Identifier
Images
=>
Cc0005;cc-rep-1
[1]=>[1,0]
[1,1]=>[1,0,1,0]
[2]=>[1,1,0,0]
[1,1,1]=>[1,0,1,0,1,0]
[1,2]=>[1,0,1,1,0,0]
[2,1]=>[1,1,0,0,1,0]
[3]=>[1,1,1,0,0,0]
[1,1,1,1]=>[1,0,1,0,1,0,1,0]
[1,1,2]=>[1,0,1,0,1,1,0,0]
[1,2,1]=>[1,0,1,1,0,0,1,0]
[1,3]=>[1,0,1,1,1,0,0,0]
[2,1,1]=>[1,1,0,0,1,0,1,0]
[2,2]=>[1,1,0,0,1,1,0,0]
[3,1]=>[1,1,1,0,0,0,1,0]
[4]=>[1,1,1,1,0,0,0,0]
[1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]
[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]
[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]
[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]
[1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]
[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]
[1,3,1]=>[1,0,1,1,1,0,0,0,1,0]
[1,4]=>[1,0,1,1,1,1,0,0,0,0]
[2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]
[2,1,2]=>[1,1,0,0,1,0,1,1,0,0]
[2,2,1]=>[1,1,0,0,1,1,0,0,1,0]
[2,3]=>[1,1,0,0,1,1,1,0,0,0]
[3,1,1]=>[1,1,1,0,0,0,1,0,1,0]
[3,2]=>[1,1,1,0,0,0,1,1,0,0]
[4,1]=>[1,1,1,1,0,0,0,0,1,0]
[5]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[6]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,4,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[3,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[3,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[5,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[5,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[6,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,3,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,4,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,2,1,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,2,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,2,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,2,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,2,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,2,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,3,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,3,1,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,3,3]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,4,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,4,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,5,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,2,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,2,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,2,1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,2,1,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,2,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,2,1,2,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,2,1,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,2,1,4]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,2,2,1,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,2,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,2,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,3,1,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,2,3,2]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,2,4,1]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,2,5]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,3,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,3,1,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,3,1,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,3,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,3,2,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,3,2,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,3,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,3,4]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,4,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,4,1,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,4,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,5,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,5,2]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,6,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,1,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,1,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,1,1,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,2,1,1,3,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,1,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,1,2,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,2,1,2,3]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,1,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,1,3,2]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,1,4,1]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,1,5]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,2,1,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,2,1,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,2,1,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,2,2,1,3]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,2,3,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,2,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,3,1,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,2,3,1,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,2,3,2,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,2,3,3]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,4,1,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,2,4,2]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,5,1]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,3,1,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,3,1,2,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,3,1,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,3,1,3,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,3,1,4]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,3,2,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,3,2,1,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,3,2,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,3,2,3]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,3,3,1,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,3,3,2]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,3,4,1]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,3,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,4,1,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,4,1,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,4,1,3]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,4,2,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,4,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,4,3,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,4,4]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,5,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,5,1,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,5,2,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,6,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[2,1,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,1,1,2,1,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,1,2,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[2,1,1,2,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[2,1,1,2,3]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[2,1,1,3,1,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[2,1,1,3,2]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[2,1,1,4,1]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[2,1,1,5]=>[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,2,1,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,2,1,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[2,1,2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[2,1,2,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[2,1,2,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[2,1,2,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,2,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[2,1,2,4]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,3,1,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[2,1,3,1,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[2,1,3,2,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[2,1,3,3]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,1,4,1,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[2,1,4,2]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,5,1]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,1,6]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,2,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[2,2,1,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[2,2,1,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[2,2,1,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[2,2,1,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[2,2,1,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[2,2,1,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[2,2,1,4]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[2,2,2,1,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[2,2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[2,2,2,3]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[2,2,3,1,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[2,2,3,2]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[2,2,4,1]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,2,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,3,1,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[2,3,1,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[2,3,1,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[2,3,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[2,3,2,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[2,3,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[2,3,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[2,3,4]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,4,1,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[2,4,1,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[2,4,2,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[2,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[2,5,1,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[2,5,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,6,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[3,1,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,1,2,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,1,3,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[3,1,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[3,1,2,1,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,2,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,2,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,2,3]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[3,1,3,1,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[3,1,3,2]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[3,1,4,1]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[3,1,5]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,1,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[3,2,1,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[3,2,1,3]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[3,2,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[3,2,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,2,3,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[3,2,4]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[3,3,1,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[3,3,1,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[3,3,2,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[3,4,1,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[3,4,2]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[3,5,1]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[4,1,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]
[4,1,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,0]
[4,1,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]
[4,1,2,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,1,0]
[4,1,2,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0]
[4,1,3,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]
[4,1,4]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]
[4,2,1,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]
[4,2,1,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0]
[4,2,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[4,2,3]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[4,3,1,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]
[4,3,2]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[4,4,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[4,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[5,1,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]
[5,1,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]
[5,1,3]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]
[5,2,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]
[5,2,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[5,3,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]
[5,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[6,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[6,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]
[6,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]
[6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[7,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[7,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[8,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[9]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,1,3,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,1,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,2,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,2,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,2,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,2,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,3,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,3,1,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,3,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,4,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,4,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,5,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,2,1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,2,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,2,1,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,2,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,2,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,2,1,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,2,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,2,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,2,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,2,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,2,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,2,3,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,2,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,2,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,2,5]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,3,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,3,1,1,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,3,1,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,3,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,3,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,3,2,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,3,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,4,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,4,1,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,4,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,4,3]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,5,1,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,5,2]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,6,1]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,7]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,2,1,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,2,1,1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,2,1,1,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,2,1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,2,1,1,2,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,2,1,1,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,2,1,1,4]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,2,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,2,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,2,1,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,1,3,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,2,1,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,2,1,4,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,2,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,2,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,2,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,2,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,2,2,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,2,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,2,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,2,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,2,2,4]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,2,3,1,1,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,2,3,1,2]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,2,3,2,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,2,3,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,2,4,1,1]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,2,4,2]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,2,5,1]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,2,6]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,3,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,3,1,1,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,3,1,1,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,3,1,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,3,1,2,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,3,1,2,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,3,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,3,1,4]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,3,2,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,3,2,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,3,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,3,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,3,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,3,4,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,3,5]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,4,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,4,1,1,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,4,1,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,4,1,3]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,4,2,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,4,2,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,4,3,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,4,4]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,5,1,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,5,1,2]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,5,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,6,1,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,6,2]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,7,1]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,1,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,1,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,1,1,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,1,1,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,1,1,1,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,2,1,1,1,3,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,1,1,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,1,1,2,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,1,1,2,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,2,1,1,2,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,1,1,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,1,1,3,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,1,1,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,1,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,2,1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,1,2,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,2,1,2,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,1,2,3,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,2,1,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,1,3,1,1,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,2,1,3,1,2]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,2,1,3,2,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,2,1,3,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,1,4,1,1]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,2,1,4,2]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,1,5,1]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,2,1,6]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,2,2,1,1,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,2,2,1,1,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,2,2,1,1,3]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,2,2,1,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,2,2,1,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,2,2,1,3,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,2,2,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,2,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,2,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,2,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,2,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,2,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,2,2,3,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,2,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,2,2,5]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,1,1,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,2,3,1,1,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,2,3,1,2,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,2,3,1,3]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,2,3,2,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,2,3,2,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,2,3,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,2,3,4]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,2,4,1,1,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,2,4,1,2]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,2,4,2,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,2,4,3]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,2,5,1,1]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,2,5,2]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,2,6,1]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,2,7]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,1,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,1,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,1,1,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,1,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,3,1,1,2,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,1,1,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,3,1,1,3,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,3,1,1,4]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,3,1,2,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,1,2,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,3,1,2,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,1,2,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,3,1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,3,1,3,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,3,1,4,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,3,1,5]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,3,2,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,2,1,1,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,3,2,1,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,2,1,3]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,3,2,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,2,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,2,3,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,3,2,4]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,3,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,3,3,1,2]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,3,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,3,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,3,4,1,1]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,3,4,2]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,3,5,1]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,3,6]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,1,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,4,1,1,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,4,1,1,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,4,1,1,3]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,4,1,2,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,4,1,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,4,1,3,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,4,1,4]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,4,2,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,4,2,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,4,2,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,4,2,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,4,3,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,4,3,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,4,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,4,5]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,5,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,5,1,1,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]
[1,5,1,2,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]
[1,5,1,3]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]
[1,5,2,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]
[1,5,2,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[1,5,3,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]
[1,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[1,6,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,6,1,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]
[1,6,2,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]
[1,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[1,7,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,1,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,1,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,1,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,1,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[2,1,1,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,1,1,1,2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,1,1,2,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[2,1,1,1,2,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[2,1,1,1,2,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[2,1,1,1,3,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[2,1,1,1,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[2,1,1,1,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[2,1,1,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,1,2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,1,2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[2,1,1,2,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[2,1,1,2,1,3]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[2,1,1,2,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[2,1,1,2,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,1,2,3,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[2,1,1,2,4]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,1,3,1,1,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[2,1,1,3,1,2]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[2,1,1,3,2,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[2,1,1,3,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,1,1,4,1,1]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[2,1,1,4,2]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,1,5,1]=>[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,1,1,6]=>[1,1,0,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,2,1,1,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[2,1,2,1,1,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[2,1,2,1,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[2,1,2,1,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[2,1,2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[2,1,2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[2,1,2,1,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[2,1,2,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,1,2,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[2,1,2,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[2,1,2,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[2,1,2,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[2,1,2,3,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[2,1,2,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[2,1,2,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,1,2,5]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,1,1,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[2,1,3,1,1,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[2,1,3,1,2,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[2,1,3,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[2,1,3,2,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[2,1,3,2,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,3,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[2,1,3,4]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,1,4,1,1,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[2,1,4,1,2]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[2,1,4,2,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[2,1,4,3]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[2,1,5,1,1]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[2,1,5,2]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,1,6,1]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,1,7]=>[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,2,1,1,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,2,1,1,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[2,2,1,1,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,1,1,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[2,2,1,1,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[2,2,1,1,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[2,2,1,1,4]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,2,1,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[2,2,1,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[2,2,1,2,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[2,2,1,2,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[2,2,1,3,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[2,2,1,3,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[2,2,1,4,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[2,2,1,5]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[2,2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[2,2,2,1,3]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[2,2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[2,2,2,4]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,2,3,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[2,2,3,1,2]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[2,2,3,2,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[2,2,3,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,2,4,1,1]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[2,2,4,2]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,2,5,1]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,2,6]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,1,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[2,3,1,1,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[2,3,1,1,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[2,3,1,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[2,3,1,2,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[2,3,1,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[2,3,1,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[2,3,1,4]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[2,3,2,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[2,3,2,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[2,3,2,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[2,3,2,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[2,3,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[2,3,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[2,3,4,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[2,3,5]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[2,4,1,1,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[2,4,1,1,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[2,4,1,2,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[2,4,1,3]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[2,4,2,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[2,4,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,4,3,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[2,4,4]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[2,5,1,1,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[2,5,1,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[2,5,2,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[2,5,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[2,6,1,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[2,6,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,7,1]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,1,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,1,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,1,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[3,1,1,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,1,1,2,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,1,1,3,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[3,1,1,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[3,1,1,2,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,1,2,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,1,2,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,1,2,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[3,1,1,3,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[3,1,1,3,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[3,1,1,4,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[3,1,1,5]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[3,1,2,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,2,1,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,2,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,2,1,3]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[3,1,2,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,2,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,2,3,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[3,1,2,4]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[3,1,3,1,1,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[3,1,3,1,2]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[3,1,3,2,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[3,1,3,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[3,1,4,1,1]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[3,1,4,2]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[3,1,5,1]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[3,1,6]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,1,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[3,2,1,1,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[3,2,1,1,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[3,2,1,1,3]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[3,2,1,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[3,2,1,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[3,2,1,3,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[3,2,1,4]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[3,2,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[3,2,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[3,2,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[3,2,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[3,2,3,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[3,2,3,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[3,2,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[3,2,5]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[3,3,1,1,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[3,3,1,1,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[3,3,1,2,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[3,3,1,3]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[3,3,2,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[3,3,2,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[3,3,4]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,4,1,1,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[3,4,1,2]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[3,4,2,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[3,4,3]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[3,5,1,1]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[3,5,2]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[3,6,1]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,1,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[4,1,1,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,1,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[4,1,1,2,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,1,2,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[4,1,1,3,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[4,1,1,4]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[4,1,2,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,2,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[4,1,2,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[4,1,2,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[4,1,3,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,3,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[4,1,4,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[4,1,5]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[4,2,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,1,1,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[4,2,1,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[4,2,1,3]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[4,2,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[4,2,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,2,3,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[4,2,4]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[4,3,1,1,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[4,3,1,2]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[4,3,2,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[4,3,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[4,4,1,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[4,4,2]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[4,5,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[5,1,1,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]
[5,1,1,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0,1,0]
[5,1,1,3]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,1,0,0,0]
[5,1,2,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0]
[5,1,2,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,1,0,0]
[5,1,3,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0]
[5,1,4]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0]
[5,2,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0,1,0]
[5,2,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,1,0,0]
[5,2,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[5,2,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[5,3,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0,1,0]
[5,3,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[5,4,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[6,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[6,1,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]
[6,1,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0]
[6,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]
[6,2,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0,1,0]
[6,2,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[6,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]
[6,4]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[7,1,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[7,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]
[7,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]
[7,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[8,1,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[8,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[9,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,10]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,7,2,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]
[1,6,3,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]
[1,5,4,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,4,5,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,3,6,1]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,2,7,1]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,8,1]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[10,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[1,8,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[1,7,1,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]
[1,6,1,1,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]
[1,5,1,1,1,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,4,1,1,1,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,1,1,1,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,1,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,7,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[1,6,2,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[1,5,2,1,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,4,2,1,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,3,2,1,1,1,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,2,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,2,1,1,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,2,2,1,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,2,1,3,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,2,1,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,2,1,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,3,2,2]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,2,1,3,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,2,1,2,3,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,1,2,2,3]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,1,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,1,1,3,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,1,1,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,1,1,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,3,2,2,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,3,2,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,3,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,3,1,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,1,1,4]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,3,2,2]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,2,3,1,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,2,2,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,2,2,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,2,1,4]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,1,4,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,2,1,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,2,1,2,4]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,2,1,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,4,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,4,1,3]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,3,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,3,2,3]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,3,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,2,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,2,3,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,2,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,2,1,5]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,5,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,4,3]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,3,4]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,1,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,1,2,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,3,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,2,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,2,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,2,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,2,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,2,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,3,3,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,3,2,1,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,3,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,4,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,2,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,2,2,1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,2,2,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,2,2,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,2,2,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,2,1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,2,1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,2,1,1,1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,2,1,1,1,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,2,1,1,1,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,1,2,3,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,2,1,2,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,2,1,2,1,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,2,1,3,4]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,3,3,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,3,3,2,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,3,2,1,2,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,3,2,1,1,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,3,2,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,3,1,1,2,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,3,1,1,1,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,3,1,2,4]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,4,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,4,3,1,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,4,2,1,3]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,4,1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,5,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,2,1,1,1,1,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[2,2,1,1,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,1,1,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[2,2,1,1,3,3]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,2,2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,2,2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,2,2,1,1,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[2,2,2,1,1,1,1,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,2,2,1,2,3]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[2,2,3,3,1,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[2,2,3,2,1,2]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[2,2,3,1,1,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[2,2,4,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,1,2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,1,2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,1,2,2,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[2,1,1,2,2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[2,1,1,2,3,3]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,1,1,1,1,2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,1,1,1,2,2,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,1,1,1,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,1,1,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,1,1,1,1,2,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[2,1,1,1,2,3,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[2,1,1,1,2,2,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[2,1,1,1,2,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[2,1,1,1,3,4]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,1,2,3,1,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[2,1,2,3,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,2,2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[2,1,2,2,1,1,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[2,1,2,2,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[2,1,2,1,1,3,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[2,1,2,1,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[2,1,2,1,1,1,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,2,1,2,4]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,3,4,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[2,1,3,3,1,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[2,1,3,2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[2,1,3,1,1,4]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,1,4,5]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,3,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[3,3,1,1,2,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[3,3,2,2,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[3,3,2,1,1,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[3,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[3,2,1,2,1,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,1,2,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,2,1,1,1,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,1,1,1,1,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[3,2,1,1,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[3,2,2,3,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[3,2,2,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[3,2,2,1,1,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[3,2,3,4]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,1,1,3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[3,1,1,3,2,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,1,1,2,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[3,1,1,2,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[3,1,1,2,2,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[3,1,1,1,1,3,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[3,1,1,1,1,2,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,1,1,1,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[3,1,1,1,2,4]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[3,1,2,4,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[3,1,2,3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[3,1,2,2,1,3]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[3,1,2,1,1,4]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[3,1,3,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[4,4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[4,4,2,2]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[4,3,1,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[4,3,1,1,1,2]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[4,3,2,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[4,2,1,3,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[4,2,1,2,1,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[4,2,1,1,1,3]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[4,2,2,4]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[4,1,1,4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[4,1,1,3,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[4,1,1,2,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[4,1,1,1,1,4]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[4,1,2,5]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[5,5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,4,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[5,3,1,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[5,2,1,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[5,1,1,5]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[6,6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,2,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,2,2,2,3,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,2,3,3,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,2,2,3,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,2,2,4,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,2,3,3,2,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,2,3,4,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,3,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,2,3,2,2,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,3,3,3]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,4,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,2,4,3,2]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,4,2,3]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,5,4]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[1,3,3,2,2,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,3,3,3,2]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,3,4,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,3,4,2,2]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,3,5,3]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,3,2,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,3,2,4,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,3,2,2,3,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,3,2,2,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,2,3,3]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,3,3,4,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,3,3,2,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,3,4,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,4,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,4,5,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,4,3,3,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,4,3,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,4,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,4,2,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,4,2,3,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,4,2,2,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,4,3,4]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,5,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,5,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,5,3,3]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,5,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[2,3,2,2,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[2,3,2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[2,3,3,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[2,3,3,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[2,3,4,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[2,4,3,2,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[2,4,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,4,2,3,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[2,4,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,4,3,3]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,5,4,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[2,5,3,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[2,5,2,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[2,6,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[2,2,3,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[2,2,3,3,2]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[2,2,4,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[2,2,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,2,5,3]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[2,2,2,3,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[2,2,2,4,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,2,2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[2,2,2,3,3]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,2,3,4,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[2,2,3,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[2,3,4,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[2,3,5,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,3,2,4,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,3,2,2,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[2,3,3,4]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,4,5,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,4,2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,5,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,4,2,2,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[3,4,3,2]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[3,5,3,1]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]
[3,5,2,2]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[3,6,3]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[3,3,3,2,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[3,3,4,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[3,3,2,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[3,3,2,2,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,4,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[3,4,2,3]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[3,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[3,2,4,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[3,2,5,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[3,2,3,3,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[3,2,3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,2,4,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[3,2,2,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[3,2,2,3,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[3,2,2,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[3,3,5,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[3,3,2,4]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[3,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[4,5,2,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[4,6,2]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[4,5,3]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[4,3,4,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[4,3,3,2]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,2,5,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[4,2,4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[4,2,3,3]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[4,3,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,6,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[5,5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,4,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[5,3,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[5,2,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,11]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,9,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]
[1,8,1,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,1,0,0]
[1,7,1,1,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,1,0,0]
[1,6,1,1,1,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,5,1,1,1,1,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,1,1,1,1,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,1,1,1,1,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,1,1,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,2,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,2,2,2,1,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,2,2,1,3,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,2,2,1,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,2,2,1,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,2,1,3,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,2,2,1,3,1,3]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,2,2,1,2,3,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,2,1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,2,1,2,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,2,2,1,1,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,2,1,1,3,3]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,2,1,1,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,2,1,1,1,5]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,1,3,2,2,2]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,1,3,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,1,3,1,3,2]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,1,3,1,2,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,1,3,1,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,2,3,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,2,1,2,3,1,3]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,2,1,2,2,3,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,1,2,2,2,3]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,1,2,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,2,1,4,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,1,2,1,3,3]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,1,2,1,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,1,2,1,1,5]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,1,1,4,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,2,1,1,4,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,2,1,1,3,3,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,1,1,3,2,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,1,1,3,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,1,2,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,1,1,2,3,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,1,1,2,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,1,1,2,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,1,1,1,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,2,1,1,1,4,3]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,2,1,1,1,3,4]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,2,1,1,1,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,2,1,1,1,1,6]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,3,2,2,2,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,3,2,2,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,3,2,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,3,2,1,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,2,1,1,4]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,3,1,3,2,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,3,1,3,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,3,1,2,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,3,1,2,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,1,2,1,4]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,3,1,1,4,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,3,1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,3,1,1,2,4]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,3,1,1,1,5]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,2,3,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,2,3,2,1,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,2,3,1,3,2]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,2,3,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,3,1,1,4]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,2,3,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,2,2,3,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,2,2,2,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,2,2,2,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,2,2,1,4]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,2,1,4,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,2,2,1,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,2,2,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,2,2,1,1,5]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,2,1,4,2,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,2,1,4,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,2,1,3,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,2,1,3,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,1,3,1,4]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,1,2,4,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,2,1,2,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,2,1,2,2,4]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,2,1,2,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,2,1,1,5,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,2,1,1,4,3]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,2,1,1,3,4]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,2,1,1,2,5]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,2,1,1,1,6]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,4,2,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,4,2,1,3]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,4,1,3,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,4,1,2,3]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,4,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,3,3,2,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,3,3,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,3,2,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,3,2,2,3]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,3,2,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,3,1,4,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,3,1,3,3]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,3,1,2,4]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,3,1,1,5]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,2,4,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,2,4,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,2,3,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,2,3,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,2,3,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,2,2,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,2,2,3,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,2,2,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,2,2,1,5]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,2,1,5,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,2,1,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,2,1,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,2,1,2,5]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,2,1,1,6]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,5,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,5,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,4,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,4,2,3]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,4,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,3,4,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,3,3,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,3,2,4]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,3,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,2,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,2,4,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,2,3,4]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,2,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,2,1,6]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,4,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
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(only identities of compositions of up to three maps are shown)
Description
The bounce path determined by an integer composition.
Properties
injective, graded
Sage code
def mapping(c): return DyckWord(sum([[1]*a + [0]*a for a in c], []))
Weight
40
Created
May 11, 2021 at 15:03 by Martin Rubey
Updated
May 11, 2021 at 15:03 by Martin Rubey
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