,8,10,9,1,4,6,2,5,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[7,10,12,8,11,9,1,4,6,2,5,3]=>[1,1,1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[7,8,9,12,11,10,1,4,6,2,5,3]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,9,10,1,6,8,4,7,2,5,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,1,6,8,4,7,2,5,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,1,8,10,6,9,4,7,2,5,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,8,11,6,9,4,7,2,5,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,9,12,11,6,10,4,7,2,5,3]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,1,6,7,10,9,4,8,2,5,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,6,7,11,9,4,8,2,5,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,6,9,12,7,11,10,4,8,2,5,3]=>[1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[1,6,7,8,12,11,10,4,9,2,5,3]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[11,12,9,10,1,4,5,8,7,2,6,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,1,4,5,8,7,2,6,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,1,8,10,4,5,9,7,2,6,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,8,11,4,5,9,7,2,6,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,9,12,11,4,5,10,7,2,6,3]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,1,4,7,10,5,9,8,2,6,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,4,7,11,5,9,8,2,6,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,4,9,12,7,11,5,10,8,2,6,3]=>[1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,7,8,12,11,5,10,9,2,6,3]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[11,12,1,4,5,6,10,9,8,2,7,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,4,5,6,11,9,8,2,7,3]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,4,9,12,5,6,11,10,8,2,7,3]=>[1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,5,8,12,6,11,10,9,2,7,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[1,4,5,6,7,12,11,10,9,2,8,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[11,12,9,10,7,8,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,7,8,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,7,8,10,9,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[7,10,12,8,11,9,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[7,8,9,12,11,10,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,9,10,1,6,8,2,3,7,5,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,1,6,8,2,3,7,5,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,1,8,10,6,9,2,3,7,5,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,8,11,6,9,2,3,7,5,4]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,9,12,11,6,10,2,3,7,5,4]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,1,6,7,10,9,2,3,8,5,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,6,7,11,9,2,3,8,5,4]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,6,9,12,7,11,10,2,3,8,5,4]=>[1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[1,6,7,8,12,11,10,2,3,9,5,4]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[11,12,9,10,1,2,5,8,3,7,6,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,1,2,5,8,3,7,6,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,1,8,10,2,5,9,3,7,6,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,8,11,2,5,9,3,7,6,4]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,9,12,11,2,5,10,3,7,6,4]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,1,2,7,10,5,9,3,8,6,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,2,7,11,5,9,3,8,6,4]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,9,12,7,11,5,10,3,8,6,4]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,7,8,12,11,5,10,3,9,6,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[11,12,1,2,5,6,10,9,3,8,7,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,2,5,6,11,9,3,8,7,4]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,9,12,5,6,11,10,3,8,7,4]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,5,8,12,6,11,10,3,9,7,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,5,6,7,12,11,10,3,9,8,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[11,12,9,10,1,2,3,4,8,7,6,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,12,11,1,2,3,4,8,7,6,5]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[11,12,1,8,10,2,3,4,9,7,6,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,8,11,2,3,4,9,7,6,5]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,9,12,11,2,3,4,10,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,12,1,2,7,10,3,4,9,8,6,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,2,7,11,3,4,9,8,6,5]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,9,12,7,11,3,4,10,8,6,5]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,7,8,12,11,3,4,10,9,6,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[11,12,1,2,3,6,10,4,9,8,7,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,2,3,6,11,4,9,8,7,5]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,9,12,3,6,11,4,10,8,7,5]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,8,12,6,11,4,10,9,7,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,6,7,12,11,4,10,9,8,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[11,12,1,2,3,4,5,10,9,8,7,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,12,2,3,4,5,11,9,8,7,6]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[1,2,9,12,3,4,5,11,10,8,7,6]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[1,2,3,8,12,4,5,11,10,9,7,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,3,4,7,12,5,11,10,9,8,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,3,4,5,6,12,11,10,9,8,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[10,12,9,11,7,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,7,9,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,7,9,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,7,10,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,6,8,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,9,11,6,8,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,6,9,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,6,9,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,6,10,5,7,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,10,6,9,5,8,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,7,11,6,9,5,8,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,7,11,6,10,5,8,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,7,11,6,10,5,9,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,9,11,7,8,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,7,9,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,7,9,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,7,10,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,6,8,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,9,11,6,8,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,6,9,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,6,9,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,6,10,4,7,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,10,6,9,4,8,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,7,11,6,9,4,8,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,7,11,6,10,4,8,3,5,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,7,11,6,10,4,9,3,5,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,5,8,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,9,11,5,8,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,5,9,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,5,9,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,5,10,4,7,3,6,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,10,5,9,4,8,3,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,7,11,5,9,4,8,3,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,7,11,5,10,4,8,3,6,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,7,11,5,10,4,9,3,6,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,6,10,5,9,4,8,3,7,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,6,11,5,9,4,8,3,7,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,6,11,5,10,4,8,3,7,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,6,11,5,10,4,9,3,7,1,2]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[7,12,6,11,5,10,4,9,3,8,1,2]=>[1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,9,11,7,8,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,7,9,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,7,9,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,7,10,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,6,8,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,9,11,6,8,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,6,9,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,6,9,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,6,10,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,10,6,9,5,8,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,7,11,6,9,5,8,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,7,11,6,10,5,8,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,7,11,6,10,5,9,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,9,11,7,8,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,7,9,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,7,9,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,7,10,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,6,8,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,9,11,6,8,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,6,9,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,6,9,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,6,10,4,7,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,10,6,9,4,8,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,7,11,6,9,4,8,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,7,11,6,10,4,8,2,5,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,7,11,6,10,4,9,2,5,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,5,8,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,9,11,5,8,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,5,9,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,5,9,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,5,10,4,7,2,6,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,10,5,9,4,8,2,6,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,7,11,5,9,4,8,2,6,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,7,11,5,10,4,8,2,6,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,7,11,5,10,4,9,2,6,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,6,10,5,9,4,8,2,7,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,6,11,5,9,4,8,2,7,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,6,11,5,10,4,8,2,7,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,6,11,5,10,4,9,2,7,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[7,12,6,11,5,10,4,9,2,8,1,3]=>[1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,9,11,7,8,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,7,9,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,7,9,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,7,10,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,6,8,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,9,11,6,8,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,6,9,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,6,9,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,6,10,3,7,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,10,6,9,3,8,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,7,11,6,9,3,8,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,7,11,6,10,3,8,2,5,1,4]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,7,11,6,10,3,9,2,5,1,4]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,5,8,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,9,11,5,8,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,5,9,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,5,9,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,5,10,3,7,2,6,1,4]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,10,5,9,3,8,2,6,1,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,7,11,5,9,3,8,2,6,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,7,11,5,10,3,8,2,6,1,4]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,7,11,5,10,3,9,2,6,1,4]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,6,10,5,9,3,8,2,7,1,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,6,11,5,9,3,8,2,7,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,6,11,5,10,3,8,2,7,1,4]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,6,11,5,10,3,9,2,7,1,4]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[7,12,6,11,5,10,3,9,2,8,1,4]=>[1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,4,8,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,9,11,4,8,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,10,4,9,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,8,11,4,9,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,8,11,4,10,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,10,4,9,3,8,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,7,11,4,9,3,8,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,7,11,4,10,3,8,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,7,11,4,10,3,9,2,6,1,5]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,6,10,4,9,3,8,2,7,1,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,6,11,4,9,3,8,2,7,1,5]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,6,11,4,10,3,8,2,7,1,5]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,6,11,4,10,3,9,2,7,1,5]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[7,12,6,11,4,10,3,9,2,8,1,5]=>[1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,5,10,4,9,3,8,2,7,1,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,12,5,11,4,9,3,8,2,7,1,6]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,5,11,4,10,3,8,2,7,1,6]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[8,12,5,11,4,10,3,9,2,7,1,6]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[7,12,5,11,4,10,3,9,2,8,1,6]=>[1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,10,3,9,2,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,9,7,5,3,1,12,10,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,7,5,3,1,12,11,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,7,5,3,1,12,10,9,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,7,5,3,1,12,11,9,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,7,5,3,1,12,11,10,6,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,9,6,5,3,1,12,10,8,7,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,6,5,3,1,12,11,8,7,4,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,6,5,3,1,12,10,9,7,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,6,5,3,1,12,11,9,7,4,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,6,5,3,1,12,11,10,7,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,7,6,5,3,1,12,10,9,8,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,7,6,5,3,1,12,11,9,8,4,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,7,6,5,3,1,12,11,10,8,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,7,6,5,3,1,12,11,10,9,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[11,9,7,4,3,1,12,10,8,6,5,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,7,4,3,1,12,11,8,6,5,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,7,4,3,1,12,10,9,6,5,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,7,4,3,1,12,11,9,6,5,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,7,4,3,1,12,11,10,6,5,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,9,6,4,3,1,12,10,8,7,5,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,6,4,3,1,12,11,8,7,5,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,6,4,3,1,12,10,9,7,5,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,6,4,3,1,12,11,9,7,5,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,6,4,3,1,12,11,10,7,5,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,7,6,4,3,1,12,10,9,8,5,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,7,6,4,3,1,12,11,9,8,5,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,7,6,4,3,1,12,11,10,8,5,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,7,6,4,3,1,12,11,10,9,5,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[11,9,5,4,3,1,12,10,8,7,6,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,5,4,3,1,12,11,8,7,6,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,5,4,3,1,12,10,9,7,6,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,5,4,3,1,12,11,9,7,6,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,5,4,3,1,12,11,10,7,6,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,7,5,4,3,1,12,10,9,8,6,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,7,5,4,3,1,12,11,9,8,6,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,7,5,4,3,1,12,11,10,8,6,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,7,5,4,3,1,12,11,10,9,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[11,6,5,4,3,1,12,10,9,8,7,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,6,5,4,3,1,12,11,9,8,7,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,6,5,4,3,1,12,11,10,8,7,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,6,5,4,3,1,12,11,10,9,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[7,6,5,4,3,1,12,11,10,9,8,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[11,9,7,5,2,1,12,10,8,6,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,7,5,2,1,12,11,8,6,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,7,5,2,1,12,10,9,6,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,7,5,2,1,12,11,9,6,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,7,5,2,1,12,11,10,6,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,9,6,5,2,1,12,10,8,7,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,6,5,2,1,12,11,8,7,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,6,5,2,1,12,10,9,7,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,6,5,2,1,12,11,9,7,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,6,5,2,1,12,11,10,7,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,7,6,5,2,1,12,10,9,8,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,7,6,5,2,1,12,11,9,8,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,7,6,5,2,1,12,11,10,8,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,7,6,5,2,1,12,11,10,9,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[11,9,7,4,2,1,12,10,8,6,5,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,7,4,2,1,12,11,8,6,5,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,7,4,2,1,12,10,9,6,5,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,7,4,2,1,12,11,9,6,5,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,7,4,2,1,12,11,10,6,5,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,9,6,4,2,1,12,10,8,7,5,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,6,4,2,1,12,11,8,7,5,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,6,4,2,1,12,10,9,7,5,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,6,4,2,1,12,11,9,7,5,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,6,4,2,1,12,11,10,7,5,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,7,6,4,2,1,12,10,9,8,5,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,7,6,4,2,1,12,11,9,8,5,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,7,6,4,2,1,12,11,10,8,5,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,7,6,4,2,1,12,11,10,9,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[11,9,5,4,2,1,12,10,8,7,6,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,5,4,2,1,12,11,8,7,6,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,5,4,2,1,12,10,9,7,6,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,5,4,2,1,12,11,9,7,6,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,5,4,2,1,12,11,10,7,6,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,7,5,4,2,1,12,10,9,8,6,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,7,5,4,2,1,12,11,9,8,6,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,7,5,4,2,1,12,11,10,8,6,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,7,5,4,2,1,12,11,10,9,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[11,6,5,4,2,1,12,10,9,8,7,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,6,5,4,2,1,12,11,9,8,7,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,6,5,4,2,1,12,11,10,8,7,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,6,5,4,2,1,12,11,10,9,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[7,6,5,4,2,1,12,11,10,9,8,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[11,9,7,3,2,1,12,10,8,6,5,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,7,3,2,1,12,11,8,6,5,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,7,3,2,1,12,10,9,6,5,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,7,3,2,1,12,11,9,6,5,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,7,3,2,1,12,11,10,6,5,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,9,6,3,2,1,12,10,8,7,5,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,6,3,2,1,12,11,8,7,5,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,6,3,2,1,12,10,9,7,5,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,6,3,2,1,12,11,9,7,5,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,6,3,2,1,12,11,10,7,5,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,7,6,3,2,1,12,10,9,8,5,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,7,6,3,2,1,12,11,9,8,5,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,7,6,3,2,1,12,11,10,8,5,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,7,6,3,2,1,12,11,10,9,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[11,9,5,3,2,1,12,10,8,7,6,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,5,3,2,1,12,11,8,7,6,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,5,3,2,1,12,10,9,7,6,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,5,3,2,1,12,11,9,7,6,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,5,3,2,1,12,11,10,7,6,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,7,5,3,2,1,12,10,9,8,6,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,7,5,3,2,1,12,11,9,8,6,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,7,5,3,2,1,12,11,10,8,6,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,7,5,3,2,1,12,11,10,9,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[11,6,5,3,2,1,12,10,9,8,7,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,6,5,3,2,1,12,11,9,8,7,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,6,5,3,2,1,12,11,10,8,7,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,6,5,3,2,1,12,11,10,9,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[7,6,5,3,2,1,12,11,10,9,8,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[11,9,4,3,2,1,12,10,8,7,6,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,9,4,3,2,1,12,11,8,7,6,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,8,4,3,2,1,12,10,9,7,6,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,8,4,3,2,1,12,11,9,7,6,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,8,4,3,2,1,12,11,10,7,6,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[11,7,4,3,2,1,12,10,9,8,6,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,7,4,3,2,1,12,11,9,8,6,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,7,4,3,2,1,12,11,10,8,6,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,7,4,3,2,1,12,11,10,9,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[11,6,4,3,2,1,12,10,9,8,7,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,6,4,3,2,1,12,11,9,8,7,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,6,4,3,2,1,12,11,10,8,7,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,6,4,3,2,1,12,11,10,9,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[7,6,4,3,2,1,12,11,10,9,8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[11,5,4,3,2,1,12,10,9,8,7,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,5,4,3,2,1,12,11,9,8,7,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[9,5,4,3,2,1,12,11,10,8,7,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,5,4,3,2,1,12,11,10,9,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[7,5,4,3,2,1,12,11,10,9,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[7,1,8,2,9,3,10,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[7,1,8,2,9,3,10,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0]
[7,1,8,2,9,3,10,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0]
[7,1,8,2,9,3,10,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,0]
[7,1,8,2,9,3,10,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0]
[7,1,8,2,9,10,3,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0]
[7,1,8,2,9,10,3,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0]
[7,1,8,2,9,10,3,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0,0,0,1,0,0]
[7,1,8,2,9,10,3,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0,0,0]
[7,1,8,2,9,10,3,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,0,0]
[7,1,8,2,9,10,11,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0,1,0,0]
[7,1,8,2,9,10,11,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,1,0,0,0]
[7,1,8,2,9,10,11,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0]
[7,1,8,2,9,10,11,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]
[7,1,8,9,2,3,10,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]
[7,1,8,9,2,3,10,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0]
[7,1,8,9,2,3,10,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0]
[7,1,8,9,2,3,10,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,1,0,0,0]
[7,1,8,9,2,3,10,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0]
[7,1,8,9,2,10,3,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]
[7,1,8,9,2,10,3,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,1,0,0,0]
[7,1,8,9,2,10,3,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]
[7,1,8,9,2,10,3,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]
[7,1,8,9,2,10,3,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0]
[7,1,8,9,2,10,11,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,0,1,0,0]
[7,1,8,9,2,10,11,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,0,0,0]
[7,1,8,9,2,10,11,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,0,0]
[7,1,8,9,2,10,11,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0]
[7,1,8,9,10,2,3,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0,0,1,0,0]
[7,1,8,9,10,2,3,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0,1,0,0,0]
[7,1,8,9,10,2,3,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0]
[7,1,8,9,10,2,3,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,0,1,0,0,0]
[7,1,8,9,10,2,3,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0,0,0,0]
[7,1,8,9,10,2,11,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0,1,0,0]
[7,1,8,9,10,2,11,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0]
[7,1,8,9,10,2,11,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0,0,0,0]
[7,1,8,9,10,2,11,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]
[7,1,8,9,10,11,2,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0]
[7,1,8,9,10,11,2,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0]
[7,1,8,9,10,11,2,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]
[7,1,8,9,10,11,2,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]
[7,1,8,9,10,11,12,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[7,8,1,2,9,3,10,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[7,8,1,2,9,3,10,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0,0]
[7,8,1,2,9,3,10,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0,0]
[7,8,1,2,9,3,10,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,0,0]
[7,8,1,2,9,3,10,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0,0,0,0]
[7,8,1,2,9,10,3,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,1,0,0]
[7,8,1,2,9,10,3,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0]
[7,8,1,2,9,10,3,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,0,0,1,0,0]
[7,8,1,2,9,10,3,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0,0]
[7,8,1,2,9,10,3,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,1,0,0,0,0]
[7,8,1,2,9,10,11,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0,1,0,0]
[7,8,1,2,9,10,11,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,1,0,0,0]
[7,8,1,2,9,10,11,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,1,0,0,0,0]
[7,8,1,2,9,10,11,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0,0]
[7,8,1,9,2,3,10,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0,0]
[7,8,1,9,2,3,10,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0,0]
[7,8,1,9,2,3,10,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0]
[7,8,1,9,2,3,10,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0]
[7,8,1,9,2,3,10,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0,0]
[7,8,1,9,2,10,3,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0]
[7,8,1,9,2,10,3,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0,0]
[7,8,1,9,2,10,3,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0,0]
[7,8,1,9,2,10,3,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0]
[7,8,1,9,2,10,3,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0,0]
[7,8,1,9,2,10,11,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,1,0,0]
[7,8,1,9,2,10,11,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0,0]
[7,8,1,9,2,10,11,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,0,0]
[7,8,1,9,2,10,11,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0,0]
[7,8,1,9,10,2,3,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,1,0,0,1,0,0]
[7,8,1,9,10,2,3,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0]
[7,8,1,9,10,2,3,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0,0,1,0,0]
[7,8,1,9,10,2,3,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0,0]
[7,8,1,9,10,2,3,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0]
[7,8,1,9,10,2,11,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0,0,1,0,0]
[7,8,1,9,10,2,11,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0,1,0,0,0]
[7,8,1,9,10,2,11,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,0,0,0]
[7,8,1,9,10,2,11,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,0,0,0]
[7,8,1,9,10,11,2,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,1,0,0]
[7,8,1,9,10,11,2,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,1,0,0,0]
[7,8,1,9,10,11,2,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0]
[7,8,1,9,10,11,2,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0,0]
[7,8,1,9,10,11,12,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[7,8,9,1,2,3,10,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,0]
[7,8,9,1,2,3,10,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0,0]
[7,8,9,1,2,3,10,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,0,0,1,0,0]
[7,8,9,1,2,3,10,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0]
[7,8,9,1,2,3,10,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,0,0,0]
[7,8,9,1,2,10,3,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,0]
[7,8,9,1,2,10,3,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0]
[7,8,9,1,2,10,3,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0]
[7,8,9,1,2,10,3,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0]
[7,8,9,1,2,10,3,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,0]
[7,8,9,1,2,10,11,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,0,1,0,0]
[7,8,9,1,2,10,11,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0]
[7,8,9,1,2,10,11,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0]
[7,8,9,1,2,10,11,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0]
[7,8,9,1,10,2,3,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0,0]
[7,8,9,1,10,2,3,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0,0]
[7,8,9,1,10,2,3,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0,0]
[7,8,9,1,10,2,3,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0]
[7,8,9,1,10,2,3,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0,0,0,0]
[7,8,9,1,10,2,11,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0,0]
[7,8,9,1,10,2,11,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0]
[7,8,9,1,10,2,11,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0]
[7,8,9,1,10,2,11,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0]
[7,8,9,1,10,11,2,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0,1,0,0]
[7,8,9,1,10,11,2,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,1,0,0,0]
[7,8,9,1,10,11,2,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0,0,0,0]
[7,8,9,1,10,11,2,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0]
[7,8,9,1,10,11,12,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[7,8,9,10,1,2,3,4,11,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0,1,0,0]
[7,8,9,10,1,2,3,4,11,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0,0,0]
[7,8,9,10,1,2,3,11,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0,1,0,0]
[7,8,9,10,1,2,3,11,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0]
[7,8,9,10,1,2,3,11,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0]
[7,8,9,10,1,2,11,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0,1,0,0]
[7,8,9,10,1,2,11,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0]
[7,8,9,10,1,2,11,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0,0,0,0]
[7,8,9,10,1,2,11,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[7,8,9,10,1,11,2,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,1,0,0]
[7,8,9,10,1,11,2,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,1,0,0,0]
[7,8,9,10,1,11,2,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0,0]
[7,8,9,10,1,11,2,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[7,8,9,10,1,11,12,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[7,8,9,10,11,1,2,3,4,5,12,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0,0]
[7,8,9,10,11,1,2,3,4,12,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0,0]
[7,8,9,10,11,1,2,3,12,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[7,8,9,10,11,1,2,12,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[7,8,9,10,11,1,12,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[9,10,11,12,7,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,7,8,9,10,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[7,10,11,8,9,12,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]
[7,8,9,10,11,12,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[11,12,9,10,5,6,7,8,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,11,12,5,6,7,8,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,5,8,9,6,7,10,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[5,10,11,8,9,6,7,12,3,4,1,2]=>[1,1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0]
[5,8,9,10,11,6,7,12,3,4,1,2]=>[1,1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[11,12,5,6,7,8,9,10,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[5,10,11,6,7,8,9,12,3,4,1,2]=>[1,1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0]
[5,6,9,10,7,8,11,12,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,9,10,11,12,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[11,12,9,10,7,8,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,11,12,7,8,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,7,8,9,10,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[7,10,11,8,9,12,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]
[7,8,9,10,11,12,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[11,12,9,10,3,6,7,4,5,8,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,11,12,3,6,7,4,5,8,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,3,8,9,6,7,4,5,10,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,10,11,8,9,6,7,4,5,12,1,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]
[3,8,9,10,11,6,7,4,5,12,1,2]=>[1,1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0,0]
[11,12,3,6,7,8,9,4,5,10,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,10,11,6,7,8,9,4,5,12,1,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]
[3,6,9,10,7,8,11,4,5,12,1,2]=>[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,0]
[3,6,7,8,9,10,11,4,5,12,1,2]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]
[11,12,9,10,3,4,5,6,7,8,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,11,12,3,4,5,6,7,8,1,2]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,3,8,9,4,5,6,7,10,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,10,11,8,9,4,5,6,7,12,1,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]
[3,8,9,10,11,4,5,6,7,12,1,2]=>[1,1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0,0]
[11,12,3,4,7,8,5,6,9,10,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,10,11,4,7,8,5,6,9,12,1,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]
[3,4,9,10,7,8,5,6,11,12,1,2]=>[1,1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0]
[3,4,7,8,9,10,5,6,11,12,1,2]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0,0]
[11,12,3,4,5,6,7,8,9,10,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,10,11,4,5,6,7,8,9,12,1,2]=>[1,1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]
[3,4,9,10,5,6,7,8,11,12,1,2]=>[1,1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0]
[3,4,5,8,9,6,7,10,11,12,1,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0]
[3,4,5,6,7,8,9,10,11,12,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[11,12,9,10,7,8,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,11,12,7,8,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,7,8,9,10,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[7,10,11,8,9,12,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]
[7,8,9,10,11,12,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[11,12,9,10,5,6,7,8,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,11,12,5,6,7,8,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,5,8,9,6,7,10,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[5,10,11,8,9,6,7,12,1,2,3,4]=>[1,1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0]
[5,8,9,10,11,6,7,12,1,2,3,4]=>[1,1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[11,12,5,6,7,8,9,10,1,2,3,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[5,10,11,6,7,8,9,12,1,2,3,4]=>[1,1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0]
[5,6,9,10,7,8,11,12,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[5,6,7,8,9,10,11,12,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[11,12,9,10,7,8,1,4,5,2,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,11,12,7,8,1,4,5,2,3,6]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,7,8,9,10,1,4,5,2,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[7,10,11,8,9,12,1,4,5,2,3,6]=>[1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]
[7,8,9,10,11,12,1,4,5,2,3,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[11,12,9,10,1,6,7,4,5,2,3,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,11,12,1,6,7,4,5,2,3,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,1,8,9,6,7,4,5,2,3,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,8,9,6,7,4,5,2,3,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,8,9,10,11,6,7,4,5,2,3,12]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[11,12,1,6,7,8,9,4,5,2,3,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,6,7,8,9,4,5,2,3,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,6,9,10,7,8,11,4,5,2,3,12]=>[1,0,1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0,1,0]
[1,6,7,8,9,10,11,4,5,2,3,12]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]
[11,12,9,10,1,4,5,6,7,2,3,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,11,12,1,4,5,6,7,2,3,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,1,8,9,4,5,6,7,2,3,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,8,9,4,5,6,7,2,3,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,8,9,10,11,4,5,6,7,2,3,12]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[11,12,1,4,7,8,5,6,9,2,3,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,4,7,8,5,6,9,2,3,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,4,9,10,7,8,5,6,11,2,3,12]=>[1,0,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,1,0]
[1,4,7,8,9,10,5,6,11,2,3,12]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,1,0]
[11,12,1,4,5,6,7,8,9,2,3,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,4,5,6,7,8,9,2,3,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,4,9,10,5,6,7,8,11,2,3,12]=>[1,0,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,1,0]
[1,4,5,8,9,6,7,10,11,2,3,12]=>[1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0]
[1,4,5,6,7,8,9,10,11,2,3,12]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[11,12,9,10,7,8,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,11,12,7,8,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,7,8,9,10,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[7,10,11,8,9,12,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]
[11,12,9,10,1,6,7,2,3,4,5,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,11,12,1,6,7,2,3,4,5,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,1,8,9,6,7,2,3,4,5,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,8,9,6,7,2,3,4,5,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,8,9,10,11,6,7,2,3,4,5,12]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[11,12,1,6,7,8,9,2,3,4,5,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,6,7,8,9,2,3,4,5,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,6,9,10,7,8,11,2,3,4,5,12]=>[1,0,1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0,1,0]
[1,6,7,8,9,10,11,2,3,4,5,12]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]
[11,12,9,10,1,2,5,6,3,4,7,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,11,12,1,2,5,6,3,4,7,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,1,8,9,2,5,6,3,4,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,8,9,2,5,6,3,4,7,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,8,9,10,11,2,5,6,3,4,7,12]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[11,12,1,2,7,8,5,6,3,4,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,2,7,8,5,6,3,4,9,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,2,9,10,7,8,5,6,3,4,11,12]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]
[1,2,7,8,9,10,5,6,3,4,11,12]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0]
[11,12,1,2,5,6,7,8,3,4,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,2,5,6,7,8,3,4,9,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,2,9,10,5,6,7,8,3,4,11,12]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]
[1,2,5,8,9,6,7,10,3,4,11,12]=>[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0]
[1,2,5,6,7,8,9,10,3,4,11,12]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[11,12,9,10,1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,11,12,1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[11,12,1,8,9,2,3,4,5,6,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,8,9,2,3,4,5,6,7,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,8,9,10,11,2,3,4,5,6,7,12]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[11,12,1,2,7,8,3,4,5,6,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,2,7,8,3,4,5,6,9,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,2,9,10,7,8,3,4,5,6,11,12]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]
[1,2,7,8,9,10,3,4,5,6,11,12]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0]
[11,12,1,2,3,6,7,4,5,8,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,2,3,6,7,4,5,8,9,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,2,9,10,3,6,7,4,5,8,11,12]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]
[1,2,3,8,9,6,7,4,5,10,11,12]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]
[1,2,3,6,7,8,9,4,5,10,11,12]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[11,12,1,2,3,4,5,6,7,8,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,10,11,2,3,4,5,6,7,8,9,12]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[1,2,9,10,3,4,5,6,7,8,11,12]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]
[1,2,3,8,9,4,5,6,7,10,11,12]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]
[1,2,3,4,7,8,5,6,9,10,11,12]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[11,1,12,10,9,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[2,12,11,10,9,8,7,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,1,2,3,4,5,6,7,8,9,12,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]
[2,12,1,3,4,5,6,7,8,9,10,11]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,4,2,5,1,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,6,5,7,8,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,6,5,7,8,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,6,4,7,3,5,8,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,6,4,7,2,5,1,3,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,6,3,7,2,1,4,5,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,5,4,3,6,7,8,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,5,4,2,6,7,1,3,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,5,3,2,6,1,4,7,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,4,3,2,1,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,7,9,10,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,7,9,10,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,7,9,10,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,7,9,10,4,2,5,1,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,7,9,10,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,6,9,5,7,10,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,6,9,5,7,10,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,6,9,4,7,3,5,10,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,6,9,4,7,2,5,1,3,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,6,9,3,7,2,1,4,5,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,5,9,4,3,6,7,10,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,5,9,4,2,6,7,1,3,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,5,9,3,2,6,1,4,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,4,9,3,2,1,5,6,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,6,5,8,9,10,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,6,5,8,9,10,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,6,4,8,9,3,5,10,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,6,4,8,9,2,5,1,3,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,6,3,8,9,2,1,4,5,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,5,4,8,3,6,9,10,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,5,4,8,2,6,9,1,3,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,5,3,8,2,6,1,4,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,4,3,8,2,1,5,6,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,6,5,4,3,7,8,9,10,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,6,5,4,2,7,8,9,1,3,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,6,5,3,2,7,8,1,4,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,6,4,3,2,7,1,5,8,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,5,4,3,2,1,6,7,8,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,9,11,12,7,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,11,12,7,8,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,11,12,7,8,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,11,12,7,8,4,2,5,1,3,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,11,12,7,8,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,11,12,6,5,7,8,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,11,12,6,5,7,8,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,11,12,6,4,7,3,5,8,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,11,12,6,4,7,2,5,1,3,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,11,12,6,3,7,2,1,4,5,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,11,12,5,4,3,6,7,8,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,11,12,5,4,2,6,7,1,3,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,11,12,5,3,2,6,1,4,7,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,9,11,12,4,3,2,1,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[10,8,11,7,9,12,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0]
[10,8,11,7,9,12,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0]
[10,8,11,7,9,12,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0]
[10,8,11,7,9,12,4,2,5,1,3,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0]
[10,8,11,7,9,12,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0]
[10,8,11,6,9,5,7,12,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0]
[10,8,11,6,9,5,7,12,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0]
[10,8,11,6,9,4,7,3,5,12,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0]
[10,8,11,6,9,4,7,2,5,1,3,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[10,8,11,6,9,3,7,2,1,4,5,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[10,8,11,5,9,4,3,6,7,12,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0]
[10,8,11,5,9,4,2,6,7,1,3,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[10,8,11,5,9,3,2,6,1,4,7,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[10,8,11,4,9,3,2,1,5,6,7,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[10,7,11,6,5,8,9,12,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0]
[10,7,11,6,5,8,9,12,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0]
[10,7,11,6,4,8,9,3,5,12,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0]
[10,7,11,6,4,8,9,2,5,1,3,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[10,7,11,6,3,8,9,2,1,4,5,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[10,7,11,5,4,8,3,6,9,12,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0]
[10,7,11,5,4,8,2,6,9,1,3,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[10,7,11,5,3,8,2,6,1,4,9,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[10,7,11,4,3,8,2,1,5,6,9,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[10,6,11,5,4,3,7,8,9,12,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0]
[10,6,11,5,4,2,7,8,9,1,3,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[10,6,11,5,3,2,7,8,1,4,9,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[10,6,11,4,3,2,7,1,5,8,9,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[10,5,11,4,3,2,1,6,7,8,9,12]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[9,8,7,10,11,12,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[9,8,7,10,11,12,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[9,8,7,10,11,12,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[9,8,7,10,11,12,4,2,5,1,3,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[9,8,7,10,11,12,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[9,8,6,10,11,5,7,12,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0]
[9,8,6,10,11,5,7,12,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0]
[9,8,6,10,11,4,7,3,5,12,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0]
[9,8,6,10,11,4,7,2,5,1,3,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0]
[9,8,6,10,11,3,7,2,1,4,5,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0]
[9,8,5,10,11,4,3,6,7,12,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0]
[9,8,5,10,11,4,2,6,7,1,3,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0]
[9,8,5,10,11,3,2,6,1,4,7,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0]
[9,8,4,10,11,3,2,1,5,6,7,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0]
[9,7,6,10,5,8,11,12,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0]
[9,7,6,10,5,8,11,12,2,1,3,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0]
[9,7,6,10,4,8,11,3,5,12,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0]
[9,7,6,10,4,8,11,2,5,1,3,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0]
[9,7,6,10,3,8,11,2,1,4,5,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0]
[9,7,5,10,4,8,3,6,11,12,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0]
[9,7,5,10,4,8,2,6,11,1,3,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0]
[9,7,5,10,3,8,2,6,1,4,11,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0]
[9,7,4,10,3,8,2,1,5,6,11,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0]
[9,6,5,10,4,3,7,8,11,12,1,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0]
[9,6,5,10,4,2,7,8,11,1,3,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0]
[9,6,5,10,3,2,7,8,1,4,11,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0]
[9,6,4,10,3,2,7,1,5,8,11,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0]
[9,5,4,10,3,2,1,6,7,8,11,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0]
[8,7,6,5,9,10,11,12,3,4,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,5,9,10,11,12,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0,0,0,0]
[8,7,6,4,9,10,11,3,5,12,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,1,0,0,0]
[8,7,6,4,9,10,11,2,5,1,3,12]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,0,0,1,0]
[8,7,6,3,9,10,11,2,1,4,5,12]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,0,0,1,0]
[8,7,5,4,9,10,3,6,11,12,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0]
[8,7,5,4,9,10,2,6,11,1,3,12]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0]
[8,7,5,3,9,10,2,6,1,4,11,12]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0]
[8,7,4,3,9,10,2,1,5,6,11,12]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0]
[8,6,5,4,9,3,7,10,11,12,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,0,0]
[8,6,5,4,9,2,7,10,11,1,3,12]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0]
[8,6,5,3,9,2,7,10,1,4,11,12]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0,0,1,0,1,0]
[8,6,4,3,9,2,7,1,5,10,11,12]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0,1,0,1,0]
[8,5,4,3,9,2,1,6,7,10,11,12]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0,1,0,1,0]
[7,6,5,4,3,8,9,10,11,12,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0]
[7,6,5,4,2,8,9,10,11,1,3,12]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0,0,1,0]
[7,6,5,3,2,8,9,10,1,4,11,12]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0,0,1,0,1,0]
[7,6,4,3,2,8,9,1,5,10,11,12]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0,1,0,1,0,1,0]
[7,5,4,3,2,8,1,6,9,10,11,12]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0]
[6,5,4,3,2,1,7,8,9,10,11,12]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[12,2,1,4,3,6,5,8,7,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,4,3,6,5,8,7,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,4,3,6,5,7,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,4,3,6,5,7,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,4,3,6,5,7,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,4,3,5,7,8,6,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,4,3,5,7,8,6,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,4,3,5,7,6,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,4,3,5,7,6,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,4,3,5,7,6,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,4,3,5,6,8,9,10,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,4,3,5,6,8,9,7,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,4,3,5,6,8,7,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,4,3,5,6,7,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,6,4,8,7,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,6,4,8,7,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,6,4,7,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,6,4,7,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,6,4,7,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,4,7,8,6,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,4,7,8,6,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,4,7,6,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,4,7,6,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,4,7,6,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,4,6,8,9,10,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,4,6,8,9,7,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,4,6,8,7,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,5,4,6,7,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,6,7,8,5,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,6,7,8,5,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,6,7,5,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,6,7,5,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,6,7,5,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,6,5,8,9,10,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,6,5,8,9,7,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,6,5,8,7,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,6,5,7,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,5,7,8,9,10,6,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,5,7,8,9,6,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,5,7,8,6,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,5,7,6,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,5,6,8,9,10,11,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,6,5,8,7,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,6,5,8,7,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,6,5,7,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,6,5,7,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,6,5,7,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,5,7,8,6,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,5,7,8,6,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,5,7,6,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,5,7,6,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,5,7,6,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,5,6,8,9,10,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,5,6,8,9,7,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,5,6,8,7,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,4,2,5,6,7,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,6,4,8,7,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,6,4,8,7,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,6,4,7,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,6,4,7,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,6,4,7,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,4,7,8,6,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,4,7,8,6,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,4,7,6,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,4,7,6,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,4,7,6,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,4,6,8,9,10,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,4,6,8,9,7,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,4,6,8,7,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,4,6,7,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,6,7,8,5,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,6,7,8,5,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,6,7,5,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,6,7,5,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,6,7,5,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,6,5,8,9,10,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,6,5,8,9,7,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,6,5,8,7,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,6,5,7,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,5,7,8,9,10,6,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,5,7,8,9,6,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,5,7,8,6,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,5,7,6,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,4,5,6,8,9,10,11,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,6,3,8,7,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,6,3,8,7,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,6,3,7,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,6,3,7,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,6,3,7,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,3,7,8,6,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,3,7,8,6,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,3,7,6,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,3,7,6,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,3,7,6,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,3,6,8,9,10,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,3,6,8,9,7,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,3,6,8,7,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,5,3,6,7,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,6,7,8,5,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,6,7,8,5,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,6,7,5,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,6,7,5,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,6,7,5,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,6,5,8,9,10,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,6,5,8,9,7,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,6,5,8,7,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,6,5,7,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,5,7,8,9,10,6,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,5,7,8,9,6,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,5,7,8,6,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,5,7,6,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,4,3,5,6,8,9,10,11,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,6,7,8,4,10,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,6,7,8,4,9,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,6,7,4,9,10,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,6,7,4,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,6,7,4,8,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,6,4,8,9,10,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,6,4,8,9,7,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,6,4,8,7,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,6,4,7,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,4,7,8,9,10,6,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,4,7,8,9,6,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,4,7,8,6,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,4,7,6,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,5,4,6,8,9,10,11,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,4,6,7,8,9,10,5,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,4,6,7,8,9,5,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,4,6,7,8,5,10,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,4,6,7,5,9,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,4,6,5,8,9,10,11,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,4,5,7,8,9,10,11,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,2,4,6,8,10,1,3,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,2,4,6,8,12,1,3,5,7,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[2,12,9,11,4,6,8,10,1,3,5,7]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,2,4,6,8,1,3,5,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,7,2,4,6,10,12,1,3,5,9,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0,0,0,0]
[8,12,7,11,2,4,6,10,1,3,5,9]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,10,7,9,4,6,8,12,1,3,5,11]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0]
[2,4,12,7,9,11,6,8,10,1,3,5]=>[1,1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,11,2,10,7,9,4,6,8,1,3,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,2,4,6,12,1,3,5,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0]
[12,9,2,8,7,11,4,6,10,1,3,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,12,7,11,10,9,2,4,6,1,3,5]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,7,2,4,6,1,3,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[6,5,2,4,8,10,12,1,3,7,9,11]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[6,12,5,11,2,4,8,10,1,3,7,9]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,10,5,9,2,4,8,12,1,3,7,11]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0]
[6,5,12,9,11,2,4,8,10,1,3,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,11,6,10,5,9,2,4,8,1,3,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,8,5,7,4,6,10,12,1,3,9,11]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0,0,0]
[2,8,12,5,7,11,4,6,10,1,3,9]=>[1,1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,5,2,4,7,9,6,8,12,1,3,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0]
[12,5,7,2,4,6,9,11,8,10,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,11,10,2,4,7,9,6,8,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,2,8,5,7,4,6,12,1,3,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0]
[12,5,9,8,2,4,7,11,6,10,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,12,5,11,8,10,7,9,4,6,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,2,8,5,7,4,6,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,7,6,5,2,4,10,12,1,3,9,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,1,0,0,0,0,0]
[8,7,6,12,5,11,2,4,10,1,3,9]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10,7,2,6,5,9,4,8,12,1,3,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0]
[7,6,12,5,2,4,9,11,8,10,1,3]=>[1,1,1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,12,7,11,6,10,5,9,4,8,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,10,5,9,8,7,2,4,12,1,3,11]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0]
[2,12,6,9,5,8,7,11,4,10,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,8,12,5,7,11,10,9,2,4,1,3]=>[1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,11,6,10,5,9,8,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,2,4,12,1,3,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0]
[12,9,8,7,2,6,5,11,4,10,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,7,6,12,5,11,10,9,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,12,6,11,10,9,8,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[4,3,2,6,8,10,12,1,5,7,9,11]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[4,12,3,11,2,6,8,10,1,5,7,9]=>[1,1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[4,10,3,9,2,6,8,12,1,5,7,11]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0]
[4,3,12,9,11,2,6,8,10,1,5,7]=>[1,1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,11,4,10,3,9,2,6,8,1,5,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[4,8,3,7,2,6,10,12,1,5,9,11]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0,0,0]
[4,8,12,3,7,11,2,6,10,1,5,9]=>[1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,3,10,7,9,2,6,8,12,1,5,11]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]
[4,3,7,9,12,11,2,6,8,10,1,5]=>[1,1,1,1,0,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[12,4,11,3,10,7,9,2,6,8,1,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,4,8,3,7,2,6,12,1,5,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0]
[12,4,9,3,8,7,11,2,6,10,1,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[4,8,12,11,10,3,7,9,2,6,1,5]=>[1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,4,8,3,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[3,6,2,5,4,8,10,12,1,7,9,11]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,6,12,2,5,11,4,8,10,1,7,9]=>[1,1,1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[3,6,10,2,5,9,4,8,12,1,7,11]=>[1,1,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]
[3,12,6,2,5,9,11,4,8,10,1,7]=>[1,1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[12,11,3,6,10,2,5,9,4,8,1,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[3,5,8,2,4,7,6,10,12,1,9,11]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0,0]
[3,5,8,12,2,4,7,11,6,10,1,9]=>[1,1,1,0,1,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,5,7,10,2,4,6,9,8,12,1,11]=>[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[3,5,7,9,12,2,4,6,8,11,10,1]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[12,11,3,5,7,10,2,4,6,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,3,5,8,2,4,7,6,12,1,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0]
[9,8,3,5,7,12,2,4,6,11,10,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0]
[3,5,12,11,8,10,2,4,7,9,6,1]=>[1,1,1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,3,5,8,2,4,7,6,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,7,3,6,2,5,4,10,12,1,9,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,1,0,0,0,0]
[8,7,3,6,12,2,5,11,4,10,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
[7,6,3,5,10,2,4,9,8,12,1,11]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,1,1,0,0,0]
[7,6,3,5,9,12,2,4,8,11,10,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0]
[7,12,6,11,3,5,10,2,4,9,8,1]=>[1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,6,10,9,8,2,5,7,4,12,1,11]=>[1,1,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[3,9,6,8,5,7,12,2,4,11,10,1]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[3,2,12,6,8,11,10,5,7,9,4,1]=>[1,1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,11,3,6,10,9,8,2,5,7,4,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,3,6,2,5,4,12,1,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0]
[9,8,7,6,3,5,12,2,4,11,10,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,7,3,6,12,11,10,2,5,9,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
[3,12,7,11,10,9,6,8,2,5,4,1]=>[1,1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[6,5,4,3,2,8,10,12,1,7,9,11]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[6,5,4,12,3,11,2,8,10,1,7,9]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,10,3,9,2,8,12,1,7,11]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]
[6,12,5,4,3,9,11,2,8,10,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[5,4,3,8,2,7,6,10,12,1,9,11]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0]
[5,4,3,8,12,2,7,11,6,10,1,9]=>[1,1,1,1,1,0,0,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[5,4,3,7,10,2,6,9,8,12,1,11]=>[1,1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]
[5,4,3,7,9,12,2,6,8,11,10,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]
[5,12,4,11,3,7,10,2,6,9,8,1]=>[1,1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[5,10,4,9,3,8,2,7,6,12,1,11]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]
[5,9,4,8,3,7,12,2,6,11,10,1]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,0]
[12,11,5,4,3,8,10,2,7,9,6,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,5,10,4,9,3,8,2,7,6,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[4,8,3,7,6,5,2,10,12,1,9,11]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,1,1,0,0,0,0]
[4,8,3,7,6,12,5,11,2,10,1,9]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[4,7,3,6,5,10,2,9,8,12,1,11]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0]
[4,7,3,6,5,9,12,2,8,11,10,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0,0,0]
[4,7,12,3,6,11,5,10,2,9,8,1]=>[1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,6,10,3,5,9,8,7,2,12,1,11]=>[1,1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]
[4,6,9,3,5,8,7,12,2,11,10,1]=>[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[4,6,8,12,3,5,7,11,10,9,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[12,11,4,6,10,3,5,9,8,7,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,4,8,3,7,6,5,2,12,1,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0]
[9,8,4,7,3,6,5,12,2,11,10,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0]
[8,7,4,6,12,3,5,11,10,9,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
[4,7,12,11,10,3,6,9,8,5,2,1]=>[1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,4,8,3,7,6,5,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,7,6,5,4,3,2,10,12,1,9,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,1,0,0,0,0]
[8,7,6,5,4,12,3,11,2,10,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,4,3,10,2,9,8,12,1,11]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0]
[7,6,5,4,3,9,12,2,8,11,10,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,1,1,0,0,0,0,0,0]
[7,6,5,12,4,11,3,10,2,9,8,1]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,10,3,9,8,7,2,12,1,11]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[6,5,4,9,3,8,7,12,2,11,10,1]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]
[6,5,4,8,12,3,7,11,10,9,2,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[6,12,5,11,4,10,3,9,8,7,2,1]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[5,10,4,9,8,7,6,3,2,12,1,11]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]
[5,9,4,8,7,6,3,12,2,11,10,1]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0]
[5,8,4,7,6,12,3,11,10,9,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[5,7,12,4,6,11,10,9,8,3,2,1]=>[1,1,1,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,11,5,10,4,9,8,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,8,7,6,5,4,3,2,12,1,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0]
[9,8,7,6,5,4,3,12,2,11,10,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0]
[8,7,6,5,4,12,3,11,10,9,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[7,6,5,12,4,11,10,9,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,12,5,11,10,9,8,7,4,3,2,1]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,3,4,5,6,7,8,9,10,1,12,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]
[2,12,4,5,6,7,8,9,10,11,1,3]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,1,2,4,5,6,7,8,9,10,11,12]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,3,6,5,8,7,11,12,9,10]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,4,3,6,5,9,10,7,8,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[2,1,4,3,6,5,9,11,7,12,8,10]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[2,1,4,3,6,5,10,11,12,7,8,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,4,3,7,8,5,6,10,9,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,4,3,7,8,5,6,11,12,9,10]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[2,1,4,3,7,9,5,10,6,8,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[2,1,4,3,7,9,5,11,6,12,8,10]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[2,1,4,3,7,10,5,11,12,6,8,9]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[2,1,4,3,8,9,10,5,6,7,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[2,1,4,3,8,9,11,5,6,12,7,10]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[2,1,4,3,8,10,11,5,12,6,7,9]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[2,1,4,3,9,10,11,12,5,6,7,8]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[2,1,5,6,3,4,8,7,10,9,12,11]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,5,6,3,4,8,7,11,12,9,10]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,5,6,3,4,9,10,7,8,12,11]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[2,1,5,6,3,4,9,11,7,12,8,10]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[2,1,5,6,3,4,10,11,12,7,8,9]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,5,7,3,8,4,6,10,9,12,11]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,5,7,3,8,4,6,11,12,9,10]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0]
[2,1,5,7,3,9,4,10,6,8,12,11]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0]
[2,1,5,7,3,9,4,11,6,12,8,10]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[2,1,5,7,3,10,4,11,12,6,8,9]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0]
[2,1,5,8,3,9,10,4,6,7,12,11]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]
[2,1,5,8,3,9,11,4,6,12,7,10]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]
[2,1,5,8,3,10,11,4,12,6,7,9]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]
[2,1,5,9,3,10,11,12,4,6,7,8]=>[1,1,0,0,1,1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]
[2,1,6,7,8,3,4,5,10,9,12,11]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,6,7,8,3,4,5,11,12,9,10]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]
[2,1,6,7,9,3,4,10,5,8,12,11]=>[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]
[2,1,6,7,9,3,4,11,5,12,8,10]=>[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[2,1,6,7,10,3,4,11,12,5,8,9]=>[1,1,0,0,1,1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]
[2,1,6,8,9,3,10,4,5,7,12,11]=>[1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0]
[2,1,6,8,9,3,11,4,5,12,7,10]=>[1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]
[2,1,6,8,10,3,11,4,12,5,7,9]=>[1,1,0,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0]
[2,1,6,9,10,3,11,12,4,5,7,8]=>[1,1,0,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]
[2,1,7,8,9,10,3,4,5,6,12,11]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,1,0,0]
[2,1,7,8,9,11,3,4,5,12,6,10]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0,0]
[2,1,7,8,10,11,3,4,12,5,6,9]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0,0,0]
[2,1,7,9,10,11,3,12,4,5,6,8]=>[1,1,0,0,1,1,1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[2,1,8,9,10,11,12,3,4,5,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[3,4,1,2,6,5,8,7,10,9,12,11]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,4,1,2,6,5,8,7,11,12,9,10]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[3,4,1,2,6,5,9,10,7,8,12,11]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[3,4,1,2,6,5,9,11,7,12,8,10]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[3,4,1,2,6,5,10,11,12,7,8,9]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,4,1,2,7,8,5,6,10,9,12,11]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[3,4,1,2,7,8,5,6,11,12,9,10]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[3,4,1,2,7,9,5,10,6,8,12,11]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[3,4,1,2,7,9,5,11,6,12,8,10]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[3,4,1,2,7,10,5,11,12,6,8,9]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,4,1,2,8,9,10,5,6,7,12,11]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[3,4,1,2,8,9,11,5,6,12,7,10]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[3,4,1,2,8,10,11,5,12,6,7,9]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[3,4,1,2,9,10,11,12,5,6,7,8]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[3,5,1,6,2,4,8,7,10,9,12,11]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,5,1,6,2,4,8,7,11,12,9,10]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[3,5,1,6,2,4,9,10,7,8,12,11]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[3,5,1,6,2,4,9,11,7,12,8,10]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[3,5,1,6,2,4,10,11,12,7,8,9]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,5,1,7,2,8,4,6,10,9,12,11]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]
[3,5,1,7,2,8,4,6,11,12,9,10]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0]
[3,5,1,7,2,9,4,10,6,8,12,11]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0]
[3,5,1,7,2,9,4,11,6,12,8,10]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[3,5,1,7,2,10,4,11,12,6,8,9]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0]
[3,5,1,8,2,9,10,4,6,7,12,11]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]
[3,5,1,8,2,9,11,4,6,12,7,10]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]
[3,5,1,8,2,10,11,4,12,6,7,9]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]
[3,5,1,9,2,10,11,12,4,6,7,8]=>[1,1,1,0,1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]
[3,6,1,7,8,2,4,5,10,9,12,11]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0]
[3,6,1,7,8,2,4,5,11,12,9,10]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]
[3,6,1,7,9,2,4,10,5,8,12,11]=>[1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]
[3,6,1,7,9,2,4,11,5,12,8,10]=>[1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[3,6,1,7,10,2,4,11,12,5,8,9]=>[1,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]
[3,6,1,8,9,2,10,4,5,7,12,11]=>[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0]
[3,6,1,8,9,2,11,4,5,12,7,10]=>[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]
[3,6,1,8,10,2,11,4,12,5,7,9]=>[1,1,1,0,1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0]
[3,6,1,9,10,2,11,12,4,5,7,8]=>[1,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]
[3,7,1,8,9,10,2,4,5,6,12,11]=>[1,1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,1,1,0,0]
[3,7,1,8,9,11,2,4,5,12,6,10]=>[1,1,1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,1,0,0,0]
[3,7,1,8,10,11,2,4,12,5,6,9]=>[1,1,1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,0,0,0]
[3,7,1,9,10,11,2,12,4,5,6,8]=>[1,1,1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[3,8,1,9,10,11,12,2,4,5,6,7]=>[1,1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[4,5,6,1,2,3,8,7,10,9,12,11]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,5,6,1,2,3,8,7,11,12,9,10]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[4,5,6,1,2,3,9,10,7,8,12,11]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[4,5,6,1,2,3,9,11,7,12,8,10]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[4,5,6,1,2,3,10,11,12,7,8,9]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[4,5,7,1,2,8,3,6,10,9,12,11]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0]
[4,5,7,1,2,8,3,6,11,12,9,10]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,1,0,1,0,0,0]
[4,5,7,1,2,9,3,10,6,8,12,11]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,1,0,0]
[4,5,7,1,2,9,3,11,6,12,8,10]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]
[4,5,7,1,2,10,3,11,12,6,8,9]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,0]
[4,5,8,1,2,9,10,3,6,7,12,11]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0,1,1,0,0]
[4,5,8,1,2,9,11,3,6,12,7,10]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,0]
[4,5,8,1,2,10,11,3,12,6,7,9]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0,0]
[4,5,9,1,2,10,11,12,3,6,7,8]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0]
[4,6,7,1,8,2,3,5,10,9,12,11]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0,1,1,0,0]
[4,6,7,1,8,2,3,5,11,12,9,10]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,1,1,0,1,0,0,0]
[4,6,7,1,9,2,3,10,5,8,12,11]=>[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0,1,1,0,0]
[4,6,7,1,9,2,3,11,5,12,8,10]=>[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0]
[4,6,7,1,10,2,3,11,12,5,8,9]=>[1,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,0]
[4,6,8,1,9,2,10,3,5,7,12,11]=>[1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0,1,1,0,0]
[4,6,8,1,9,2,11,3,5,12,7,10]=>[1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]
[4,6,8,1,10,2,11,3,12,5,7,9]=>[1,1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,0,0]
[4,6,9,1,10,2,11,12,3,5,7,8]=>[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0,0]
[4,7,8,1,9,10,2,3,5,6,12,11]=>[1,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,1,1,0,0]
[4,7,8,1,9,11,2,3,5,12,6,10]=>[1,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0,1,0,0,0]
[4,7,8,1,10,11,2,3,12,5,6,9]=>[1,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,0]
[4,7,9,1,10,11,2,12,3,5,6,8]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0,0,0,0]
[4,8,9,1,10,11,12,2,3,5,6,7]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[5,6,7,8,1,2,3,4,10,9,12,11]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[5,6,7,8,1,2,3,4,11,12,9,10]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,1,1,0,1,0,0,0]
[5,6,7,9,1,2,3,10,4,8,12,11]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0,0,1,1,0,0]
[5,6,7,9,1,2,3,11,4,12,8,10]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,1,0,0,1,0,0,0]
[5,6,7,10,1,2,3,11,12,4,8,9]=>[1,1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0,0]
[5,6,8,9,1,2,10,3,4,7,12,11]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,1,0,0]
[5,6,8,9,1,2,11,3,4,12,7,10]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0,0,0]
[5,6,8,10,1,2,11,3,12,4,7,9]=>[1,1,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0]
[5,6,9,10,1,2,11,12,3,4,7,8]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[5,7,8,9,1,10,2,3,4,6,12,11]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0,0,1,1,0,0]
[5,7,8,9,1,11,2,3,4,12,6,10]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0,0,0]
[5,7,8,10,1,11,2,3,12,4,6,9]=>[1,1,1,1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0,0,0,0]
[5,7,9,10,1,11,2,12,3,4,6,8]=>[1,1,1,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[5,8,9,10,1,11,12,2,3,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[6,7,8,9,10,1,2,3,4,5,12,11]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,1,0,0]
[6,7,8,9,11,1,2,3,4,12,5,10]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0]
[6,7,8,10,11,1,2,3,12,4,5,9]=>[1,1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0,0,0]
[6,7,9,10,11,1,2,12,3,4,5,8]=>[1,1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[6,8,9,10,11,1,12,2,3,4,5,7]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[1,2,3,4,5,6,7,8,9,12,10,11]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[12,1,3,4,5,6,7,8,9,10,11,2]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[3,2,5,4,7,6,9,8,11,10,1,12]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[3,2,5,4,7,6,9,8,1,12,11,10]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[3,2,5,4,7,6,11,10,9,8,1,12]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,2,5,4,7,6,1,10,9,12,11,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[3,2,5,4,7,6,1,12,11,10,9,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,5,4,9,8,7,6,11,10,1,12]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[3,2,5,4,9,8,7,6,1,12,11,10]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[3,2,5,4,11,8,7,10,9,6,1,12]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,2,5,4,1,8,7,10,9,12,11,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,2,5,4,1,8,7,12,11,10,9,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,5,4,11,10,9,8,7,6,1,12]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[3,2,5,4,1,10,9,8,7,12,11,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[3,2,5,4,1,12,9,8,11,10,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,5,4,1,12,11,10,9,8,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,7,6,5,4,9,8,11,10,1,12]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,1,0]
[3,2,7,6,5,4,9,8,1,12,11,10]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0]
[3,2,7,6,5,4,11,10,9,8,1,12]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,1,0]
[3,2,7,6,5,4,1,10,9,12,11,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,1,0,0,0]
[3,2,7,6,5,4,1,12,11,10,9,8]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,2,9,6,5,8,7,4,11,10,1,12]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,1,0]
[3,2,9,6,5,8,7,4,1,12,11,10]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[3,2,11,6,5,8,7,10,9,4,1,12]=>[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[3,2,1,6,5,8,7,10,9,12,11,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,2,1,6,5,8,7,12,11,10,9,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,11,6,5,10,9,8,7,4,1,12]=>[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[3,2,1,6,5,10,9,8,7,12,11,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[3,2,1,6,5,12,9,8,11,10,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,1,6,5,12,11,10,9,8,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,2,9,8,7,6,5,4,11,10,1,12]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,1,0]
[3,2,9,8,7,6,5,4,1,12,11,10]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[3,2,11,8,7,6,5,10,9,4,1,12]=>[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[3,2,1,8,7,6,5,10,9,12,11,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[3,2,1,8,7,6,5,12,11,10,9,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[3,2,11,10,7,6,9,8,5,4,1,12]=>[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[3,2,1,10,7,6,9,8,5,12,11,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[3,2,1,12,7,6,9,8,11,10,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,1,12,7,6,11,10,9,8,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,11,10,9,8,7,6,5,4,1,12]=>[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[3,2,1,10,9,8,7,6,5,12,11,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[3,2,1,12,9,8,7,6,11,10,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,1,12,11,8,7,10,9,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,2,1,12,11,10,9,8,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[5,4,3,2,7,6,9,8,11,10,1,12]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[5,4,3,2,7,6,9,8,1,12,11,10]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[5,4,3,2,7,6,11,10,9,8,1,12]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[5,4,3,2,7,6,1,10,9,12,11,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[5,4,3,2,7,6,1,12,11,10,9,8]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,4,3,2,9,8,7,6,11,10,1,12]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[5,4,3,2,9,8,7,6,1,12,11,10]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,4,3,2,11,8,7,10,9,6,1,12]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,4,3,2,1,8,7,10,9,12,11,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[5,4,3,2,1,8,7,12,11,10,9,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[5,4,3,2,11,10,9,8,7,6,1,12]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[5,4,3,2,1,10,9,8,7,12,11,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,3,2,1,12,9,8,11,10,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,3,2,1,12,11,10,9,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[7,4,3,6,5,2,9,8,11,10,1,12]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0,1,0]
[7,4,3,6,5,2,9,8,1,12,11,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0]
[7,4,3,6,5,2,11,10,9,8,1,12]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,1,0]
[7,4,3,6,5,2,1,10,9,12,11,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,1,0,0,0]
[7,4,3,6,5,2,1,12,11,10,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[9,4,3,6,5,8,7,2,11,10,1,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0]
[9,4,3,6,5,8,7,2,1,12,11,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0]
[11,4,3,6,5,8,7,10,9,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,4,3,6,5,8,7,10,9,12,11,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,4,3,6,5,8,7,12,11,10,9,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[11,4,3,6,5,10,9,8,7,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,4,3,6,5,10,9,8,7,12,11,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,4,3,6,5,12,9,8,11,10,7,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,4,3,6,5,12,11,10,9,8,7,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[9,4,3,8,7,6,5,2,11,10,1,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0]
[9,4,3,8,7,6,5,2,1,12,11,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0]
[11,4,3,8,7,6,5,10,9,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,4,3,8,7,6,5,10,9,12,11,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[1,4,3,8,7,6,5,12,11,10,9,2]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[11,4,3,10,7,6,9,8,5,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,4,3,10,7,6,9,8,5,12,11,2]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[1,4,3,12,7,6,9,8,11,10,5,2]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,3,12,7,6,11,10,9,8,5,2]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[11,4,3,10,9,8,7,6,5,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,4,3,10,9,8,7,6,5,12,11,2]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[1,4,3,12,9,8,7,6,11,10,5,2]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,3,12,11,8,7,10,9,6,5,2]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,4,3,12,11,10,9,8,7,6,5,2]=>[1,0,1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,6,5,4,3,2,9,8,11,10,1,12]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0,1,0]
[7,6,5,4,3,2,9,8,1,12,11,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0]
[7,6,5,4,3,2,11,10,9,8,1,12]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,1,0]
[7,6,5,4,3,2,1,10,9,12,11,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,1,0,0,0]
[7,6,5,4,3,2,1,12,11,10,9,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[9,6,5,4,3,8,7,2,11,10,1,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0]
[9,6,5,4,3,8,7,2,1,12,11,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0]
[11,6,5,4,3,8,7,10,9,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,6,5,4,3,8,7,10,9,12,11,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,6,5,4,3,8,7,12,11,10,9,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[11,6,5,4,3,10,9,8,7,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,6,5,4,3,10,9,8,7,12,11,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,6,5,4,3,12,9,8,11,10,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,5,4,3,12,11,10,9,8,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[9,8,5,4,7,6,3,2,11,10,1,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0]
[9,8,5,4,7,6,3,2,1,12,11,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0]
[11,8,5,4,7,6,3,10,9,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,8,5,4,7,6,3,10,9,12,11,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0]
[1,8,5,4,7,6,3,12,11,10,9,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[11,10,5,4,7,6,9,8,3,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,10,5,4,7,6,9,8,3,12,11,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]
[1,12,5,4,7,6,9,8,11,10,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,12,5,4,7,6,11,10,9,8,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,10,5,4,9,8,7,6,3,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,10,5,4,9,8,7,6,3,12,11,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]
[1,12,5,4,9,8,7,6,11,10,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,12,5,4,11,8,7,10,9,6,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,12,5,4,11,10,9,8,7,6,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[9,8,7,6,5,4,3,2,11,10,1,12]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0]
[9,8,7,6,5,4,3,2,1,12,11,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0]
[11,8,7,6,5,4,3,10,9,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,8,7,6,5,4,3,10,9,12,11,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0]
[1,8,7,6,5,4,3,12,11,10,9,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[11,10,7,6,5,4,9,8,3,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,10,7,6,5,4,9,8,3,12,11,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]
[1,12,7,6,5,4,9,8,11,10,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,12,7,6,5,4,11,10,9,8,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,10,9,6,5,8,7,4,3,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,10,9,6,5,8,7,4,3,12,11,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]
[1,12,9,6,5,8,7,4,11,10,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,12,11,6,5,8,7,10,9,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,12,11,6,5,10,9,8,7,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[11,10,9,8,7,6,5,4,3,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[1,10,9,8,7,6,5,4,3,12,11,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]
[1,12,9,8,7,6,5,4,11,10,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,12,11,8,7,6,5,10,9,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,12,11,10,7,6,9,8,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,10,11,12,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,3,4,5,6,7,8,9,10,11,12,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,4,3,6,5,8,7,10,12,11,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,4,3,6,5,8,10,9,7,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[2,1,4,3,6,5,10,12,9,11,7,8]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,4,3,6,5,8,9,12,10,11,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[2,1,4,3,6,8,7,5,10,9,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,4,3,6,8,7,5,10,12,11,9]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[2,1,4,3,8,10,7,9,5,6,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[2,1,4,3,10,9,7,12,6,11,5,8]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,1,4,3,8,9,7,12,10,6,11,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[2,1,4,3,6,7,10,8,9,5,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,1,4,3,10,7,12,8,9,11,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,1,4,3,6,9,12,8,11,10,5,7]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,1,4,3,6,7,8,12,9,10,11,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,1,4,6,5,3,8,7,10,9,12,11]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,4,6,5,3,8,7,10,12,11,9]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,4,6,5,3,8,10,9,7,12,11]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[2,1,4,6,5,3,10,12,9,11,7,8]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,4,6,5,3,8,9,12,10,11,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[2,1,6,8,5,7,3,4,10,9,12,11]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,6,8,5,7,3,4,10,12,11,9]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0]
[2,1,8,7,5,10,4,9,3,6,12,11]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,1,0,0]
[2,1,10,7,5,9,4,12,6,11,3,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[2,1,8,7,5,9,4,12,10,6,11,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0,0,0]
[2,1,6,7,5,10,8,4,9,3,12,11]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,1,1,0,0]
[2,1,10,8,5,7,12,4,9,11,3,6]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]
[2,1,6,9,5,8,12,3,11,10,4,7]=>[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]
[2,1,6,7,5,8,12,9,3,10,11,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0,0]
[2,1,4,5,8,6,7,3,10,9,12,11]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,4,5,8,6,7,3,10,12,11,9]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[2,1,8,5,10,6,7,9,3,4,12,11]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,10,5,9,6,7,12,4,11,3,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]
[2,1,8,5,9,6,7,12,10,4,11,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0,0]
[2,1,4,7,10,6,9,8,3,5,12,11]=>[1,1,0,0,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,10,7,12,6,9,8,4,11,3,5]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[2,1,4,9,12,6,10,8,11,7,3,5]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,7,8,6,12,10,9,5,11,3]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0]
[2,1,4,5,6,10,7,8,9,3,12,11]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,1,10,5,6,12,7,8,9,11,3,4]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
[2,1,4,9,6,12,7,8,11,10,3,5]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,8,12,7,11,9,10,3,6]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,5,6,7,12,8,9,10,11,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,4,3,1,6,5,8,7,10,9,12,11]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,4,3,1,6,5,8,7,10,12,11,9]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[2,4,3,1,6,5,8,10,9,7,12,11]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[2,4,3,1,6,5,10,12,9,11,7,8]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,4,3,1,6,5,8,9,12,10,11,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[2,4,3,1,6,8,7,5,10,9,12,11]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[2,4,3,1,6,8,7,5,10,12,11,9]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[2,4,3,1,8,10,7,9,5,6,12,11]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[2,4,3,1,10,9,7,12,6,11,5,8]=>[1,1,0,1,1,0,0,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[2,4,3,1,8,9,7,12,10,6,11,5]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[2,4,3,1,6,7,10,8,9,5,12,11]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[2,4,3,1,10,7,12,8,9,11,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[2,4,3,1,6,9,12,8,11,10,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,4,3,1,6,7,8,12,9,10,11,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[4,6,3,5,1,2,8,7,10,9,12,11]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,6,3,5,1,2,8,7,10,12,11,9]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[4,6,3,5,1,2,8,10,9,7,12,11]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[4,6,3,5,1,2,10,12,9,11,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[4,6,3,5,1,2,8,9,12,10,11,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[6,5,3,8,2,7,1,4,10,9,12,11]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[6,5,3,8,2,7,1,4,10,12,11,9]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0]
[8,5,3,7,2,10,4,9,1,6,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0]
[10,5,3,7,2,9,4,12,6,11,1,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0]
[8,5,3,7,2,9,4,12,10,6,11,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0]
[6,5,3,7,2,10,8,4,9,1,12,11]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0,0,0,1,1,0,0]
[10,5,3,8,2,7,12,4,9,11,1,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[6,5,3,9,2,8,12,1,11,10,4,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]
[6,5,3,7,2,8,12,9,1,10,11,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0,0]
[4,5,3,8,6,2,7,1,10,9,12,11]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[4,5,3,8,6,2,7,1,10,12,11,9]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0]
[8,6,3,5,10,2,7,9,1,4,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0]
[10,6,3,5,9,2,7,12,4,11,1,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0]
[8,6,3,5,9,2,7,12,10,4,11,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,1,1,0,0,0,0,0]
[4,7,3,6,10,1,9,8,2,5,12,11]=>[1,1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,1,1,0,0]
[10,6,3,7,12,2,9,8,4,11,1,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0]
[4,9,3,6,12,1,10,8,11,7,2,5]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0]
[4,7,3,6,8,1,12,10,9,5,11,2]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0,0,0]
[4,5,3,6,10,7,1,8,9,2,12,11]=>[1,1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[10,7,3,5,6,12,2,8,9,11,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0]
[4,9,3,7,6,12,1,8,11,10,2,5]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0,0]
[4,5,3,8,7,12,2,11,9,10,1,6]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[4,5,3,6,7,12,8,2,9,10,11,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,6,4,5,1,8,7,10,9,12,11]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,3,6,4,5,1,8,7,10,12,11,9]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[2,3,6,4,5,1,8,10,9,7,12,11]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[2,3,6,4,5,1,10,12,9,11,7,8]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,3,6,4,5,1,8,9,12,10,11,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[6,3,8,4,5,7,1,2,10,9,12,11]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[6,3,8,4,5,7,1,2,10,12,11,9]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,1,0,1,1,0,0,0]
[8,3,7,4,5,10,2,9,1,6,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0]
[10,3,7,4,5,9,2,12,6,11,1,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0]
[8,3,7,4,5,9,2,12,10,6,11,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0]
[6,3,7,4,5,10,8,2,9,1,12,11]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0,0,1,1,0,0]
[10,3,8,4,5,7,12,2,9,11,1,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0]
[6,3,9,4,5,8,12,1,11,10,2,7]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[6,3,7,4,5,8,12,9,1,10,11,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0,0]
[2,5,8,4,7,6,1,3,10,9,12,11]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[2,5,8,4,7,6,1,3,10,12,11,9]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,1,1,0,0,0]
[8,5,10,4,7,6,2,9,1,3,12,11]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,5,9,4,7,6,2,12,3,11,1,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0]
[8,5,9,4,7,6,2,12,10,3,11,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,1,0,0,0,0,0]
[2,7,10,4,8,6,9,5,1,3,12,11]=>[1,1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[10,7,12,4,8,6,9,5,2,11,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0]
[2,9,8,4,12,6,10,3,11,7,1,5]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0]
[2,7,8,4,12,6,9,10,1,3,11,5]=>[1,1,0,1,1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,10,8,7,3,9,1,12,11]=>[1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[10,5,6,4,12,8,7,3,9,11,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0]
[2,9,8,4,6,12,7,3,11,10,1,5]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0,0]
[2,5,8,4,12,9,7,11,6,10,3,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
[2,5,6,4,7,12,9,8,1,10,11,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,8,5,6,7,1,10,9,12,11]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[2,3,4,8,5,6,7,1,10,12,11,9]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0]
[8,3,4,10,5,6,7,9,1,2,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0]
[10,3,4,9,5,6,7,12,2,11,1,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0]
[8,3,4,9,5,6,7,12,10,2,11,1]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,1,0,0,0,0,0]
[2,7,4,10,5,6,9,8,1,3,12,11]=>[1,1,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[10,7,4,12,5,6,9,8,2,11,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0]
[2,9,4,12,5,6,10,8,11,7,1,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0]
[2,7,4,8,5,6,12,10,9,3,11,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,1,1,0,0,0,0,0,0]
[2,3,6,10,5,9,7,8,1,4,12,11]=>[1,1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[10,3,6,12,5,9,7,8,2,11,1,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0]
[2,9,6,12,5,11,7,8,10,1,3,4]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,8,12,5,10,7,11,9,6,1,4]=>[1,1,0,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,3,6,7,5,12,10,8,9,4,11,1]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,3,4,5,10,6,7,8,9,1,12,11]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[10,3,4,5,12,6,7,8,9,11,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0]
[2,9,4,5,12,6,7,8,11,10,1,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0]
[2,3,8,5,12,6,7,11,9,10,1,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,7,12,6,11,8,9,10,1,5]=>[1,1,0,1,0,1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,3,4,5,6,12,7,8,9,10,11,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,10,11,12,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,4,3,6,5,8,9,10,7,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,4,3,6,5,10,9,11,12,7,8]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[2,1,4,3,6,5,8,9,10,11,12,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,4,3,6,7,8,5,10,9,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,4,3,6,7,8,5,10,11,12,9]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[2,1,4,3,8,7,9,10,5,6,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[2,1,4,3,10,7,11,9,5,12,8,6]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[2,1,4,3,8,7,9,10,11,12,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[2,1,4,3,6,7,8,9,10,5,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[2,1,4,3,10,7,8,9,11,12,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[2,1,4,3,6,9,8,10,11,5,12,7]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[2,1,4,3,6,7,8,9,10,11,12,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,4,5,6,3,8,7,10,9,12,11]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,4,5,6,3,8,7,10,11,12,9]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,4,5,6,3,8,9,10,7,12,11]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,4,5,6,3,10,9,11,12,7,8]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[2,1,4,5,6,3,8,9,10,11,12,7]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,6,5,7,8,3,4,10,9,12,11]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,6,5,7,8,3,4,10,11,12,9]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[2,1,8,5,9,7,3,10,6,4,12,11]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,1,0,0]
[2,1,10,5,11,7,3,9,6,12,8,4]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]
[2,1,8,5,9,7,3,10,11,12,6,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0]
[2,1,6,5,7,8,9,10,3,4,12,11]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[2,1,10,5,11,7,8,9,3,12,6,4]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]
[2,1,6,5,9,10,8,12,11,4,7,3]=>[1,1,0,0,1,1,1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[2,1,6,5,7,8,9,10,11,12,3,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[2,1,4,5,6,7,8,3,10,9,12,11]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,4,5,6,7,8,3,10,11,12,9]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[2,1,8,5,6,7,9,10,3,4,12,11]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,1,0,0]
[2,1,10,5,6,7,11,9,3,12,8,4]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0,0]
[2,1,8,5,6,7,9,10,11,12,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0,0]
[2,1,4,7,6,8,9,3,10,5,12,11]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0]
[2,1,10,7,6,8,9,3,11,12,5,4]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,0]
[2,1,4,9,6,10,8,3,11,7,12,5]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]
[2,1,4,7,6,8,9,10,11,3,12,5]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]
[2,1,4,5,6,7,8,9,10,3,12,11]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[2,1,10,5,6,7,8,9,11,12,3,4]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,0]
[2,1,4,9,6,7,8,10,11,3,12,5]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0]
[2,1,4,5,8,7,9,10,3,11,12,6]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[2,1,4,5,6,7,8,9,10,11,12,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,1,6,5,8,7,10,9,12,11]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,3,4,1,6,5,8,7,10,11,12,9]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[2,3,4,1,6,5,8,9,10,7,12,11]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[2,3,4,1,6,5,10,9,11,12,7,8]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[2,3,4,1,6,5,8,9,10,11,12,7]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,1,6,7,8,5,10,9,12,11]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[2,3,4,1,6,7,8,5,10,11,12,9]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[2,3,4,1,8,7,9,10,5,6,12,11]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[2,3,4,1,10,7,11,9,5,12,8,6]=>[1,1,0,1,0,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[2,3,4,1,8,7,9,10,11,12,5,6]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[2,3,4,1,6,7,8,9,10,5,12,11]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[2,3,4,1,10,7,8,9,11,12,5,6]=>[1,1,0,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[2,3,4,1,6,9,8,10,11,5,12,7]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[2,3,4,1,6,7,8,9,10,11,12,5]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,5,6,1,2,8,7,10,9,12,11]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,3,5,6,1,2,8,7,10,11,12,9]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[4,3,5,6,1,2,8,9,10,7,12,11]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[4,3,5,6,1,2,10,9,11,12,7,8]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[4,3,5,6,1,2,8,9,10,11,12,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[6,3,7,5,1,8,4,2,10,9,12,11]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0]
[6,3,7,5,1,8,4,2,10,11,12,9]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,1,0,1,0,1,0,0]
[8,3,9,5,1,7,4,10,6,2,12,11]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,1,1,0,0]
[10,3,11,5,1,7,4,9,6,12,8,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0]
[8,3,9,5,1,7,4,10,11,12,6,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0,1,0,0,0]
[6,3,7,5,1,8,9,10,4,2,12,11]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0,1,1,0,0]
[10,3,11,5,1,7,8,9,4,12,6,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0]
[6,3,9,5,2,10,8,12,11,4,7,1]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,0]
[6,3,7,5,1,8,9,10,11,12,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0]
[4,3,5,6,7,8,1,2,10,9,12,11]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[4,3,5,6,7,8,1,2,10,11,12,9]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[8,3,9,5,6,7,1,10,4,2,12,11]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,1,1,0,0]
[10,3,11,5,6,7,1,9,4,12,8,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0]
[8,3,9,5,6,7,1,10,11,12,4,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0,1,0,0,0]
[4,3,7,8,6,10,9,2,5,1,12,11]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0]
[10,3,11,7,6,8,9,4,1,12,5,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0]
[4,3,9,10,6,12,8,2,11,7,5,1]=>[1,1,1,1,0,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]
[4,3,7,8,6,9,10,12,11,5,1,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0,0,0]
[4,3,5,6,7,8,9,10,1,2,12,11]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[10,3,11,5,6,7,8,9,1,12,4,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0]
[4,3,9,10,6,7,8,12,11,2,5,1]=>[1,1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0,0,0]
[4,3,5,8,9,7,12,10,1,11,6,2]=>[1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]
[4,3,5,6,7,8,9,10,11,12,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[2,3,4,5,6,1,8,7,10,9,12,11]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,3,4,5,6,1,8,7,10,11,12,9]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[2,3,4,5,6,1,8,9,10,7,12,11]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[2,3,4,5,6,1,10,9,11,12,7,8]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[2,3,4,5,6,1,8,9,10,11,12,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[6,3,4,5,7,8,1,2,10,9,12,11]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[6,3,4,5,7,8,1,2,10,11,12,9]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[8,3,4,5,9,7,1,10,6,2,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0]
[10,3,4,5,11,7,1,9,6,12,8,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0]
[8,3,4,5,9,7,1,10,11,12,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,0,0]
[6,3,4,5,7,8,9,10,1,2,12,11]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[10,3,4,5,11,7,8,9,1,12,6,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0]
[6,3,4,5,9,10,8,12,11,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[6,3,4,5,7,8,9,10,11,12,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[2,5,4,6,7,1,8,3,10,9,12,11]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[2,5,4,6,7,1,8,3,10,11,12,9]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[8,5,4,6,7,1,9,10,3,2,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,0,1,1,0,0]
[10,5,4,6,7,1,11,9,3,12,8,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0]
[8,5,4,6,7,1,9,10,11,12,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0,0]
[2,7,4,8,6,1,9,5,10,3,12,11]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0]
[10,7,4,8,6,1,9,5,11,12,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0]
[2,9,4,10,6,1,8,5,11,7,12,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,1,0,0]
[2,7,4,8,6,1,9,10,11,5,12,3]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0,1,0,0]
[2,5,4,6,7,8,9,1,10,3,12,11]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[10,5,4,6,7,8,9,1,11,12,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0]
[2,9,4,10,6,7,8,1,11,5,12,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,1,0,0]
[2,5,4,8,9,7,11,10,3,6,12,1]=>[1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0]
[2,5,4,6,7,8,9,10,11,1,12,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[2,3,4,5,6,7,8,1,10,9,12,11]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[2,3,4,5,6,7,8,1,10,11,12,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[8,3,4,5,6,7,9,10,1,2,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,0,1,1,0,0]
[10,3,4,5,6,7,11,9,1,12,8,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0]
[8,3,4,5,6,7,9,10,11,12,1,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0,0]
[2,7,4,5,6,8,9,1,10,3,12,11]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0,1,1,0,0]
[10,7,4,5,6,8,9,1,11,12,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0]
[2,9,4,5,6,10,8,1,11,7,12,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0]
[2,7,4,5,6,8,9,10,11,1,12,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0,1,0,0]
[2,3,6,5,7,8,1,9,10,4,12,11]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[10,3,6,5,7,8,1,9,11,12,4,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0]
[2,9,6,5,7,8,1,10,11,4,12,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,1,0,0]
[2,3,8,5,9,7,1,10,6,11,12,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0]
[2,3,6,5,7,8,9,10,1,11,12,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[2,3,4,5,6,7,8,9,10,1,12,11]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[10,3,4,5,6,7,8,9,11,12,1,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0]
[2,9,4,5,6,7,8,10,11,1,12,3]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,1,0,0]
[2,3,8,5,6,7,9,10,1,11,12,4]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0,0]
[2,3,4,7,6,8,9,1,10,11,12,5]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0]
[2,4,3,6,5,8,7,10,9,12,11,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[12,2,3,4,5,6,7,8,9,10,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[3,12,1,4,5,6,7,8,9,10,11,2]=>[1,1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[12,3,4,5,6,7,8,9,10,11,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,11,10,12,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[2,1,4,3,6,5,9,8,10,7,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[2,1,4,3,6,5,9,8,11,10,12,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[2,1,4,3,6,5,10,9,11,8,12,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[2,1,4,3,7,6,8,5,10,9,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,4,3,7,6,8,5,11,10,12,9]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[2,1,4,3,7,6,9,8,10,5,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[2,1,4,3,7,6,9,8,11,10,12,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,1,4,3,7,6,10,9,11,8,12,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[2,1,4,3,8,7,9,6,10,5,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[2,1,4,3,8,7,9,6,11,10,12,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[2,1,4,3,8,7,10,9,11,6,12,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[2,1,4,3,9,8,10,7,11,6,12,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[2,1,5,4,6,3,8,7,10,9,12,11]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,5,4,6,3,8,7,11,10,12,9]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[2,1,5,4,6,3,9,8,10,7,12,11]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[2,1,5,4,6,3,9,8,11,10,12,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[2,1,5,4,6,3,10,9,11,8,12,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[2,1,5,4,7,6,8,3,10,9,12,11]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,5,4,7,6,8,3,11,10,12,9]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[2,1,5,4,7,6,9,8,10,3,12,11]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[2,1,5,4,7,6,9,8,11,10,12,3]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,1,5,4,7,6,10,9,11,8,12,3]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[2,1,5,4,8,7,9,6,10,3,12,11]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[2,1,5,4,8,7,9,6,11,10,12,3]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[2,1,5,4,8,7,10,9,11,6,12,3]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[2,1,5,4,9,8,10,7,11,6,12,3]=>[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[2,1,6,5,7,4,8,3,10,9,12,11]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,6,5,7,4,8,3,11,10,12,9]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[2,1,6,5,7,4,9,8,10,3,12,11]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[2,1,6,5,7,4,9,8,11,10,12,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,1,6,5,7,4,10,9,11,8,12,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[2,1,6,5,8,7,9,4,10,3,12,11]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[2,1,6,5,8,7,9,4,11,10,12,3]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[2,1,6,5,8,7,10,9,11,4,12,3]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[2,1,6,5,9,8,10,7,11,4,12,3]=>[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[2,1,7,6,8,5,9,4,10,3,12,11]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]
[2,1,7,6,8,5,9,4,11,10,12,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[2,1,7,6,8,5,10,9,11,4,12,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[2,1,7,6,9,8,10,5,11,4,12,3]=>[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[2,1,8,7,9,6,10,5,11,4,12,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[3,2,4,1,6,5,8,7,10,9,12,11]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,2,4,1,6,5,8,7,11,10,12,9]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[3,2,4,1,6,5,9,8,10,7,12,11]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[3,2,4,1,6,5,9,8,11,10,12,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[3,2,4,1,6,5,10,9,11,8,12,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[3,2,4,1,7,6,8,5,10,9,12,11]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[3,2,4,1,7,6,8,5,11,10,12,9]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[3,2,4,1,7,6,9,8,10,5,12,11]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[3,2,4,1,7,6,9,8,11,10,12,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[3,2,4,1,7,6,10,9,11,8,12,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,2,4,1,8,7,9,6,10,5,12,11]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[3,2,4,1,8,7,9,6,11,10,12,5]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[3,2,4,1,8,7,10,9,11,6,12,5]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,2,4,1,9,8,10,7,11,6,12,5]=>[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[3,2,5,4,6,1,8,7,10,9,12,11]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,2,5,4,6,1,8,7,11,10,12,9]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[3,2,5,4,6,1,9,8,10,7,12,11]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[3,2,5,4,6,1,9,8,11,10,12,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[3,2,5,4,6,1,10,9,11,8,12,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[3,2,5,4,7,6,8,1,10,9,12,11]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[3,2,5,4,7,6,8,1,11,10,12,9]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[3,2,5,4,7,6,9,8,10,1,12,11]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[3,2,5,4,7,6,9,8,11,10,12,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[3,2,5,4,7,6,10,9,11,8,12,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,2,5,4,8,7,9,6,10,1,12,11]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[3,2,5,4,8,7,9,6,11,10,12,1]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[3,2,5,4,8,7,10,9,11,6,12,1]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,2,5,4,9,8,10,7,11,6,12,1]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[3,2,6,5,7,4,8,1,10,9,12,11]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[3,2,6,5,7,4,8,1,11,10,12,9]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[3,2,6,5,7,4,9,8,10,1,12,11]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[3,2,6,5,7,4,9,8,11,10,12,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[3,2,6,5,7,4,10,9,11,8,12,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,2,6,5,8,7,9,4,10,1,12,11]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[3,2,6,5,8,7,9,4,11,10,12,1]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[3,2,6,5,8,7,10,9,11,4,12,1]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,2,6,5,9,8,10,7,11,4,12,1]=>[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[3,2,7,6,8,5,9,4,10,1,12,11]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]
[3,2,7,6,8,5,9,4,11,10,12,1]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[3,2,7,6,8,5,10,9,11,4,12,1]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,2,7,6,9,8,10,5,11,4,12,1]=>[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[3,2,8,7,9,6,10,5,11,4,12,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[4,3,5,2,6,1,8,7,10,9,12,11]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,3,5,2,6,1,8,7,11,10,12,9]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[4,3,5,2,6,1,9,8,10,7,12,11]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[4,3,5,2,6,1,9,8,11,10,12,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[4,3,5,2,6,1,10,9,11,8,12,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[4,3,5,2,7,6,8,1,10,9,12,11]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[4,3,5,2,7,6,8,1,11,10,12,9]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[4,3,5,2,7,6,9,8,10,1,12,11]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[4,3,5,2,7,6,9,8,11,10,12,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[4,3,5,2,7,6,10,9,11,8,12,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[4,3,5,2,8,7,9,6,10,1,12,11]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,3,5,2,8,7,9,6,11,10,12,1]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,3,5,2,8,7,10,9,11,6,12,1]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,3,5,2,9,8,10,7,11,6,12,1]=>[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,3,6,5,7,2,8,1,10,9,12,11]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[4,3,6,5,7,2,8,1,11,10,12,9]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[4,3,6,5,7,2,9,8,10,1,12,11]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[4,3,6,5,7,2,9,8,11,10,12,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[4,3,6,5,7,2,10,9,11,8,12,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[4,3,6,5,8,7,9,2,10,1,12,11]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,3,6,5,8,7,9,2,11,10,12,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,3,6,5,8,7,10,9,11,2,12,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,3,6,5,9,8,10,7,11,2,12,1]=>[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,3,7,6,8,5,9,2,10,1,12,11]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,3,7,6,8,5,9,2,11,10,12,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,3,7,6,8,5,10,9,11,2,12,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,3,7,6,9,8,10,5,11,2,12,1]=>[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,3,8,7,9,6,10,5,11,2,12,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[5,4,6,3,7,2,8,1,10,9,12,11]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[5,4,6,3,7,2,8,1,11,10,12,9]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[5,4,6,3,7,2,9,8,10,1,12,11]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[5,4,6,3,7,2,9,8,11,10,12,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[5,4,6,3,7,2,10,9,11,8,12,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[5,4,6,3,8,7,9,2,10,1,12,11]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[5,4,6,3,8,7,9,2,11,10,12,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[5,4,6,3,8,7,10,9,11,2,12,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[5,4,6,3,9,8,10,7,11,2,12,1]=>[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,4,7,6,8,3,9,2,10,1,12,11]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]
[5,4,7,6,8,3,9,2,11,10,12,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[5,4,7,6,8,3,10,9,11,2,12,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[5,4,7,6,9,8,10,3,11,2,12,1]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,4,8,7,9,6,10,3,11,2,12,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[6,5,7,4,8,3,9,2,10,1,12,11]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]
[6,5,7,4,8,3,9,2,11,10,12,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[6,5,7,4,8,3,10,9,11,2,12,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[6,5,7,4,9,8,10,3,11,2,12,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[6,5,8,7,9,4,10,3,11,2,12,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[7,6,8,5,9,4,10,3,11,2,12,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[2,1,4,3,6,5,8,7,11,9,12,10]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[2,1,4,3,6,5,9,7,10,8,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[2,1,4,3,6,5,9,7,11,8,12,10]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[2,1,4,3,6,5,10,7,11,8,12,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[2,1,4,3,7,5,8,6,10,9,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,4,3,7,5,8,6,11,9,12,10]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[2,1,4,3,7,5,9,6,10,8,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[2,1,4,3,7,5,9,6,11,8,12,10]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,1,4,3,7,5,10,6,11,8,12,9]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[2,1,4,3,8,5,9,6,10,7,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[2,1,4,3,8,5,9,6,11,7,12,10]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[2,1,4,3,8,5,10,6,11,7,12,9]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[2,1,4,3,9,5,10,6,11,7,12,8]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[2,1,5,3,6,4,8,7,10,9,12,11]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,5,3,6,4,8,7,11,9,12,10]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[2,1,5,3,6,4,9,7,10,8,12,11]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[2,1,5,3,6,4,9,7,11,8,12,10]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[2,1,5,3,6,4,10,7,11,8,12,9]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[2,1,5,3,7,4,8,6,10,9,12,11]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,5,3,7,4,8,6,11,9,12,10]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[2,1,5,3,7,4,9,6,10,8,12,11]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[2,1,5,3,7,4,9,6,11,8,12,10]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,1,5,3,7,4,10,6,11,8,12,9]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[2,1,5,3,8,4,9,6,10,7,12,11]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[2,1,5,3,8,4,9,6,11,7,12,10]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[2,1,5,3,8,4,10,6,11,7,12,9]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[2,1,5,3,9,4,10,6,11,7,12,8]=>[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[2,1,6,3,7,4,8,5,10,9,12,11]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,6,3,7,4,8,5,11,9,12,10]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[2,1,6,3,7,4,9,5,10,8,12,11]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[2,1,6,3,7,4,9,5,11,8,12,10]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,1,6,3,7,4,10,5,11,8,12,9]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[2,1,6,3,8,4,9,5,10,7,12,11]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[2,1,6,3,8,4,9,5,11,7,12,10]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[2,1,6,3,8,4,10,5,11,7,12,9]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[2,1,6,3,9,4,10,5,11,7,12,8]=>[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[2,1,7,3,8,4,9,5,10,6,12,11]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]
[2,1,7,3,8,4,9,5,11,6,12,10]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[2,1,7,3,8,4,10,5,11,6,12,9]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[2,1,7,3,9,4,10,5,11,6,12,8]=>[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[2,1,8,3,9,4,10,5,11,6,12,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[3,1,4,2,6,5,8,7,10,9,12,11]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,4,2,6,5,8,7,11,9,12,10]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[3,1,4,2,6,5,9,7,10,8,12,11]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[3,1,4,2,6,5,9,7,11,8,12,10]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,4,2,6,5,10,7,11,8,12,9]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[3,1,4,2,7,5,8,6,10,9,12,11]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[3,1,4,2,7,5,8,6,11,9,12,10]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[3,1,4,2,7,5,9,6,10,8,12,11]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[3,1,4,2,7,5,9,6,11,8,12,10]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[3,1,4,2,7,5,10,6,11,8,12,9]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,1,4,2,8,5,9,6,10,7,12,11]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[3,1,4,2,8,5,9,6,11,7,12,10]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[3,1,4,2,8,5,10,6,11,7,12,9]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,1,4,2,9,5,10,6,11,7,12,8]=>[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[3,1,5,2,6,4,8,7,10,9,12,11]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,5,2,6,4,8,7,11,9,12,10]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[3,1,5,2,6,4,9,7,10,8,12,11]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[3,1,5,2,6,4,9,7,11,8,12,10]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,5,2,6,4,10,7,11,8,12,9]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[3,1,5,2,7,4,8,6,10,9,12,11]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[3,1,5,2,7,4,8,6,11,9,12,10]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[3,1,5,2,7,4,9,6,10,8,12,11]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[3,1,5,2,7,4,9,6,11,8,12,10]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[3,1,5,2,7,4,10,6,11,8,12,9]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,1,5,2,8,4,9,6,10,7,12,11]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[3,1,5,2,8,4,9,6,11,7,12,10]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[3,1,5,2,8,4,10,6,11,7,12,9]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,1,5,2,9,4,10,6,11,7,12,8]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[3,1,6,2,7,4,8,5,10,9,12,11]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[3,1,6,2,7,4,8,5,11,9,12,10]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[3,1,6,2,7,4,9,5,10,8,12,11]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[3,1,6,2,7,4,9,5,11,8,12,10]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[3,1,6,2,7,4,10,5,11,8,12,9]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[3,1,6,2,8,4,9,5,10,7,12,11]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[3,1,6,2,8,4,9,5,11,7,12,10]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[3,1,6,2,8,4,10,5,11,7,12,9]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,1,6,2,9,4,10,5,11,7,12,8]=>[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[3,1,7,2,8,4,9,5,10,6,12,11]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]
[3,1,7,2,8,4,9,5,11,6,12,10]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[3,1,7,2,8,4,10,5,11,6,12,9]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[3,1,7,2,9,4,10,5,11,6,12,8]=>[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[3,1,8,2,9,4,10,5,11,6,12,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[4,1,5,2,6,3,8,7,10,9,12,11]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,1,5,2,6,3,8,7,11,9,12,10]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[4,1,5,2,6,3,9,7,10,8,12,11]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[4,1,5,2,6,3,9,7,11,8,12,10]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[4,1,5,2,6,3,10,7,11,8,12,9]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[4,1,5,2,7,3,8,6,10,9,12,11]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[4,1,5,2,7,3,8,6,11,9,12,10]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[4,1,5,2,7,3,9,6,10,8,12,11]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[4,1,5,2,7,3,9,6,11,8,12,10]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[4,1,5,2,7,3,10,6,11,8,12,9]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[4,1,5,2,8,3,9,6,10,7,12,11]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,1,5,2,8,3,9,6,11,7,12,10]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,1,5,2,8,3,10,6,11,7,12,9]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,1,5,2,9,3,10,6,11,7,12,8]=>[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,1,6,2,7,3,8,5,10,9,12,11]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[4,1,6,2,7,3,8,5,11,9,12,10]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[4,1,6,2,7,3,9,5,10,8,12,11]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[4,1,6,2,7,3,9,5,11,8,12,10]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[4,1,6,2,7,3,10,5,11,8,12,9]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[4,1,6,2,8,3,9,5,10,7,12,11]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,1,6,2,8,3,9,5,11,7,12,10]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,1,6,2,8,3,10,5,11,7,12,9]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,1,6,2,9,3,10,5,11,7,12,8]=>[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,1,7,2,8,3,9,5,10,6,12,11]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]
[4,1,7,2,8,3,9,5,11,6,12,10]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[4,1,7,2,8,3,10,5,11,6,12,9]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[4,1,7,2,9,3,10,5,11,6,12,8]=>[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[4,1,8,2,9,3,10,5,11,6,12,7]=>[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[5,1,6,2,7,3,8,4,10,9,12,11]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[5,1,6,2,7,3,8,4,11,9,12,10]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[5,1,6,2,7,3,9,4,10,8,12,11]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[5,1,6,2,7,3,9,4,11,8,12,10]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[5,1,6,2,7,3,10,4,11,8,12,9]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[5,1,6,2,8,3,9,4,10,7,12,11]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[5,1,6,2,8,3,9,4,11,7,12,10]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[5,1,6,2,8,3,10,4,11,7,12,9]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[5,1,6,2,9,3,10,4,11,7,12,8]=>[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,1,7,2,8,3,9,4,10,6,12,11]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]
[5,1,7,2,8,3,9,4,11,6,12,10]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[5,1,7,2,8,3,10,4,11,6,12,9]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[5,1,7,2,9,3,10,4,11,6,12,8]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[5,1,8,2,9,3,10,4,11,6,12,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[6,1,7,2,8,3,9,4,10,5,12,11]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]
[6,1,7,2,8,3,9,4,11,5,12,10]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]
[6,1,7,2,8,3,10,4,11,5,12,9]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]
[6,1,7,2,9,3,10,4,11,5,12,8]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]
[6,1,8,2,9,3,10,4,11,5,12,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[1,8,2,9,3,10,4,11,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0]
[1,8,2,9,3,10,4,11,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0,0]
[1,8,2,9,3,10,11,4,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0,0]
[1,8,2,9,3,10,11,4,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0,0,0,0]
[1,8,2,9,3,10,11,12,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0,0]
[1,8,2,9,10,3,4,11,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0,0]
[1,8,2,9,10,3,4,11,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0]
[1,8,2,9,10,3,11,4,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,0,0]
[1,8,2,9,10,3,11,4,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,0,0]
[1,8,2,9,10,3,11,12,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,0,0]
[1,8,2,9,10,11,3,4,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0,0,0]
[1,8,2,9,10,11,3,4,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0]
[1,8,2,9,10,11,3,12,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0,0]
[1,8,2,9,10,11,12,3,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[1,8,9,2,3,10,4,11,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0]
[1,8,9,2,3,10,4,11,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,0]
[1,8,9,2,3,10,11,4,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0]
[1,8,9,2,3,10,11,4,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0]
[1,8,9,2,3,10,11,12,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0]
[1,8,9,2,10,3,4,11,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0]
[1,8,9,2,10,3,4,11,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0,0,0]
[1,8,9,2,10,3,11,4,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0]
[1,8,9,2,10,3,11,4,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0]
[1,8,9,2,10,3,11,12,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0]
[1,8,9,2,10,11,3,4,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,1,0,0,0]
[1,8,9,2,10,11,3,4,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0,0,0]
[1,8,9,2,10,11,3,12,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0]
[1,8,9,2,10,11,12,3,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[1,8,9,10,2,3,4,11,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0]
[1,8,9,10,2,3,4,11,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0]
[1,8,9,10,2,3,11,4,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0]
[1,8,9,10,2,3,11,4,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,0,0]
[1,8,9,10,2,3,11,12,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[1,8,9,10,2,11,3,4,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0,0,0]
[1,8,9,10,2,11,3,4,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0,0]
[1,8,9,10,2,11,3,12,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[1,8,9,10,2,11,12,3,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[1,8,9,10,11,2,3,4,5,12,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0,0]
[1,8,9,10,11,2,3,4,12,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[1,8,9,10,11,2,3,12,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[1,8,9,10,11,2,12,3,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[1,8,9,10,11,12,2,3,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,1,2,9,3,10,4,11,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0]
[8,1,2,9,3,10,4,11,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0,0,0]
[8,1,2,9,3,10,11,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0,0,0]
[8,1,2,9,3,10,11,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0,0,0,0]
[8,1,2,9,3,10,11,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0,0,0,0]
[8,1,2,9,10,3,4,11,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0,1,0,0,0]
[8,1,2,9,10,3,4,11,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0]
[8,1,2,9,10,3,11,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,0,1,0,0,0]
[8,1,2,9,10,3,11,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0,0,0]
[8,1,2,9,10,3,11,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0,0,0,0]
[8,1,2,9,10,11,3,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,1,0,0,0]
[8,1,2,9,10,11,3,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0]
[8,1,2,9,10,11,3,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0,0,0,0]
[8,1,2,9,10,11,12,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[8,1,9,2,3,10,4,11,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0]
[8,1,9,2,3,10,4,11,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0,0,0]
[8,1,9,2,3,10,11,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0]
[8,1,9,2,3,10,11,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0]
[8,1,9,2,3,10,11,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0]
[8,1,9,2,10,3,4,11,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0]
[8,1,9,2,10,3,4,11,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0,0,0]
[8,1,9,2,10,3,11,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0]
[8,1,9,2,10,3,11,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0]
[8,1,9,2,10,3,11,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0]
[8,1,9,2,10,11,3,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0,1,0,0,0]
[8,1,9,2,10,11,3,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0,0,0]
[8,1,9,2,10,11,3,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0]
[8,1,9,2,10,11,12,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[8,1,9,10,2,3,4,11,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0]
[8,1,9,10,2,3,4,11,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0]
[8,1,9,10,2,3,11,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0]
[8,1,9,10,2,3,11,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0,0,0]
[8,1,9,10,2,3,11,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[8,1,9,10,2,11,3,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0,1,0,0,0]
[8,1,9,10,2,11,3,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,0,0,0]
[8,1,9,10,2,11,3,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[8,1,9,10,2,11,12,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[8,1,9,10,11,2,3,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,1,0,0,0]
[8,1,9,10,11,2,3,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[8,1,9,10,11,2,3,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[8,1,9,10,11,2,12,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[8,1,9,10,11,12,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,1,2,3,10,4,11,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,0,0]
[8,9,1,2,3,10,4,11,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0,0,0]
[8,9,1,2,3,10,11,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,1,0,0,0]
[8,9,1,2,3,10,11,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,0]
[8,9,1,2,3,10,11,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0,0,0,0]
[8,9,1,2,10,3,4,11,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,0,0]
[8,9,1,2,10,3,4,11,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0,0]
[8,9,1,2,10,3,11,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0]
[8,9,1,2,10,3,11,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,0]
[8,9,1,2,10,3,11,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,0,0]
[8,9,1,2,10,11,3,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0]
[8,9,1,2,10,11,3,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0]
[8,9,1,2,10,11,3,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0,0]
[8,9,1,2,10,11,12,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0]
[8,9,1,10,2,3,4,11,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0,0,0]
[8,9,1,10,2,3,4,11,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0,0,0]
[8,9,1,10,2,3,11,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0]
[8,9,1,10,2,3,11,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,0]
[8,9,1,10,2,3,11,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0,0,0,0]
[8,9,1,10,2,11,3,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0,0,0]
[8,9,1,10,2,11,3,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0,0]
[8,9,1,10,2,11,3,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0]
[8,9,1,10,2,11,12,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0]
[8,9,1,10,11,2,3,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,1,0,0,0]
[8,9,1,10,11,2,3,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,1,0,0,0,0]
[8,9,1,10,11,2,3,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0]
[8,9,1,10,11,2,12,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0,0]
[8,9,1,10,11,12,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,10,1,2,3,4,11,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,1,0,0,0]
[8,9,10,1,2,3,4,11,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,1,0,0,0,0]
[8,9,10,1,2,3,11,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0,1,0,0,0]
[8,9,10,1,2,3,11,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0]
[8,9,10,1,2,3,11,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,0]
[8,9,10,1,2,11,3,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,1,0,0,0]
[8,9,10,1,2,11,3,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0]
[8,9,10,1,2,11,3,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,0,0,0]
[8,9,10,1,2,11,12,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0]
[8,9,10,1,11,2,3,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,1,0,0,0]
[8,9,10,1,11,2,3,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0,0,0,0]
[8,9,10,1,11,2,3,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,9,10,1,11,2,12,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0,0]
[8,9,10,1,11,12,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,9,10,11,1,2,3,4,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0]
[8,9,10,11,1,2,3,4,12,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0,0,0]
[8,9,10,11,1,2,3,12,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0,0,0]
[8,9,10,11,1,2,12,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,10,11,1,12,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,10,11,12,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[12,10,8,6,4,2,1,3,5,7,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,6,4,2,1,3,5,7,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,10,6,4,2,1,3,5,8,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,12,6,4,2,1,3,5,8,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,11,12,6,4,2,1,3,5,9,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
[12,10,7,8,4,2,1,3,6,5,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,8,4,2,1,3,6,5,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,7,10,4,2,1,3,6,8,5,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,7,12,4,2,1,3,6,8,10,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[10,11,7,12,4,2,1,3,6,9,8,5]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0]
[12,8,9,10,4,2,1,3,7,6,5,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,8,9,12,4,2,1,3,7,6,10,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[10,8,11,12,4,2,1,3,7,9,6,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,11,12,4,2,1,3,8,7,6,5]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[12,10,8,5,6,2,1,4,3,7,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,5,6,2,1,4,3,7,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,10,5,6,2,1,4,3,8,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,12,5,6,2,1,4,3,8,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,11,12,5,6,2,1,4,3,9,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
[12,10,7,5,8,2,1,4,6,3,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,5,8,2,1,4,6,3,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,7,5,10,2,1,4,6,8,3,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,7,5,12,2,1,4,6,8,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[10,11,7,5,12,2,1,4,6,9,8,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0]
[12,8,9,5,10,2,1,4,7,6,3,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,8,9,5,12,2,1,4,7,6,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[10,8,11,5,12,2,1,4,7,9,6,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0]
[9,10,11,5,12,2,1,4,8,7,6,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0,0]
[12,10,6,7,8,2,1,5,4,3,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,6,7,8,2,1,5,4,3,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,6,7,10,2,1,5,4,8,3,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,6,7,12,2,1,5,4,8,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[10,11,6,7,12,2,1,5,4,9,8,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0]
[12,8,6,9,10,2,1,5,7,4,3,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,8,6,9,12,2,1,5,7,4,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[10,8,6,11,12,2,1,5,7,9,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0]
[9,10,6,11,12,2,1,5,8,7,4,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0]
[12,7,8,9,10,2,1,6,5,4,3,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,8,9,12,2,1,6,5,4,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[10,7,8,11,12,2,1,6,5,9,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0]
[9,7,10,11,12,2,1,6,8,5,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,11,12,2,1,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[12,10,8,6,3,4,2,1,5,7,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,6,3,4,2,1,5,7,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,10,6,3,4,2,1,5,8,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,12,6,3,4,2,1,5,8,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,11,12,6,3,4,2,1,5,9,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
[12,10,7,8,3,4,2,1,6,5,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,8,3,4,2,1,6,5,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,7,10,3,4,2,1,6,8,5,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,7,12,3,4,2,1,6,8,10,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[10,11,7,12,3,4,2,1,6,9,8,5]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0]
[12,8,9,10,3,4,2,1,7,6,5,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,8,9,12,3,4,2,1,7,6,10,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[10,8,11,12,3,4,2,1,7,9,6,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[9,10,11,12,3,4,2,1,8,7,6,5]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[12,10,8,5,3,6,2,4,1,7,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,5,3,6,2,4,1,7,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,10,5,3,6,2,4,1,8,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,12,5,3,6,2,4,1,8,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,11,12,5,3,6,2,4,1,9,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
[12,10,7,5,3,8,2,4,6,1,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,5,3,8,2,4,6,1,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,7,5,3,10,2,4,6,8,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,7,5,3,12,2,4,6,8,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,11,7,5,3,12,2,4,6,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0]
[12,8,9,5,3,10,2,4,7,6,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,8,9,5,3,12,2,4,7,6,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,8,11,5,3,12,2,4,7,9,6,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0]
[9,10,11,5,3,12,2,4,8,7,6,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0]
[12,10,6,7,3,8,2,5,4,1,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,6,7,3,8,2,5,4,1,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,6,7,3,10,2,5,4,8,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,6,7,3,12,2,5,4,8,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,11,6,7,3,12,2,5,4,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0]
[12,8,6,9,3,10,2,5,7,4,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,8,6,9,3,12,2,5,7,4,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,8,6,11,3,12,2,5,7,9,4,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0]
[9,10,6,11,3,12,2,5,8,7,4,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0]
[12,7,8,9,3,10,2,6,5,4,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,8,9,3,12,2,6,5,4,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,7,8,11,3,12,2,6,5,9,4,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0]
[9,7,10,11,3,12,2,6,8,5,4,1]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,10,11,3,12,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0]
[12,10,8,4,5,6,3,2,1,7,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,8,4,5,6,3,2,1,7,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,10,4,5,6,3,2,1,8,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,12,4,5,6,3,2,1,8,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,11,12,4,5,6,3,2,1,9,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
[12,10,7,4,5,8,3,2,6,1,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,7,4,5,8,3,2,6,1,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,7,4,5,10,3,2,6,8,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,7,4,5,12,3,2,6,8,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,11,7,4,5,12,3,2,6,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0]
[12,8,9,4,5,10,3,2,7,6,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,8,9,4,5,12,3,2,7,6,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,8,11,4,5,12,3,2,7,9,6,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0]
[9,10,11,4,5,12,3,2,8,7,6,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0]
[12,10,6,4,7,8,3,5,2,1,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,6,4,7,8,3,5,2,1,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,6,4,7,10,3,5,2,8,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,6,4,7,12,3,5,2,8,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,11,6,4,7,12,3,5,2,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0]
[12,8,6,4,9,10,3,5,7,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,8,6,4,9,12,3,5,7,2,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,8,6,4,11,12,3,5,7,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0]
[9,10,6,4,11,12,3,5,8,7,2,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0]
[12,7,8,4,9,10,3,6,5,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,8,4,9,12,3,6,5,2,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,7,8,4,11,12,3,6,5,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0]
[9,7,10,4,11,12,3,6,8,5,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,9,10,4,11,12,3,7,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0,0]
[12,10,5,6,7,8,4,3,2,1,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,5,6,7,8,4,3,2,1,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,9,5,6,7,10,4,3,2,8,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,5,6,7,12,4,3,2,8,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,11,5,6,7,12,4,3,2,9,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0]
[12,8,5,6,9,10,4,3,7,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,8,5,6,9,12,4,3,7,2,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,8,5,6,11,12,4,3,7,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0]
[9,10,5,6,11,12,4,3,8,7,2,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0]
[12,7,5,8,9,10,4,6,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,5,8,9,12,4,6,3,2,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,7,5,8,11,12,4,6,3,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0]
[9,7,5,10,11,12,4,6,8,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,5,10,11,12,4,7,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[12,6,7,8,9,10,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,6,7,8,9,12,5,4,3,2,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,6,7,8,11,12,5,4,3,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0]
[9,6,7,10,11,12,5,4,8,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,6,9,10,11,12,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[2,3,4,5,6,7,8,9,12,11,1,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[12,11,10,8,6,4,2,1,3,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,6,4,2,1,3,5,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,6,4,2,1,3,5,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,8,7,6,4,2,1,3,5,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,8,7,6,4,2,1,3,5,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,7,9,6,4,2,1,3,8,5,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,11,9,6,4,2,1,3,8,10,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,7,9,6,4,2,1,3,8,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,7,6,4,2,1,3,5,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,7,6,4,2,1,3,10,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,8,11,10,7,9,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,8,6,5,4,2,1,3,7,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,8,6,5,4,2,1,3,7,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,6,5,4,2,1,3,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,6,5,4,2,1,3,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,6,5,4,2,1,3,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,8,5,7,4,2,1,6,3,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,8,5,7,4,2,1,6,3,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,5,9,7,4,2,1,6,8,3,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,11,9,7,4,2,1,6,8,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,5,9,7,4,2,1,6,8,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,5,7,4,2,1,6,3,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,5,7,4,2,1,6,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,5,10,8,7,4,2,1,9,6,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,5,7,4,2,1,6,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,8,7,6,5,4,2,1,3,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,8,7,6,5,4,2,1,3,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,7,9,6,5,4,2,1,8,3,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,11,9,6,5,4,2,1,8,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,7,9,6,5,4,2,1,8,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,6,9,8,5,7,2,1,4,3,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,6,11,9,8,5,7,2,1,4,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,6,11,8,10,5,7,2,1,9,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,6,9,8,5,7,2,1,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,7,6,5,4,2,1,3,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,7,6,5,4,2,1,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,8,11,10,7,6,5,9,2,1,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,11,10,9,6,8,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,8,6,4,3,2,1,5,7,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,8,6,4,3,2,1,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,6,4,3,2,1,5,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,6,4,3,2,1,5,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,8,7,6,4,3,2,1,5,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,8,7,6,4,3,2,1,5,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,7,9,6,4,3,2,1,8,5,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,11,9,6,4,3,2,1,8,10,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,7,9,6,4,3,2,1,8,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,7,6,4,3,2,1,5,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,7,6,4,3,2,1,10,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,8,11,10,7,9,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,8,6,3,5,2,4,1,7,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,8,6,3,5,2,4,1,7,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,6,3,5,2,4,1,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,6,3,5,2,4,1,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,6,3,5,2,4,1,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,8,3,7,5,2,4,6,1,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,8,3,7,5,2,4,6,1,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,3,9,7,5,2,4,6,8,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,3,11,9,7,5,2,4,6,8,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,3,9,7,5,2,4,6,8,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,3,7,5,2,4,6,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,3,7,5,2,4,6,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,3,10,8,7,5,2,4,9,6,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,3,7,5,2,4,6,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,8,7,6,3,5,2,4,1,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,8,7,6,3,5,2,4,1,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,7,9,6,3,5,2,4,8,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,11,9,6,3,5,2,4,8,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,7,9,6,3,5,2,4,8,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,3,8,6,5,2,7,4,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,3,8,6,5,2,7,4,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,3,8,10,6,5,2,7,9,4,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,3,8,6,5,2,7,4,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,7,6,3,5,2,4,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,7,6,3,5,2,4,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,8,11,10,7,6,3,5,2,9,4,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,3,9,7,6,8,2,5,4,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,8,6,5,4,3,2,1,7,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,8,6,5,4,3,2,1,7,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,6,5,4,3,2,1,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,6,5,4,3,2,1,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,8,5,7,4,3,2,6,1,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,8,5,7,4,3,2,6,1,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,5,9,7,4,3,2,6,8,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,11,9,7,4,3,2,6,8,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,5,9,7,4,3,2,6,8,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,5,7,4,3,2,6,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,5,7,4,3,2,6,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,5,10,8,7,4,3,2,9,6,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,5,7,4,3,2,6,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,8,4,7,6,3,5,2,1,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,8,4,7,6,3,5,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,4,9,7,6,3,5,2,8,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,4,11,9,7,6,3,5,2,8,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,4,9,7,6,3,5,2,8,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,4,9,6,8,3,5,7,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,4,11,9,6,8,3,5,7,2,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,4,11,6,10,8,3,5,7,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,4,9,6,8,3,5,7,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,9,8,4,7,6,3,5,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,4,7,6,3,5,2,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,8,11,10,4,7,6,3,5,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,4,10,7,9,6,3,8,5,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,9,8,4,7,6,3,5,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,8,7,6,5,4,3,2,1,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,7,9,6,5,4,3,2,8,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,11,9,6,5,4,3,2,8,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,7,9,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,6,9,8,5,4,3,7,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,6,11,9,8,5,4,3,7,2,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,6,11,8,10,5,4,3,7,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,6,9,8,5,4,3,7,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,5,9,8,7,4,6,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,11,9,8,7,4,6,3,2,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,11,8,10,7,4,6,3,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,11,7,10,9,4,6,8,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,10,5,9,8,7,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,11,8,7,6,5,4,3,2,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,8,11,10,7,6,5,4,3,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,11,10,9,6,5,4,8,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,6,11,10,9,8,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,9,10,11,7,1,2,3,4,5,12,6]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,1,0,0]
[2,9,10,11,12,8,1,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[11,12,2,4,6,8,10,1,3,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,10,2,4,6,8,12,1,3,5,7,11]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0,0,0,0]
[11,9,12,2,4,6,8,10,1,3,5,7]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,11,12,9,2,4,6,8,1,3,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
[7,8,2,4,6,10,12,1,3,5,9,11]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,0,0,0]
[7,8,11,12,2,4,6,10,1,3,5,9]=>[1,1,1,1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[9,7,10,2,4,6,8,12,1,3,5,11]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0]
[9,11,7,12,2,4,6,8,10,1,3,5]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[7,10,11,12,9,2,4,6,8,1,3,5]=>[1,1,1,1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[8,9,10,7,2,4,6,12,1,3,5,11]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0,0,0,0]
[11,8,9,7,12,2,4,6,10,1,3,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[10,11,8,12,7,9,2,4,6,1,3,5]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0]
[9,10,11,12,8,7,2,4,6,1,3,5]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[5,6,2,4,8,10,12,1,3,7,9,11]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[5,6,11,12,2,4,8,10,1,3,7,9]=>[1,1,1,1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[5,6,9,10,2,4,8,12,1,3,7,11]=>[1,1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0,0,0]
[11,5,6,9,12,2,4,8,10,1,3,7]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[10,11,12,5,6,9,2,4,8,1,3,7]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
[7,5,8,2,4,6,10,12,1,3,9,11]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,1,1,0,0,0,0,0]
[7,5,8,11,12,2,4,6,10,1,3,9]=>[1,1,1,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]
[7,9,5,10,2,4,6,8,12,1,3,11]=>[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,1,0,0,0,0]
[7,9,11,5,12,2,4,6,8,10,1,3]=>[1,1,1,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0]
[10,7,11,12,5,9,2,4,6,8,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[5,8,9,10,7,2,4,6,12,1,3,11]=>[1,1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0,0,0]
[11,5,8,9,7,12,2,4,6,10,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[8,10,5,11,12,7,9,2,4,6,1,3]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0]
[9,10,11,12,5,8,7,2,4,6,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[6,7,8,5,2,4,10,12,1,3,9,11]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,0,0]
[6,7,8,5,11,12,2,4,10,1,3,9]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,0,0,0,0]
[9,6,7,5,10,2,4,8,12,1,3,11]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0]
[9,6,7,11,5,12,2,4,8,10,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0]
[6,10,7,11,12,5,9,2,4,8,1,3]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,6,10,5,7,2,4,12,1,3,11]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,1,0,0,0,0]
[8,9,11,6,5,7,12,2,4,10,1,3]=>[1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0,0,0,0]
[10,8,11,6,12,5,7,9,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0]
[9,6,10,11,12,8,5,7,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[7,8,9,10,6,5,2,4,12,1,3,11]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,1,0,0,0,0]
[11,7,8,9,6,5,12,2,4,10,1,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,11,7,8,6,12,5,9,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0]
[9,10,11,7,12,6,8,5,2,4,1,3]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0,0]
[8,9,10,11,12,7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[3,4,2,6,8,10,12,1,5,7,9,11]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[3,4,11,12,2,6,8,10,1,5,7,9]=>[1,1,1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[3,4,9,10,2,6,8,12,1,5,7,11]=>[1,1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0,0,0]
[11,3,4,9,12,2,6,8,10,1,5,7]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[10,11,12,3,4,9,2,6,8,1,5,7]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
[3,4,7,8,2,6,10,12,1,5,9,11]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,0]
[3,4,7,8,11,12,2,6,10,1,5,9]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[9,3,4,7,10,2,6,8,12,1,5,11]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0]
[9,11,3,4,7,12,2,6,8,10,1,5]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0]
[3,10,11,12,4,7,9,2,6,8,1,5]=>[1,1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[8,9,10,3,4,7,2,6,12,1,5,11]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,1,0,0,0,0]
[11,8,9,3,4,7,12,2,6,10,1,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,11,8,12,3,4,7,9,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0]
[9,10,11,12,8,3,4,7,2,6,1,5]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[5,3,6,2,4,8,10,12,1,7,9,11]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[5,3,6,11,12,2,4,8,10,1,7,9]=>[1,1,1,1,1,0,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[5,3,6,9,10,2,4,8,12,1,7,11]=>[1,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0,0]
[5,11,3,6,9,12,2,4,8,10,1,7]=>[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0]
[5,10,11,12,3,6,9,2,4,8,1,7]=>[1,1,1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[5,7,3,8,2,4,6,10,12,1,9,11]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,1,0,1,1,0,0,0,0]
[5,7,3,8,11,12,2,4,6,10,1,9]=>[1,1,1,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[5,7,9,3,10,2,4,6,8,12,1,11]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,1,0,0,0]
[5,7,9,11,3,12,2,4,6,8,10,1]=>[1,1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]
[10,5,7,11,12,3,9,2,4,6,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0]
[8,5,9,10,3,7,2,4,6,12,1,11]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,1,0,0,0]
[8,11,5,9,3,7,12,2,4,6,10,1]=>[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]
[8,10,11,5,12,3,7,9,2,4,6,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0]
[5,9,10,11,12,8,3,7,2,4,6,1]=>[1,1,1,1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[3,6,7,8,5,2,4,10,12,1,9,11]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,0]
[3,6,7,8,5,11,12,2,4,10,1,9]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,0,0,0]
[9,3,6,7,5,10,2,4,8,12,1,11]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0]
[9,3,6,7,11,5,12,2,4,8,10,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,0,0,0]
[6,10,3,7,11,12,5,9,2,4,8,1]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0]
[6,8,3,9,10,5,7,2,4,12,1,11]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0,1,1,0,0,0]
[6,8,9,3,11,5,7,12,2,4,10,1]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0,0,0]
[10,6,8,3,11,12,5,7,9,2,4,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0]
[9,6,10,11,12,3,8,5,7,2,4,1]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[7,8,9,10,3,6,5,2,4,12,1,11]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,1,0,0,0]
[11,7,8,9,3,6,5,12,2,4,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0]
[10,11,7,8,3,6,12,5,9,2,4,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0]
[9,10,11,7,12,3,6,8,5,2,4,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0,0]
[8,9,10,11,12,7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[4,5,6,3,2,8,10,12,1,7,9,11]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[4,5,6,3,11,12,2,8,10,1,7,9]=>[1,1,1,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[4,5,6,3,9,10,2,8,12,1,7,11]=>[1,1,1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[4,5,6,11,3,9,12,2,8,10,1,7]=>[1,1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[4,5,6,10,11,12,3,9,2,8,1,7]=>[1,1,1,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[7,4,5,3,8,2,6,10,12,1,9,11]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,1,0,1,1,0,0,0,0]
[7,4,5,3,8,11,12,2,6,10,1,9]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0,0,0,0]
[7,4,5,9,3,10,2,6,8,12,1,11]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0,0,1,1,0,0,0]
[7,4,5,9,11,3,12,2,6,8,10,1]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0,0,0,0,0]
[7,10,4,5,11,12,3,9,2,6,8,1]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0]
[4,8,5,9,10,3,7,2,6,12,1,11]=>[1,1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,1,0,0,0]
[4,8,11,5,9,3,7,12,2,6,10,1]=>[1,1,1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[4,8,10,11,5,12,3,7,9,2,6,1]=>[1,1,1,1,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[4,5,9,10,11,12,8,3,7,2,6,1]=>[1,1,1,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[6,7,4,8,3,5,2,10,12,1,9,11]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,1,0,0,0,0]
[6,7,4,8,3,5,11,12,2,10,1,9]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0,0,0]
[6,7,9,4,3,5,10,2,8,12,1,11]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0,1,1,0,0,0]
[6,7,9,4,11,3,5,12,2,8,10,1]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0]
[10,6,7,4,11,12,3,5,9,2,8,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0]
[8,6,9,4,10,3,5,7,2,12,1,11]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,1,1,0,0,0]
[8,6,9,11,4,3,5,7,12,2,10,1]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0]
[8,10,6,11,4,12,3,5,7,9,2,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0]
[6,9,4,10,11,12,8,3,5,7,2,1]=>[1,1,1,1,1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[7,4,8,9,10,6,3,5,2,12,1,11]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,1,1,0,0,0]
[7,11,4,8,9,6,3,5,12,2,10,1]=>[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0]
[7,8,10,4,11,6,12,3,5,9,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0,0,0,0,0]
[9,7,10,4,11,12,6,8,3,5,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0]
[4,8,9,10,11,12,7,6,3,5,2,1]=>[1,1,1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[5,6,7,8,4,3,2,10,12,1,9,11]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,0]
[5,6,7,8,4,3,11,12,2,10,1,9]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0,0]
[9,5,6,7,4,3,10,2,8,12,1,11]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,1,0,0,0]
[9,5,6,7,4,11,3,12,2,8,10,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0,0,0,0]
[5,10,6,7,4,11,12,3,9,2,8,1]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0]
[8,9,5,6,4,10,3,7,2,12,1,11]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,1,1,0,0,0]
[8,9,5,6,11,4,3,7,12,2,10,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,1,0,0,0,0]
[10,8,5,6,11,4,12,3,7,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0]
[9,5,10,6,11,12,4,8,3,7,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0]
[7,8,9,5,10,4,6,3,2,12,1,11]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,1,1,0,0,0]
[7,8,9,11,5,4,6,3,12,2,10,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0]
[10,7,8,11,5,4,6,12,3,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0]
[9,10,7,11,5,12,4,6,8,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,5,10,11,12,7,4,6,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[6,7,8,9,10,5,4,3,2,12,1,11]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,1,0,0,0]
[11,6,7,8,9,5,4,3,12,2,10,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0]
[10,11,6,7,8,5,4,12,3,9,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0,0]
[9,10,11,6,7,5,12,4,8,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0]
[8,9,10,11,6,12,5,7,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0]
[6,5,2,1,4,3,12,11,8,7,10,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,9,11,12,10]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,4,3,6,5,7,9,10,8,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,4,3,6,5,7,9,8,11,12,10]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,4,3,6,5,7,8,10,11,12,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,4,3,5,7,8,6,10,9,12,11]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,4,3,5,7,8,6,9,11,12,10]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[2,1,4,3,5,7,6,9,10,8,12,11]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[2,1,4,3,5,7,6,9,8,11,12,10]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[2,1,4,3,5,7,6,8,10,11,12,9]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[2,1,4,3,5,6,8,9,10,7,12,11]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,4,3,5,6,8,9,7,11,12,10]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,4,3,5,6,8,7,10,11,12,9]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,4,3,5,6,7,9,10,11,12,8]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,3,5,6,4,8,7,10,9,12,11]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,3,5,6,4,8,7,9,11,12,10]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,3,5,6,4,7,9,10,8,12,11]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,3,5,6,4,7,9,8,11,12,10]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,3,5,6,4,7,8,10,11,12,9]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,5,4,7,8,6,10,9,12,11]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,3,5,4,7,8,6,9,11,12,10]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[2,1,3,5,4,7,6,9,10,8,12,11]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[2,1,3,5,4,7,6,9,8,11,12,10]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[2,1,3,5,4,7,6,8,10,11,12,9]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,5,4,6,8,9,10,7,12,11]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,3,5,4,6,8,9,7,11,12,10]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,3,5,4,6,8,7,10,11,12,9]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,3,5,4,6,7,9,10,11,12,8]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,3,4,6,7,8,5,10,9,12,11]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[2,1,3,4,6,7,8,5,9,11,12,10]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[2,1,3,4,6,7,5,9,10,8,12,11]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[2,1,3,4,6,7,5,9,8,11,12,10]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[2,1,3,4,6,7,5,8,10,11,12,9]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,4,6,5,8,9,10,7,12,11]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,3,4,6,5,8,9,7,11,12,10]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,3,4,6,5,8,7,10,11,12,9]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,3,4,6,5,7,9,10,11,12,8]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,3,4,5,7,8,9,10,6,12,11]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[2,1,3,4,5,7,8,9,6,11,12,10]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[2,1,3,4,5,7,8,6,10,11,12,9]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[2,1,3,4,5,7,6,9,10,11,12,8]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[2,1,3,4,5,6,8,9,10,11,12,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,4,2,6,5,8,7,10,9,12,11]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,4,2,6,5,8,7,9,11,12,10]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,3,4,2,6,5,7,9,10,8,12,11]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,3,4,2,6,5,7,9,8,11,12,10]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,3,4,2,6,5,7,8,10,11,12,9]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,4,2,5,7,8,6,10,9,12,11]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,3,4,2,5,7,8,6,9,11,12,10]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,3,4,2,5,7,6,9,10,8,12,11]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,3,4,2,5,7,6,9,8,11,12,10]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,3,4,2,5,7,6,8,10,11,12,9]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,3,4,2,5,6,8,9,10,7,12,11]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,4,2,5,6,8,9,7,11,12,10]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,3,4,2,5,6,8,7,10,11,12,9]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,4,2,5,6,7,9,10,11,12,8]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,5,6,4,8,7,10,9,12,11]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,2,5,6,4,8,7,9,11,12,10]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,3,2,5,6,4,7,9,10,8,12,11]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,3,2,5,6,4,7,9,8,11,12,10]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,3,2,5,6,4,7,8,10,11,12,9]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,2,5,4,7,8,6,10,9,12,11]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,3,2,5,4,7,8,6,9,11,12,10]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,3,2,5,4,7,6,9,10,8,12,11]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,3,2,5,4,7,6,9,8,11,12,10]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,3,2,5,4,7,6,8,10,11,12,9]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,3,2,5,4,6,8,9,10,7,12,11]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,2,5,4,6,8,9,7,11,12,10]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,3,2,5,4,6,8,7,10,11,12,9]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,2,5,4,6,7,9,10,11,12,8]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,4,6,7,8,5,10,9,12,11]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,3,2,4,6,7,8,5,9,11,12,10]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,3,2,4,6,7,5,9,10,8,12,11]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,3,2,4,6,7,5,9,8,11,12,10]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,3,2,4,6,7,5,8,10,11,12,9]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,3,2,4,6,5,8,9,10,7,12,11]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,2,4,6,5,8,9,7,11,12,10]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,3,2,4,6,5,8,7,10,11,12,9]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,2,4,6,5,7,9,10,11,12,8]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,4,5,7,8,9,10,6,12,11]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,3,2,4,5,7,8,9,6,11,12,10]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,3,2,4,5,7,8,6,10,11,12,9]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,3,2,4,5,7,6,9,10,11,12,8]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,4,5,6,8,9,10,11,12,7]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,4,5,6,3,8,7,10,9,12,11]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,4,5,6,3,8,7,9,11,12,10]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,2,4,5,6,3,7,9,10,8,12,11]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,4,5,6,3,7,9,8,11,12,10]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,2,4,5,6,3,7,8,10,11,12,9]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,4,5,3,7,8,6,10,9,12,11]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,2,4,5,3,7,8,6,9,11,12,10]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,2,4,5,3,7,6,9,10,8,12,11]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,2,4,5,3,7,6,9,8,11,12,10]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,2,4,5,3,7,6,8,10,11,12,9]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,2,4,5,3,6,8,9,10,7,12,11]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,4,5,3,6,8,9,7,11,12,10]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,2,4,5,3,6,8,7,10,11,12,9]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,2,4,5,3,6,7,9,10,11,12,8]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,4,3,6,7,8,5,10,9,12,11]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,2,4,3,6,7,8,5,9,11,12,10]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,2,4,3,6,7,5,9,10,8,12,11]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,2,4,3,6,7,5,9,8,11,12,10]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,2,4,3,6,7,5,8,10,11,12,9]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,2,4,3,6,5,8,9,10,7,12,11]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,4,3,6,5,8,9,7,11,12,10]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,2,4,3,6,5,8,7,10,11,12,9]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,2,4,3,6,5,7,9,10,11,12,8]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,4,3,5,7,8,9,10,6,12,11]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,2,4,3,5,7,8,9,6,11,12,10]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,2,4,3,5,7,8,6,10,11,12,9]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,2,4,3,5,7,6,9,10,11,12,8]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,2,4,3,5,6,8,9,10,11,12,7]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,3,5,6,7,8,4,10,9,12,11]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,2,3,5,6,7,8,4,9,11,12,10]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,2,3,5,6,7,4,9,10,8,12,11]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,2,3,5,6,7,4,9,8,11,12,10]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,2,3,5,6,7,4,8,10,11,12,9]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,2,3,5,6,4,8,9,10,7,12,11]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,3,5,6,4,8,9,7,11,12,10]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,2,3,5,6,4,8,7,10,11,12,9]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,2,3,5,6,4,7,9,10,11,12,8]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,5,4,7,8,9,10,6,12,11]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,2,3,5,4,7,8,9,6,11,12,10]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,2,3,5,4,7,8,6,10,11,12,9]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,2,3,5,4,7,6,9,10,11,12,8]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,5,4,6,8,9,10,11,12,7]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,3,4,6,7,8,9,10,5,12,11]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,2,3,4,6,7,8,9,5,11,12,10]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,2,3,4,6,7,8,5,10,11,12,9]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,2,3,4,6,7,5,9,10,11,12,8]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,4,6,5,8,9,10,11,12,7]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,3,4,5,7,8,9,10,11,12,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[12,1,2,3,4,5,6,7,8,11,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,1,2,3,4,5,6,7,8,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,2,1,3,4,5,6,7,8,9,10,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,10,3,9,2,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,10,3,2,9,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,10,3,2,9,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,10,3,2,1,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,3,10,9,2,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,3,10,9,2,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,3,10,2,9,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,3,10,2,9,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,3,10,2,1,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,3,2,10,9,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,3,2,10,9,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,3,2,10,1,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,11,4,3,2,1,10,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,10,3,9,2,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,10,3,9,2,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,10,3,2,9,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,10,3,2,9,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,10,3,2,1,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,3,10,9,2,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,3,10,9,2,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,3,10,2,9,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,3,10,2,9,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,3,10,2,1,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,3,2,10,9,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,3,2,10,9,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,3,2,10,1,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,11,3,2,1,10,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,11,10,9,2,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,11,10,9,2,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,11,10,2,9,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,11,10,2,9,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,11,10,2,1,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,11,2,10,9,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,11,2,10,9,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,11,2,10,1,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,11,2,1,10,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,2,11,10,9,8,1,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,2,11,10,9,1,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,2,11,10,1,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,2,11,1,10,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,12,5,4,3,2,1,11,10,9,8,7]=>[1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,10,3,9,2,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,10,3,9,2,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,10,3,2,9,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,10,3,2,9,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,10,3,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,3,10,9,2,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,3,10,9,2,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,3,10,2,9,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,3,10,2,9,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,3,10,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,3,2,10,9,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,3,2,10,9,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,3,2,10,1,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,11,4,3,2,1,10,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,10,3,9,2,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,10,3,9,2,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,10,3,2,9,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,10,3,2,9,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,10,3,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,3,10,9,2,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,3,10,9,2,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,3,10,2,9,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,3,10,2,9,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,3,10,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,3,2,10,9,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,3,2,10,9,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,3,2,10,1,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,11,3,2,1,10,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,11,10,9,2,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,11,10,9,2,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,11,10,2,9,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,11,10,2,9,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,11,10,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,11,2,10,9,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,11,2,10,9,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,11,2,10,1,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,11,2,1,10,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,2,11,10,9,8,1,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,2,11,10,9,1,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,2,11,10,1,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,2,11,1,10,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,12,4,3,2,1,11,10,9,8,7]=>[1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,10,3,9,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,10,3,9,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,10,3,2,9,8,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,10,3,2,9,1,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,10,3,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,3,10,9,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,3,10,9,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,3,10,2,9,8,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,3,10,2,9,1,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,3,10,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,3,2,10,9,8,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,3,2,10,9,1,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,3,2,10,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,11,3,2,1,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,11,10,9,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,11,10,9,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,11,10,2,9,8,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,11,10,2,9,1,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,11,10,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,11,2,10,9,8,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,11,2,10,9,1,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,11,2,10,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,11,2,1,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,2,11,10,9,8,1,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,2,11,10,9,1,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,2,11,10,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,2,11,1,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,12,3,2,1,11,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[6,5,4,3,12,11,10,9,2,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,12,11,10,9,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,12,11,10,2,9,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,12,11,10,2,9,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,12,11,10,2,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,12,11,2,10,9,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,12,11,2,10,9,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,12,11,2,10,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,12,11,2,1,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,12,2,11,10,9,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,12,2,11,10,9,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,12,2,11,10,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,12,2,11,1,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,12,2,1,11,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,4,3,2,12,11,10,9,8,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,2,12,11,10,9,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,2,12,11,10,1,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,2,12,11,1,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[6,5,4,3,2,12,1,11,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,12,9,11,10]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,4,3,6,5,10,7,9,8,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,4,3,6,5,12,11,9,7,8,10]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,6,5,12,7,8,10,11,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,8,5,7,6,10,9,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,4,3,8,5,7,6,12,9,11,10]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,4,3,10,9,7,5,6,8,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,4,3,12,9,7,11,6,5,8,10]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,12,10,7,5,8,6,11,9]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,10,5,6,8,9,7,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,4,3,12,11,6,8,9,5,7,10]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,12,5,11,8,6,10,7,9]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,12,5,6,7,9,10,11,8]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,5,4,8,7,10,9,12,11]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,6,3,5,4,8,7,12,9,11,10]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,6,3,5,4,10,7,9,8,12,11]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,6,3,5,4,12,11,9,7,8,10]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,3,5,4,12,7,8,10,11,9]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,7,5,3,4,6,10,9,12,11]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,8,7,5,3,4,6,12,9,11,10]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,10,7,5,9,4,3,6,8,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,7,5,9,4,11,6,3,8,10]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,7,5,10,4,3,8,6,11,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,8,5,3,6,4,9,7,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,8,5,11,6,4,9,3,7,10]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,8,5,3,11,4,6,10,7,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,9,5,3,6,7,4,10,11,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,8,3,4,6,7,5,10,9,12,11]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,8,3,4,6,7,5,12,9,11,10]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,10,9,4,6,7,3,5,8,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,9,4,6,7,11,5,3,8,10]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,10,4,6,7,3,8,5,11,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,3,9,6,4,8,5,7,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,11,9,6,4,8,5,3,7,10]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,3,10,6,11,8,4,5,7,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,3,10,6,4,7,9,5,11,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,3,4,5,7,8,9,6,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,11,4,5,7,8,9,3,6,10]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,3,11,5,7,8,4,10,6,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,3,4,11,7,5,9,10,6,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,3,4,5,6,8,9,10,11,7]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,1,3,2,6,5,8,7,10,9,12,11]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,1,3,2,6,5,8,7,12,9,11,10]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[4,1,3,2,6,5,10,7,9,8,12,11]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[4,1,3,2,6,5,12,11,9,7,8,10]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,2,6,5,12,7,8,10,11,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,2,8,5,7,6,10,9,12,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[4,1,3,2,8,5,7,6,12,9,11,10]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,1,3,2,10,9,7,5,6,8,12,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,1,3,2,12,9,7,11,6,5,8,10]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,12,10,7,5,8,6,11,9]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,10,5,6,8,9,7,12,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,1,3,2,12,11,6,8,9,5,7,10]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,12,5,11,8,6,10,7,9]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,12,5,6,7,9,10,11,8]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,3,1,2,4,8,7,10,9,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[6,5,3,1,2,4,8,7,12,9,11,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[6,5,3,1,2,4,10,7,9,8,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[6,5,3,1,2,4,12,11,9,7,8,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,5,3,1,2,4,12,7,8,10,11,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,5,3,7,2,1,4,6,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,5,3,7,2,1,4,6,12,9,11,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,5,3,7,2,9,4,1,6,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,5,3,7,2,9,4,11,6,1,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,3,7,2,10,4,1,8,6,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,5,3,8,2,1,6,4,9,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,5,3,8,2,11,6,4,9,1,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,3,8,2,1,11,4,6,10,7,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,3,9,2,1,6,7,4,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,6,3,1,4,2,7,5,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,6,3,1,4,2,7,5,12,9,11,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,6,3,9,4,2,7,1,5,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,6,3,9,4,2,7,11,5,1,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,6,3,10,4,2,7,1,8,5,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,6,3,1,9,2,4,8,5,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,6,3,11,9,2,4,8,5,1,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,6,3,1,10,2,11,8,4,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,6,3,1,10,2,4,7,9,5,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,7,3,1,4,5,2,8,9,6,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,7,3,11,4,5,2,8,9,1,6,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,3,1,11,5,2,8,4,10,6,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,3,1,4,11,2,5,9,10,6,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,8,3,1,4,5,6,2,9,10,11,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[6,1,2,4,5,3,8,7,10,9,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[6,1,2,4,5,3,8,7,12,9,11,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[6,1,2,4,5,3,10,7,9,8,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[6,1,2,4,5,3,12,11,9,7,8,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,4,5,3,12,7,8,10,11,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,7,2,4,5,1,3,6,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,7,2,4,5,1,3,6,12,9,11,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,7,2,4,5,9,3,1,6,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,7,2,4,5,9,3,11,6,1,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,2,4,5,10,3,1,8,6,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,8,2,4,5,1,6,3,9,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,8,2,4,5,11,6,3,9,1,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,8,2,4,5,1,11,3,6,10,7,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,9,2,4,5,1,6,7,3,10,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,1,7,4,2,6,3,5,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,1,7,4,2,6,3,5,12,9,11,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,9,7,4,2,6,3,1,5,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,9,7,4,2,6,3,11,5,1,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,7,4,2,6,3,1,8,5,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,1,8,4,9,6,2,3,5,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,11,8,4,9,6,2,3,5,1,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,8,4,10,6,11,3,2,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,9,4,10,6,2,7,3,5,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,1,8,4,2,5,7,3,9,6,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,11,8,4,2,5,7,3,9,1,6,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,8,4,11,5,7,3,2,10,6,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,9,4,2,11,7,5,3,10,6,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,9,4,2,5,6,8,3,10,11,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,1,2,3,5,6,7,4,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,1,2,3,5,6,7,4,12,9,11,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,9,2,3,5,6,7,1,4,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,9,2,3,5,6,7,11,4,1,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,10,2,3,5,6,7,1,8,4,11,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,1,9,3,5,6,2,8,4,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,11,9,3,5,6,2,8,4,1,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,10,3,5,6,11,8,2,4,7,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,10,3,5,6,2,7,9,4,11,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,1,2,9,5,3,7,8,4,6,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,11,2,9,5,3,7,8,4,1,6,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,11,10,5,3,7,8,2,4,6,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,10,5,11,7,3,9,4,6,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,10,5,3,6,8,9,4,11,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,4,6,7,8,9,5,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,11,2,3,4,6,7,8,9,1,5,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,11,3,4,6,7,8,2,10,5,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,11,4,6,7,3,9,10,5,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,11,6,4,8,9,10,5,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,8,7,12,9,10,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,4,3,6,5,10,7,8,9,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,4,3,6,5,12,11,8,7,10,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,6,5,12,7,8,9,10,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,8,5,6,7,10,9,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,4,3,8,5,6,7,12,9,10,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,4,3,10,9,6,5,8,7,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,4,3,12,9,6,11,8,5,10,7]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,12,11,6,5,8,9,10,7]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,10,5,6,7,8,9,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,4,3,12,11,6,7,8,5,10,9]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,12,5,10,7,6,9,8,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,12,5,6,7,8,9,10,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,6,3,4,5,8,7,10,9,12,11]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,6,3,4,5,8,7,12,9,10,11]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,6,3,4,5,10,7,8,9,12,11]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,6,3,4,5,12,11,8,7,10,9]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,3,4,5,12,7,8,9,10,11]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,8,7,4,3,6,5,10,9,12,11]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,8,7,4,3,6,5,12,9,10,11]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,10,7,4,9,6,3,8,5,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,7,4,9,6,11,8,3,10,5]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,7,4,11,6,3,8,9,10,5]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,9,4,3,6,7,8,5,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,9,4,11,6,7,8,3,10,5]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,11,4,3,10,7,6,9,8,5]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,11,4,3,6,7,8,9,10,5]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,8,3,4,5,6,7,10,9,12,11]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,8,3,4,5,6,7,12,9,10,11]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,10,9,4,5,6,3,8,7,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,9,4,5,6,11,8,3,10,7]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,11,4,5,6,3,8,9,10,7]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,3,8,5,4,7,6,9,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,11,8,5,4,7,6,3,10,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,3,8,5,10,7,4,9,6,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,3,10,5,4,7,8,9,6,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,3,4,5,6,7,8,9,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,11,4,5,6,7,8,3,10,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,3,10,5,6,7,4,9,8,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,3,4,9,6,5,8,7,10,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,12,3,4,5,6,7,8,9,10,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[4,1,2,3,6,5,8,7,10,9,12,11]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,1,2,3,6,5,8,7,12,9,10,11]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[4,1,2,3,6,5,10,7,8,9,12,11]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[4,1,2,3,6,5,12,11,8,7,10,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,3,6,5,12,7,8,9,10,11]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,2,3,8,5,6,7,10,9,12,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[4,1,2,3,8,5,6,7,12,9,10,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,1,2,3,10,9,6,5,8,7,12,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,1,2,3,12,9,6,11,8,5,10,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,12,11,6,5,8,9,10,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,10,5,6,7,8,9,12,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,1,2,3,12,11,6,7,8,5,10,9]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,12,5,10,7,6,9,8,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,2,3,12,5,6,7,8,9,10,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[6,5,2,1,4,3,8,7,10,9,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[6,5,2,1,4,3,8,7,12,9,10,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[6,5,2,1,4,3,10,7,8,9,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[6,5,2,1,4,3,12,7,8,9,10,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,5,2,7,4,1,6,3,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,5,2,7,4,1,6,3,12,9,10,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,5,2,7,4,9,6,1,8,3,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,5,2,7,4,9,6,11,8,1,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,2,7,4,11,6,1,8,9,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,5,2,9,4,1,6,7,8,3,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,5,2,9,4,11,6,7,8,1,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,2,11,4,1,10,7,6,9,8,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,5,2,11,4,1,6,7,8,9,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,7,2,1,4,5,6,3,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,7,2,1,4,5,6,3,12,9,10,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,7,2,9,4,5,6,1,8,3,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,7,2,9,4,5,6,11,8,1,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,2,11,4,5,6,1,8,9,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,2,1,8,5,4,7,6,3,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,9,2,11,8,5,4,7,6,1,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,2,1,8,5,10,7,4,9,6,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,2,1,10,5,4,7,8,9,6,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,2,1,4,5,6,7,8,3,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,9,2,11,4,5,6,7,8,1,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,2,1,10,5,6,7,4,9,8,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,2,1,4,9,6,5,8,7,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,2,1,4,5,6,7,8,9,10,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[6,1,2,3,4,5,8,7,10,9,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[6,1,2,3,4,5,8,7,12,9,10,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[6,1,2,3,4,5,10,7,8,9,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[6,1,2,3,4,5,12,11,8,7,10,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,2,3,4,5,12,7,8,9,10,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,7,2,3,4,1,6,5,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,7,2,3,4,1,6,5,12,9,10,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,7,2,3,4,9,6,1,8,5,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,7,2,3,4,9,6,11,8,1,10,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,7,2,3,4,11,6,1,8,9,10,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,9,2,3,4,1,6,7,8,5,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,9,2,3,4,11,6,7,8,1,10,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,2,3,4,1,10,7,6,9,8,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,2,3,4,1,6,7,8,9,10,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,1,6,3,2,5,4,7,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,1,6,3,2,5,4,7,12,9,10,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,9,6,3,2,5,4,1,8,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,9,6,3,2,5,4,11,8,1,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,6,3,2,5,4,1,8,9,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,1,6,3,8,5,2,7,4,9,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,11,6,3,8,5,2,7,4,1,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,6,3,8,5,10,7,2,9,4,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,6,3,10,5,2,7,8,9,4,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,1,8,3,2,5,6,7,4,9,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,11,8,3,2,5,6,7,4,1,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,8,3,10,5,6,7,2,9,4,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,10,3,2,9,6,5,8,7,4,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,10,3,2,5,6,7,8,9,4,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,1,2,3,4,5,6,7,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,1,2,3,4,5,6,7,12,9,10,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,9,2,3,4,5,6,1,8,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,9,2,3,4,5,6,11,8,1,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,2,3,4,5,6,1,8,9,10,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,1,8,3,4,5,2,7,6,9,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,11,8,3,4,5,2,7,6,1,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,8,3,4,5,10,7,2,9,6,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,10,3,4,5,2,7,8,9,6,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,1,2,7,4,3,6,5,8,9,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,11,2,7,4,3,6,5,8,1,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,10,7,4,3,6,5,2,9,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,7,4,9,6,3,8,5,10,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,9,4,3,6,7,8,5,10,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,1,2,3,4,5,6,7,8,9,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,11,2,3,4,5,6,7,8,1,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,10,3,4,5,6,7,2,9,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,9,4,5,6,3,8,7,10,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,8,5,4,7,6,9,10,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,1,2,3,4,5,6,7,8,9,10,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,4,3,6,5,12,7,9,8,11,10]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,4,3,6,5,11,8,12,7,10,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[2,1,4,3,10,5,7,6,9,8,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,4,3,12,5,7,6,9,8,11,10]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,11,8,12,5,7,6,10,9]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,1,4,3,9,6,10,5,8,7,12,11]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[2,1,4,3,9,6,12,5,8,7,11,10]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[2,1,4,3,12,5,8,7,11,6,10,9]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,4,3,11,6,10,7,12,5,9,8]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[2,1,6,3,5,4,12,7,9,8,11,10]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,6,3,5,4,11,8,12,7,10,9]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[2,1,8,3,5,4,7,6,10,9,12,11]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,8,3,5,4,7,6,12,9,11,10]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,10,3,5,4,7,6,9,8,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,3,5,4,7,6,9,8,11,10]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,11,8,12,3,5,4,7,6,10,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[2,1,9,6,10,3,5,4,8,7,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]
[2,1,9,6,12,3,5,4,8,7,11,10]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[2,1,12,3,5,4,8,7,11,6,10,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,11,6,10,7,12,3,5,4,9,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[2,1,7,4,8,3,6,5,10,9,12,11]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,1,7,4,8,3,6,5,12,9,11,10]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,7,4,10,3,6,5,9,8,12,11]=>[1,1,0,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,1,7,4,12,3,6,5,9,8,11,10]=>[1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,7,4,11,8,12,3,6,5,10,9]=>[1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,1,10,3,6,5,9,4,8,7,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[2,1,12,3,6,5,9,4,8,7,11,10]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,11,4,8,7,12,3,6,5,10,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[2,1,12,3,6,5,10,7,11,4,9,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,9,4,8,5,10,3,7,6,12,11]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,1,0,0]
[2,1,9,4,8,5,12,3,7,6,11,10]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[2,1,12,3,7,6,11,4,8,5,10,9]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,10,5,12,3,7,6,11,4,9,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[2,1,10,5,11,4,9,6,12,3,8,7]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0]
[4,1,3,2,6,5,12,7,9,8,11,10]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,3,2,6,5,11,8,12,7,10,9]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[4,1,3,2,10,5,7,6,9,8,12,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,1,3,2,12,5,7,6,9,8,11,10]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,11,8,12,5,7,6,10,9]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,1,3,2,9,6,10,5,8,7,12,11]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[4,1,3,2,9,6,12,5,8,7,11,10]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[4,1,3,2,12,5,8,7,11,6,10,9]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,1,3,2,11,6,10,7,12,5,9,8]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[6,1,3,2,5,4,8,7,10,9,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[6,1,3,2,5,4,8,7,12,9,11,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[6,1,3,2,5,4,10,7,9,8,12,11]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[6,1,3,2,5,4,12,7,9,8,11,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,1,3,2,5,4,11,8,12,7,10,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[8,1,3,2,5,4,7,6,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,1,3,2,5,4,7,6,12,9,11,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,1,3,2,5,4,7,6,9,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[11,8,12,1,3,2,5,4,7,6,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[9,6,10,1,3,2,5,4,8,7,12,11]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0]
[9,6,12,1,3,2,5,4,8,7,11,10]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,1,3,2,5,4,8,7,11,6,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,6,10,7,12,1,3,2,5,4,9,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[7,4,8,1,3,2,6,5,10,9,12,11]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[7,4,8,1,3,2,6,5,12,9,11,10]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[7,4,10,1,3,2,6,5,9,8,12,11]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[7,4,12,1,3,2,6,5,9,8,11,10]=>[1,1,1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[7,4,11,8,12,1,3,2,6,5,10,9]=>[1,1,1,1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[10,1,3,2,6,5,9,4,8,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,1,3,2,6,5,9,4,8,7,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,4,8,7,12,1,3,2,6,5,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[12,1,3,2,6,5,10,7,11,4,9,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[9,4,8,5,10,1,3,2,7,6,12,11]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0]
[9,4,8,5,12,1,3,2,7,6,11,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0]
[12,1,3,2,7,6,11,4,8,5,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,5,12,1,3,2,7,6,11,4,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0]
[10,5,11,4,9,6,12,1,3,2,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0]
[5,2,6,1,4,3,8,7,10,9,12,11]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[5,2,6,1,4,3,8,7,12,9,11,10]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[5,2,6,1,4,3,10,7,9,8,12,11]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[5,2,6,1,4,3,12,7,9,8,11,10]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,2,6,1,4,3,11,8,12,7,10,9]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[5,2,8,1,4,3,7,6,10,9,12,11]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[5,2,8,1,4,3,7,6,12,9,11,10]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[5,2,10,1,4,3,7,6,9,8,12,11]=>[1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[5,2,12,1,4,3,7,6,9,8,11,10]=>[1,1,1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,2,11,8,12,1,4,3,7,6,10,9]=>[1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[5,2,9,6,10,1,4,3,8,7,12,11]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]
[5,2,9,6,12,1,4,3,8,7,11,10]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[5,2,12,1,4,3,8,7,11,6,10,9]=>[1,1,1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[5,2,11,6,10,7,12,1,4,3,9,8]=>[1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[8,1,4,3,7,2,6,5,10,9,12,11]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[8,1,4,3,7,2,6,5,12,9,11,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,1,4,3,7,2,6,5,9,8,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,1,4,3,7,2,6,5,9,8,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,8,12,1,4,3,7,2,6,5,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[9,2,6,5,10,1,4,3,8,7,12,11]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0]
[9,2,6,5,12,1,4,3,8,7,11,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0]
[12,1,4,3,8,7,11,2,6,5,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,2,6,5,10,7,12,1,4,3,9,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,1,4,3,8,5,9,2,7,6,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,1,4,3,8,5,9,2,7,6,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,2,7,6,12,1,4,3,8,5,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[10,5,11,2,7,6,12,1,4,3,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0]
[10,5,12,1,4,3,9,6,11,2,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0]
[7,2,6,3,8,1,5,4,10,9,12,11]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,1,0,0,1,1,0,0]
[7,2,6,3,8,1,5,4,12,9,11,10]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,1,1,1,0,0,0,0]
[7,2,6,3,10,1,5,4,9,8,12,11]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,2,6,3,12,1,5,4,9,8,11,10]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[7,2,6,3,11,8,12,1,5,4,10,9]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,0,0,0,0,0,0]
[10,1,5,4,9,2,6,3,8,7,12,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[12,1,5,4,9,2,6,3,8,7,11,10]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,2,6,3,8,7,12,1,5,4,10,9]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[12,1,5,4,10,7,11,2,6,3,9,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,3,10,1,5,4,9,2,7,6,12,11]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[8,3,12,1,5,4,9,2,7,6,11,10]=>[1,1,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,3,11,2,7,6,12,1,5,4,10,9]=>[1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[11,2,7,6,12,1,5,4,10,3,9,8]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[12,1,5,4,10,3,9,6,11,2,8,7]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,3,9,2,7,4,10,1,6,5,12,11]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0,1,1,0,0]
[8,3,9,2,7,4,12,1,6,5,11,10]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0]
[8,3,12,1,6,5,11,2,7,4,10,9]=>[1,1,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,1,6,5,11,2,7,4,10,3,9,8]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,3,9,4,12,1,6,5,11,2,8,7]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0]
[10,3,9,4,11,2,8,5,12,1,7,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0]
[11,12,8,2,1,6,4,3,5,7,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[12,2,9,1,10,6,4,3,5,7,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,2,1,9,6,4,3,5,7,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[10,2,4,1,11,3,12,6,5,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0]
[7,12,10,2,1,8,4,3,5,6,9,11]=>[1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,11,7,1,12,8,4,3,5,6,9,10]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]
[9,12,2,1,10,7,4,3,5,6,8,11]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,11,1,12,9,7,4,3,5,6,8,10]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[10,11,2,1,4,3,12,7,5,6,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0]
[8,12,2,1,9,4,3,10,5,6,7,11]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,11,1,12,8,4,3,9,5,6,7,10]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[2,10,1,11,4,3,12,8,5,6,7,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0]
[2,9,1,10,4,3,11,5,12,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0,0]
[12,10,8,5,2,1,6,3,4,7,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[5,11,2,1,12,8,6,3,4,7,9,10]=>[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]
[12,9,5,2,1,10,6,3,4,7,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,5,2,1,12,9,6,3,4,7,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[10,11,2,1,5,3,12,6,4,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0]
[12,10,7,2,1,8,5,3,4,6,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,2,1,12,8,5,3,4,6,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[12,9,2,1,10,7,5,3,4,6,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,2,1,12,9,7,5,3,4,6,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[10,11,2,1,3,12,7,5,4,6,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0]
[8,9,2,1,12,3,10,5,4,6,7,11]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0]
[11,8,2,1,12,3,9,5,4,6,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[2,10,1,11,3,12,8,5,4,6,7,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0]
[2,9,1,10,3,11,5,4,12,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0,0]
[12,10,6,2,1,7,3,8,4,5,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,6,2,1,12,7,3,8,4,5,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[12,9,2,1,10,6,3,7,4,5,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,2,1,12,9,6,3,7,4,5,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[10,2,1,11,6,3,12,7,4,5,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0]
[12,8,2,1,9,3,10,6,4,5,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,2,1,12,8,3,9,6,4,5,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[10,2,1,11,3,12,8,6,4,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0]
[2,9,1,10,3,11,4,12,6,5,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0]
[12,7,2,1,8,3,9,4,10,5,6,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,2,1,12,7,3,8,4,9,5,6,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[10,2,1,11,3,12,7,4,8,5,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0]
[9,2,1,10,3,11,4,12,7,5,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0]
[8,2,1,9,3,10,4,11,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0]
[12,10,8,6,3,1,4,2,5,7,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,12,3,1,8,6,4,2,5,7,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[9,12,3,1,10,6,4,2,5,7,8,11]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,11,1,12,9,6,4,2,5,7,8,10]=>[1,1,1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[3,10,4,1,11,2,12,6,5,7,8,9]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0,0]
[12,10,7,3,1,8,4,2,5,6,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,3,1,12,8,4,2,5,6,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[12,9,3,1,10,7,4,2,5,6,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,3,1,12,9,7,4,2,5,6,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[3,10,1,11,4,2,12,7,5,6,8,9]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0]
[12,8,3,1,9,4,2,10,5,6,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,3,1,12,8,4,2,9,5,6,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[10,3,1,11,4,2,12,8,5,6,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0]
[9,3,1,10,4,2,11,5,12,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0]
[12,10,8,5,1,6,3,2,4,7,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[5,11,1,12,8,6,3,2,4,7,9,10]=>[1,1,1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[12,9,5,1,10,6,3,2,4,7,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,5,1,12,9,6,3,2,4,7,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[3,10,1,11,5,2,12,6,4,7,8,9]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0]
[12,10,7,1,8,5,3,2,4,6,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,1,12,8,5,3,2,4,6,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[12,9,1,10,7,5,3,2,4,6,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,1,12,9,7,5,3,2,4,6,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[3,10,1,11,2,12,7,5,4,6,8,9]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,1,12,3,2,10,5,4,6,7,11]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0]
[11,8,1,12,3,2,9,5,4,6,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[10,3,1,11,2,12,8,5,4,6,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0]
[9,3,1,10,2,11,5,4,12,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0]
[12,10,6,1,7,3,2,8,4,5,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,6,1,12,7,3,2,8,4,5,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[12,9,1,10,6,3,2,7,4,5,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,1,12,9,6,3,2,7,4,5,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,1,11,6,3,2,12,7,4,5,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0]
[12,8,1,9,3,2,10,6,4,5,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,1,12,8,3,2,9,6,4,5,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,1,11,3,2,12,8,6,4,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0]
[9,3,1,10,2,11,4,12,6,5,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0]
[12,7,1,8,3,2,9,4,10,5,6,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,1,12,7,3,2,8,4,9,5,6,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,1,11,3,2,12,7,4,8,5,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0]
[9,1,10,3,2,11,4,12,7,5,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0]
[8,1,9,3,2,10,4,11,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0]
[12,10,8,4,1,5,2,6,3,7,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[4,11,1,12,8,5,2,6,3,7,9,10]=>[1,1,1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[12,9,4,1,10,5,2,6,3,7,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,4,1,12,9,5,2,6,3,7,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[10,4,1,11,5,2,12,6,3,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0]
[12,10,7,1,8,4,2,5,3,6,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,1,12,8,4,2,5,3,6,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[12,9,1,10,7,4,2,5,3,6,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,1,12,9,7,4,2,5,3,6,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,4,1,11,2,12,7,5,3,6,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0]
[12,8,1,9,4,2,10,5,3,6,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,1,12,8,4,2,9,5,3,6,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,1,11,4,2,12,8,5,3,6,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0]
[9,1,10,4,2,11,5,3,12,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0]
[12,10,6,1,7,2,8,4,3,5,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,6,1,12,7,2,8,4,3,5,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[12,9,1,10,6,2,7,4,3,5,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,1,12,9,6,2,7,4,3,5,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,1,11,6,2,12,7,4,3,5,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0]
[12,8,1,9,2,10,6,4,3,5,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,1,12,8,2,9,6,4,3,5,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,1,11,2,12,8,6,4,3,5,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0]
[9,1,10,4,2,11,3,12,6,5,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0]
[12,7,1,8,2,9,4,3,10,5,6,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,1,12,7,2,8,4,3,9,5,6,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,1,11,2,12,7,4,3,8,5,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0]
[9,1,10,2,11,4,3,12,7,5,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,1,9,2,10,4,3,11,5,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0]
[12,10,5,1,6,2,7,3,8,4,9,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,5,1,12,6,2,7,3,8,4,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[12,9,1,10,5,2,6,3,7,4,8,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,1,12,9,5,2,6,3,7,4,8,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,1,11,5,2,12,6,3,7,4,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0]
[12,8,1,9,2,10,5,3,6,4,7,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,1,12,8,2,9,5,3,6,4,7,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,1,11,2,12,8,5,3,6,4,7,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0]
[9,1,10,2,11,5,3,12,6,4,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0]
[12,7,1,8,2,9,3,10,5,4,6,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,1,12,7,2,8,3,9,5,4,6,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,1,11,2,12,7,3,8,5,4,6,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0]
[9,1,10,2,11,3,12,7,5,4,6,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0]
[8,1,9,2,10,3,11,5,4,12,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0]
[12,6,1,7,2,8,3,9,4,10,5,11]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,1,12,6,2,7,3,8,4,9,5,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,1,11,2,12,6,3,7,4,8,5,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0]
[9,1,10,2,11,3,12,6,4,7,5,8]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0]
[8,1,9,2,10,3,11,4,12,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0]
[3,2,5,4,7,6,9,8,10,12,11,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[3,2,5,4,7,6,8,11,9,10,12,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[3,2,5,4,7,6,8,10,9,12,11,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[3,2,5,4,7,6,8,9,12,10,11,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[3,2,5,4,6,9,7,8,11,10,12,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[3,2,5,4,6,9,7,8,10,12,11,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[3,2,5,4,6,8,7,11,9,10,12,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,2,5,4,6,8,7,10,9,12,11,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,2,5,4,6,8,7,9,12,10,11,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,2,5,4,6,7,11,8,9,10,12,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[3,2,5,4,6,7,10,8,9,12,11,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[3,2,5,4,6,7,9,8,12,10,11,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[3,2,5,4,6,7,8,12,9,10,11,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[3,2,4,7,5,6,9,8,11,10,12,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[3,2,4,7,5,6,9,8,10,12,11,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0]
[3,2,4,7,5,6,8,11,9,10,12,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]
[3,2,4,7,5,6,8,10,9,12,11,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,0]
[3,2,4,7,5,6,8,9,12,10,11,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0]
[3,2,4,6,5,9,7,8,11,10,12,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[3,2,4,6,5,9,7,8,10,12,11,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[3,2,4,6,5,8,7,11,9,10,12,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[3,2,4,6,5,8,7,10,9,12,11,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[3,2,4,6,5,8,7,9,12,10,11,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[3,2,4,6,5,7,11,8,9,10,12,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[3,2,4,6,5,7,10,8,9,12,11,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[3,2,4,6,5,7,9,8,12,10,11,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[3,2,4,6,5,7,8,12,9,10,11,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[3,2,4,5,9,6,7,8,11,10,12,1]=>[1,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[3,2,4,5,9,6,7,8,10,12,11,1]=>[1,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[3,2,4,5,8,6,7,11,9,10,12,1]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[3,2,4,5,8,6,7,10,9,12,11,1]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[3,2,4,5,8,6,7,9,12,10,11,1]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[3,2,4,5,7,6,11,8,9,10,12,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[3,2,4,5,7,6,10,8,9,12,11,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[3,2,4,5,7,6,9,8,12,10,11,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[3,2,4,5,7,6,8,12,9,10,11,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[3,2,4,5,6,11,7,8,9,10,12,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,2,4,5,6,10,7,8,9,12,11,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[3,2,4,5,6,9,7,8,12,10,11,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[3,2,4,5,6,8,7,12,9,10,11,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,2,4,5,6,7,12,8,9,10,11,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,5,3,4,7,6,9,8,11,10,12,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,5,3,4,7,6,9,8,10,12,11,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[2,5,3,4,7,6,8,11,9,10,12,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[2,5,3,4,7,6,8,10,9,12,11,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[2,5,3,4,7,6,8,9,12,10,11,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[2,5,3,4,6,9,7,8,11,10,12,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[2,5,3,4,6,9,7,8,10,12,11,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[2,5,3,4,6,8,7,11,9,10,12,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[2,5,3,4,6,8,7,10,9,12,11,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,5,3,4,6,8,7,9,12,10,11,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[2,5,3,4,6,7,11,8,9,10,12,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,5,3,4,6,7,10,8,9,12,11,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,5,3,4,6,7,9,8,12,10,11,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,5,3,4,6,7,8,12,9,10,11,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,4,3,7,5,6,9,8,11,10,12,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,4,3,7,5,6,9,8,10,12,11,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0]
[2,4,3,7,5,6,8,11,9,10,12,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]
[2,4,3,7,5,6,8,10,9,12,11,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,0]
[2,4,3,7,5,6,8,9,12,10,11,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0]
[2,4,3,6,5,9,7,8,11,10,12,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[2,4,3,6,5,9,7,8,10,12,11,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[2,4,3,6,5,8,7,11,9,10,12,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[2,4,3,6,5,8,7,9,12,10,11,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[2,4,3,6,5,7,11,8,9,10,12,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,4,3,6,5,7,10,8,9,12,11,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,4,3,6,5,7,9,8,12,10,11,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,3,6,5,7,8,12,9,10,11,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,4,3,5,9,6,7,8,11,10,12,1]=>[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[2,4,3,5,9,6,7,8,10,12,11,1]=>[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[2,4,3,5,8,6,7,11,9,10,12,1]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[2,4,3,5,8,6,7,10,9,12,11,1]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[2,4,3,5,8,6,7,9,12,10,11,1]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[2,4,3,5,7,6,11,8,9,10,12,1]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[2,4,3,5,7,6,10,8,9,12,11,1]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[2,4,3,5,7,6,9,8,12,10,11,1]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[2,4,3,5,7,6,8,12,9,10,11,1]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[2,4,3,5,6,11,7,8,9,10,12,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,4,3,5,6,10,7,8,9,12,11,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,4,3,5,6,9,7,8,12,10,11,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,4,3,5,6,8,7,12,9,10,11,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,4,3,5,6,7,12,8,9,10,11,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,7,4,5,6,9,8,11,10,12,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,3,7,4,5,6,9,8,10,12,11,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0,0]
[2,3,7,4,5,6,8,11,9,10,12,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0,0]
[2,3,7,4,5,6,8,10,9,12,11,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0,0]
[2,3,7,4,5,6,8,9,12,10,11,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0,0]
[2,3,6,4,5,9,7,8,11,10,12,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[2,3,6,4,5,9,7,8,10,12,11,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[2,3,6,4,5,8,7,11,9,10,12,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[2,3,6,4,5,8,7,10,9,12,11,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,3,6,4,5,8,7,9,12,10,11,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[2,3,6,4,5,7,11,8,9,10,12,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,3,6,4,5,7,10,8,9,12,11,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,3,6,4,5,7,9,8,12,10,11,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,3,6,4,5,7,8,12,9,10,11,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,5,4,9,6,7,8,11,10,12,1]=>[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[2,3,5,4,9,6,7,8,10,12,11,1]=>[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[2,3,5,4,8,6,7,11,9,10,12,1]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[2,3,5,4,8,6,7,10,9,12,11,1]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[2,3,5,4,8,6,7,9,12,10,11,1]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[2,3,5,4,7,6,11,8,9,10,12,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[2,3,5,4,7,6,10,8,9,12,11,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[2,3,5,4,7,6,9,8,12,10,11,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[2,3,5,4,7,6,8,12,9,10,11,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,5,4,6,11,7,8,9,10,12,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,3,5,4,6,10,7,8,9,12,11,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,3,5,4,6,9,7,8,12,10,11,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,3,5,4,6,8,7,12,9,10,11,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,3,5,4,6,7,12,8,9,10,11,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,9,5,6,7,8,11,10,12,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]
[2,3,4,9,5,6,7,8,10,12,11,1]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]
[2,3,4,8,5,6,7,11,9,10,12,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0]
[2,3,4,8,5,6,7,10,9,12,11,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[2,3,4,8,5,6,7,9,12,10,11,1]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]
[2,3,4,7,5,6,11,8,9,10,12,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]
[2,3,4,7,5,6,10,8,9,12,11,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0]
[2,3,4,7,5,6,9,8,12,10,11,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0]
[2,3,4,7,5,6,8,12,9,10,11,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]
[2,3,4,6,5,11,7,8,9,10,12,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,3,4,6,5,10,7,8,9,12,11,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,3,4,6,5,9,7,8,12,10,11,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,3,4,6,5,8,7,12,9,10,11,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,3,4,6,5,7,12,8,9,10,11,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,3,4,5,11,6,7,8,9,10,12,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,3,4,5,10,6,7,8,9,12,11,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[2,3,4,5,9,6,7,8,12,10,11,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[2,3,4,5,8,6,7,12,9,10,11,1]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[2,3,4,5,7,6,12,8,9,10,11,1]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[12,11,9,5,10,7,1,2,4,8,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,5,12,10,7,1,2,4,8,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[10,7,1,2,4,9,5,12,11,8,3,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0]
[12,10,7,1,2,4,9,5,11,8,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,7,1,2,4,12,9,5,11,8,3,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0]
[8,3,7,1,2,4,12,11,9,5,10,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0]
[8,3,7,1,2,4,11,9,5,12,10,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0,0,0]
[12,11,8,3,7,1,2,4,9,5,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,8,3,7,1,2,4,9,5,12,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0]
[12,9,5,11,8,3,7,1,2,4,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,3,12,11,7,1,2,4,9,5,10,6]=>[1,1,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,3,11,7,1,2,4,9,5,12,10,6]=>[1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[8,3,12,9,5,11,7,1,2,4,10,6]=>[1,1,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,8,3,9,5,11,7,1,2,4,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,7,1,2,5,12,11,9,4,8,3,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0]
[12,10,7,1,2,5,11,9,4,8,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[9,4,10,7,1,2,5,12,11,8,3,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0]
[9,4,12,10,7,1,2,5,11,8,3,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,9,4,10,7,1,2,5,11,8,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,9,4,8,3,7,1,2,5,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,4,8,3,7,1,2,5,12,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0]
[9,4,12,11,8,3,7,1,2,5,10,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,4,11,8,3,7,1,2,5,12,10,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0]
[11,8,3,7,1,2,5,12,9,4,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0]
[8,3,9,4,12,11,7,1,2,5,10,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[8,3,9,4,11,7,1,2,5,12,10,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0,1,0,0,0]
[8,3,11,7,1,2,5,12,9,4,10,6]=>[1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[11,7,1,2,5,12,8,3,9,4,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[10,5,12,11,9,4,8,3,7,1,2,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0]
[12,10,5,11,9,4,8,3,7,1,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[9,4,10,5,12,11,8,3,7,1,2,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0]
[9,4,12,10,5,11,8,3,7,1,2,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,9,4,10,5,11,8,3,7,1,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,3,9,4,10,5,12,11,7,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,0,0,0,0]
[8,3,9,4,12,10,5,11,7,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[8,3,12,9,4,10,5,11,7,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,8,3,9,4,10,5,11,7,1,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[7,1,2,8,3,9,4,10,5,12,11,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]
[7,1,2,8,3,9,4,12,10,5,11,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,1,0,0,0,0,0]
[7,1,2,8,3,12,9,4,10,5,11,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[7,1,2,12,8,3,9,4,10,5,11,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[12,7,1,2,8,3,9,4,10,5,11,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,2,4,12,11,9,5,10,7,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[8,2,4,11,9,5,12,10,7,1,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0,0,0,0]
[12,11,8,2,4,9,5,10,7,1,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,8,2,4,9,5,12,10,7,1,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[12,9,5,11,8,2,4,10,7,1,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[7,1,3,8,2,4,12,11,9,5,10,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,1,0,0,0,0,0,0]
[7,1,3,8,2,4,11,9,5,12,10,6]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0,0]
[7,1,3,12,11,8,2,4,9,5,10,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,3,11,8,2,4,9,5,12,10,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[7,1,3,12,9,5,11,8,2,4,10,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[12,11,7,1,3,8,2,4,9,5,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,1,3,8,2,4,9,5,12,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0]
[12,9,5,11,7,1,3,8,2,4,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,1,3,9,5,12,8,2,4,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[12,11,9,4,8,2,5,10,7,1,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,4,8,2,5,12,10,7,1,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[9,4,12,11,8,2,5,10,7,1,3,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,4,11,8,2,5,12,10,7,1,3,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0]
[11,8,2,5,12,9,4,10,7,1,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[7,1,3,12,11,9,4,8,2,5,10,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,3,11,9,4,8,2,5,12,10,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[7,1,3,9,4,12,11,8,2,5,10,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[7,1,3,9,4,11,8,2,5,12,10,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0,1,0,0,0]
[7,1,3,11,8,2,5,12,9,4,10,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[9,4,12,11,7,1,3,8,2,5,10,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
[9,4,11,7,1,3,8,2,5,12,10,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0]
[11,7,1,3,8,2,5,12,9,4,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0]
[12,8,2,5,11,7,1,3,9,4,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[7,1,3,10,5,12,11,9,4,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[7,1,3,12,10,5,11,9,4,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[7,1,3,9,4,10,5,12,11,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,0,0,0]
[7,1,3,9,4,12,10,5,11,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[7,1,3,12,9,4,10,5,11,8,2,6]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[9,4,10,5,12,11,7,1,3,8,2,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0]
[9,4,12,10,5,11,7,1,3,8,2,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
[12,9,4,10,5,11,7,1,3,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,1,3,9,4,10,5,12,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0]
[8,2,7,1,3,9,4,10,5,12,11,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0,1,1,0,0,0]
[8,2,7,1,3,9,4,12,10,5,11,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0]
[8,2,7,1,3,12,9,4,10,5,11,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0]
[12,8,2,7,1,3,9,4,10,5,11,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[8,2,12,7,1,3,9,4,10,5,11,6]=>[1,1,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,7,1,4,8,2,5,12,11,9,3,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0]
[12,10,7,1,4,8,2,5,11,9,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[12,11,8,2,5,10,7,1,4,9,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,8,2,5,12,10,7,1,4,9,3,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[10,7,1,4,11,8,2,5,12,9,3,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0]
[12,11,9,3,7,1,4,8,2,5,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,3,7,1,4,8,2,5,12,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0]
[9,3,7,1,4,12,11,8,2,5,10,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0]
[9,3,7,1,4,11,8,2,5,12,10,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0]
[11,8,2,5,12,9,3,7,1,4,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[12,11,7,1,4,9,3,8,2,5,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,1,4,9,3,8,2,5,12,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0]
[12,9,3,8,2,5,11,7,1,4,10,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[9,3,12,8,2,5,11,7,1,4,10,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
[10,5,12,11,9,3,7,1,4,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0]
[12,10,5,11,9,3,7,1,4,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[9,3,7,1,4,10,5,12,11,8,2,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0,0,0,0]
[9,3,7,1,4,12,10,5,11,8,2,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0]
[12,9,3,7,1,4,10,5,11,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,5,12,11,7,1,4,9,3,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0]
[12,10,5,11,7,1,4,9,3,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,1,4,10,5,12,9,3,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[9,3,11,7,1,4,10,5,12,8,2,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0]
[9,3,8,2,7,1,4,10,5,12,11,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0]
[9,3,8,2,7,1,4,12,10,5,11,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0]
[12,9,3,8,2,7,1,4,10,5,11,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[9,3,12,8,2,7,1,4,10,5,11,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
[8,2,9,3,12,7,1,4,10,5,11,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[12,11,9,3,7,1,5,10,4,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,9,3,7,1,5,12,10,4,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0]
[10,4,9,3,7,1,5,12,11,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0]
[12,10,4,9,3,7,1,5,11,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,4,12,9,3,7,1,5,11,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0]
[12,11,7,1,5,10,4,9,3,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,7,1,5,12,10,4,9,3,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[10,4,11,7,1,5,12,9,3,8,2,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0]
[9,3,10,4,11,7,1,5,12,8,2,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0]
[10,4,9,3,8,2,7,1,5,12,11,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0]
[12,10,4,9,3,8,2,7,1,5,11,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[10,4,12,9,3,8,2,7,1,5,11,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0]
[9,3,10,4,12,8,2,7,1,5,11,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0]
[8,2,9,3,10,4,12,7,1,5,11,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,0,0,0,0]
[12,11,5,10,4,9,3,8,2,7,1,6]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[11,5,12,10,4,9,3,8,2,7,1,6]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[10,4,11,5,12,9,3,8,2,7,1,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0]
[9,3,10,4,11,5,12,8,2,7,1,6]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0]
[8,2,9,3,10,4,11,5,12,7,1,6]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0]
[3,4,1,5,6,7,8,9,10,11,12,2]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[8,2,9,3,10,4,11,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0]
[8,2,9,3,10,4,11,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0]
[8,2,9,3,10,4,11,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0]
[8,2,9,3,10,4,11,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0]
[8,2,9,3,10,4,11,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0]
[8,2,9,3,10,11,4,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0,0,0]
[8,2,9,3,10,11,4,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0,0,0]
[8,2,9,3,10,11,4,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0]
[8,2,9,3,10,11,4,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0]
[8,2,9,3,10,11,4,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0]
[8,2,9,3,10,11,12,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[8,2,9,3,10,11,12,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[8,2,9,3,10,11,12,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[8,2,9,3,10,11,12,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0]
[8,2,9,10,3,4,11,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0,0,0]
[8,2,9,10,3,4,11,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0,0,0]
[8,2,9,10,3,4,11,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[8,2,9,10,3,4,11,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[8,2,9,10,3,4,11,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0]
[8,2,9,10,3,11,4,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,0,0,0]
[8,2,9,10,3,11,4,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,0,0,0]
[8,2,9,10,3,11,4,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[8,2,9,10,3,11,4,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[8,2,9,10,3,11,4,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0]
[8,2,9,10,3,11,12,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[8,2,9,10,3,11,12,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[8,2,9,10,3,11,12,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[8,2,9,10,3,11,12,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0]
[8,2,9,10,11,3,4,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[8,2,9,10,11,3,4,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[8,2,9,10,11,3,4,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[8,2,9,10,11,3,4,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[8,2,9,10,11,3,4,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0]
[8,2,9,10,11,3,12,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[8,2,9,10,11,3,12,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[8,2,9,10,11,3,12,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[8,2,9,10,11,3,12,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[8,2,9,10,11,12,3,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,2,9,10,11,12,3,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,2,9,10,11,12,3,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,2,9,10,11,12,3,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,2,9,10,11,12,1,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,2,3,10,4,11,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,0]
[8,9,2,3,10,4,11,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,0]
[8,9,2,3,10,4,11,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,0,0]
[8,9,2,3,10,4,11,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,0,0]
[8,9,2,3,10,4,11,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,0,0]
[8,9,2,3,10,11,4,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0]
[8,9,2,3,10,11,4,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0]
[8,9,2,3,10,11,4,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0,0]
[8,9,2,3,10,11,4,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0,0]
[8,9,2,3,10,11,4,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,0,0,0,0]
[8,9,2,3,10,11,12,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0]
[8,9,2,3,10,11,12,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0]
[8,9,2,3,10,11,12,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0]
[8,9,2,3,10,11,12,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0]
[8,9,2,10,3,4,11,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,0]
[8,9,2,10,3,4,11,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,0]
[8,9,2,10,3,4,11,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0,0,0,0]
[8,9,2,10,3,4,11,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0,0,0,0]
[8,9,2,10,3,4,11,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0,0,0,0]
[8,9,2,10,3,11,4,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0,0]
[8,9,2,10,3,11,4,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0,0]
[8,9,2,10,3,11,4,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0]
[8,9,2,10,3,11,4,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0]
[8,9,2,10,3,11,4,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0]
[8,9,2,10,3,11,12,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0]
[8,9,2,10,3,11,12,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0]
[8,9,2,10,3,11,12,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0]
[8,9,2,10,3,11,12,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0]
[8,9,2,10,11,3,4,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,1,0,0,0,0]
[8,9,2,10,11,3,4,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,1,0,0,0,0]
[8,9,2,10,11,3,4,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0]
[8,9,2,10,11,3,4,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0]
[8,9,2,10,11,3,4,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0]
[8,9,2,10,11,3,12,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0,0]
[8,9,2,10,11,3,12,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0,0]
[8,9,2,10,11,3,12,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0,0]
[8,9,2,10,11,3,12,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0,0]
[8,9,2,10,11,12,3,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,2,10,11,12,3,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,2,10,11,12,3,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,2,10,11,12,3,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,2,10,11,12,1,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0,0,0]
[8,9,10,2,3,4,11,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0]
[8,9,10,2,3,4,11,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0]
[8,9,10,2,3,4,11,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,0]
[8,9,10,2,3,4,11,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,0]
[8,9,10,2,3,4,11,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,0]
[8,9,10,2,3,11,4,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0]
[8,9,10,2,3,11,4,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0]
[8,9,10,2,3,11,4,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,0,0,0]
[8,9,10,2,3,11,4,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,0,0,0]
[8,9,10,2,3,11,4,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,0,0,0]
[8,9,10,2,3,11,12,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0]
[8,9,10,2,3,11,12,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0]
[8,9,10,2,3,11,12,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0]
[8,9,10,2,3,11,12,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0]
[8,9,10,2,11,3,4,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0,0,0,0]
[8,9,10,2,11,3,4,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0,0,0,0]
[8,9,10,2,11,3,4,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,9,10,2,11,3,4,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,9,10,2,11,3,4,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0,0,0]
[8,9,10,2,11,3,12,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0,0]
[8,9,10,2,11,3,12,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0,0]
[8,9,10,2,11,3,12,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0,0]
[8,9,10,2,11,3,12,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0,0]
[8,9,10,2,11,12,3,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,9,10,2,11,12,3,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,9,10,2,11,12,3,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,9,10,2,11,12,3,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,9,10,2,11,12,1,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0,0]
[8,9,10,11,2,3,4,5,12,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0,0,0]
[8,9,10,11,2,3,4,5,12,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0,0,0]
[8,9,10,11,2,3,4,12,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0,0,0]
[8,9,10,11,2,3,4,12,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0,0,0]
[8,9,10,11,2,3,4,12,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0,0,0]
[8,9,10,11,2,3,12,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,10,11,2,3,12,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,10,11,2,3,12,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,10,11,2,3,12,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0]
[8,9,10,11,2,12,3,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,10,11,2,12,3,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,10,11,2,12,3,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,10,11,2,12,3,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,10,11,2,12,1,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0]
[8,9,10,11,12,2,3,4,5,6,1,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,11,12,2,3,4,5,1,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,11,12,2,3,4,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,11,12,2,3,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[8,9,10,11,12,2,1,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[11,2,3,4,5,6,7,8,9,10,12,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]
[11,12,9,10,7,8,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,8,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,5,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,5,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,5,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,5,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,5,8,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,5,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,5,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,5,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,10,7,5,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,8,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,8,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,8,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,8,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,5,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,5,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,5,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,5,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,5,8,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,5,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,5,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,5,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,10,5,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,10,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,10,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,10,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,10,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,10,8,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,10,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,10,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,10,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,10,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,3,10,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,3,10,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,3,10,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,3,10,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,12,9,7,5,3,1,10,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,8,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,8,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,8,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,8,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,5,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,5,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,5,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,5,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,5,8,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,5,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,5,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,5,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,10,7,5,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,8,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,8,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,8,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,8,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,5,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,5,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,5,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,5,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,5,8,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,5,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,5,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,5,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,10,5,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,10,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,10,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,10,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,10,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,10,8,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,10,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,10,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,10,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,10,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,3,10,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,3,10,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,3,10,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,3,10,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,12,7,5,3,1,10,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,8,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,8,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,8,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,8,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,8,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,5,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,5,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,5,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,5,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,5,8,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,5,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,5,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,5,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,10,5,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,10,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,10,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,10,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,10,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,10,8,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,10,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,10,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,10,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,10,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,3,10,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,3,10,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,3,10,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,3,10,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,12,5,3,1,10,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[11,9,7,5,12,10,8,6,3,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,12,10,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,12,10,8,3,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,12,10,8,3,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,12,10,8,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,12,10,3,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,12,10,3,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,12,10,3,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,12,10,3,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,12,3,10,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,12,3,10,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,12,3,10,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,12,3,10,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,12,3,1,10,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[11,9,7,5,3,12,10,8,6,4,1,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[11,9,7,5,3,12,10,8,6,1,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[11,9,7,5,3,12,10,8,1,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[11,9,7,5,3,12,10,1,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[11,9,7,5,3,12,1,10,8,6,4,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
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(only identities of compositions of up to three maps are shown)
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Properties
surjective, graded
Sage code
def mapping(pi): l = [(0,0)] for i, e in enumerate(pi): if e > l[-1][1]: l.append((i,e)) l.append((len(pi), len(pi))) D = [] for i in range(len(l)-2): D.extend([1]*(l[i+1][1]-l[i][1])+[0]*(l[i+2][0]-l[i+1][0])) return DyckWord(D)
Weight
26
Created
Jan 29, 2020 at 13:26 by FindStatCrew
Updated
Jun 07, 2023 at 13:40 by Martin Rubey
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