Identifier
Images
=>
[]=>[]
[1]=>[1]
[1,1]=>[2]
[2]=>[1,1]
[1,1,1]=>[3]
[1,2]=>[2,1]
[2,1]=>[1,2]
[3]=>[1,1,1]
[1,1,1,1]=>[4]
[1,1,2]=>[3,1]
[1,2,1]=>[2,2]
[1,3]=>[2,1,1]
[2,1,1]=>[1,3]
[2,2]=>[1,2,1]
[3,1]=>[1,1,2]
[4]=>[1,1,1,1]
[1,1,1,1,1]=>[5]
[1,1,1,2]=>[4,1]
[1,1,2,1]=>[3,2]
[1,1,3]=>[3,1,1]
[1,2,1,1]=>[2,3]
[1,2,2]=>[2,2,1]
[1,3,1]=>[2,1,2]
[1,4]=>[2,1,1,1]
[2,1,1,1]=>[1,4]
[2,1,2]=>[1,3,1]
[2,2,1]=>[1,2,2]
[2,3]=>[1,2,1,1]
[3,1,1]=>[1,1,3]
[3,2]=>[1,1,2,1]
[4,1]=>[1,1,1,2]
[5]=>[1,1,1,1,1]
[1,1,1,1,1,1]=>[6]
[1,1,1,1,2]=>[5,1]
[1,1,1,2,1]=>[4,2]
[1,1,1,3]=>[4,1,1]
[1,1,2,1,1]=>[3,3]
[1,1,2,2]=>[3,2,1]
[1,1,3,1]=>[3,1,2]
[1,1,4]=>[3,1,1,1]
[1,2,1,1,1]=>[2,4]
[1,2,1,2]=>[2,3,1]
[1,2,2,1]=>[2,2,2]
[1,2,3]=>[2,2,1,1]
[1,3,1,1]=>[2,1,3]
[1,3,2]=>[2,1,2,1]
[1,4,1]=>[2,1,1,2]
[1,5]=>[2,1,1,1,1]
[2,1,1,1,1]=>[1,5]
[2,1,1,2]=>[1,4,1]
[2,1,2,1]=>[1,3,2]
[2,1,3]=>[1,3,1,1]
[2,2,1,1]=>[1,2,3]
[2,2,2]=>[1,2,2,1]
[2,3,1]=>[1,2,1,2]
[2,4]=>[1,2,1,1,1]
[3,1,1,1]=>[1,1,4]
[3,1,2]=>[1,1,3,1]
[3,2,1]=>[1,1,2,2]
[3,3]=>[1,1,2,1,1]
[4,1,1]=>[1,1,1,3]
[4,2]=>[1,1,1,2,1]
[5,1]=>[1,1,1,1,2]
[6]=>[1,1,1,1,1,1]
[1,1,1,1,1,1,1]=>[7]
[1,1,1,1,1,2]=>[6,1]
[1,1,1,1,2,1]=>[5,2]
[1,1,1,1,3]=>[5,1,1]
[1,1,1,2,1,1]=>[4,3]
[1,1,1,2,2]=>[4,2,1]
[1,1,1,3,1]=>[4,1,2]
[1,1,1,4]=>[4,1,1,1]
[1,1,2,1,1,1]=>[3,4]
[1,1,2,1,2]=>[3,3,1]
[1,1,2,2,1]=>[3,2,2]
[1,1,2,3]=>[3,2,1,1]
[1,1,3,1,1]=>[3,1,3]
[1,1,3,2]=>[3,1,2,1]
[1,1,4,1]=>[3,1,1,2]
[1,1,5]=>[3,1,1,1,1]
[1,2,1,1,1,1]=>[2,5]
[1,2,1,1,2]=>[2,4,1]
[1,2,1,2,1]=>[2,3,2]
[1,2,1,3]=>[2,3,1,1]
[1,2,2,1,1]=>[2,2,3]
[1,2,2,2]=>[2,2,2,1]
[1,2,3,1]=>[2,2,1,2]
[1,2,4]=>[2,2,1,1,1]
[1,3,1,1,1]=>[2,1,4]
[1,3,1,2]=>[2,1,3,1]
[1,3,2,1]=>[2,1,2,2]
[1,3,3]=>[2,1,2,1,1]
[1,4,1,1]=>[2,1,1,3]
[1,4,2]=>[2,1,1,2,1]
[1,5,1]=>[2,1,1,1,2]
[1,6]=>[2,1,1,1,1,1]
[2,1,1,1,1,1]=>[1,6]
[2,1,1,1,2]=>[1,5,1]
[2,1,1,2,1]=>[1,4,2]
[2,1,1,3]=>[1,4,1,1]
[2,1,2,1,1]=>[1,3,3]
[2,1,2,2]=>[1,3,2,1]
[2,1,3,1]=>[1,3,1,2]
[2,1,4]=>[1,3,1,1,1]
[2,2,1,1,1]=>[1,2,4]
[2,2,1,2]=>[1,2,3,1]
[2,2,2,1]=>[1,2,2,2]
[2,2,3]=>[1,2,2,1,1]
[2,3,1,1]=>[1,2,1,3]
[2,3,2]=>[1,2,1,2,1]
[2,4,1]=>[1,2,1,1,2]
[2,5]=>[1,2,1,1,1,1]
[3,1,1,1,1]=>[1,1,5]
[3,1,1,2]=>[1,1,4,1]
[3,1,2,1]=>[1,1,3,2]
[3,1,3]=>[1,1,3,1,1]
[3,2,1,1]=>[1,1,2,3]
[3,2,2]=>[1,1,2,2,1]
[3,3,1]=>[1,1,2,1,2]
[3,4]=>[1,1,2,1,1,1]
[4,1,1,1]=>[1,1,1,4]
[4,1,2]=>[1,1,1,3,1]
[4,2,1]=>[1,1,1,2,2]
[4,3]=>[1,1,1,2,1,1]
[5,1,1]=>[1,1,1,1,3]
[5,2]=>[1,1,1,1,2,1]
[6,1]=>[1,1,1,1,1,2]
[7]=>[1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1]=>[8]
[1,1,1,1,1,1,2]=>[7,1]
[1,1,1,1,1,2,1]=>[6,2]
[1,1,1,1,1,3]=>[6,1,1]
[1,1,1,1,2,1,1]=>[5,3]
[1,1,1,1,2,2]=>[5,2,1]
[1,1,1,1,3,1]=>[5,1,2]
[1,1,1,1,4]=>[5,1,1,1]
[1,1,1,2,1,1,1]=>[4,4]
[1,1,1,2,1,2]=>[4,3,1]
[1,1,1,2,2,1]=>[4,2,2]
[1,1,1,2,3]=>[4,2,1,1]
[1,1,1,3,1,1]=>[4,1,3]
[1,1,1,3,2]=>[4,1,2,1]
[1,1,1,4,1]=>[4,1,1,2]
[1,1,1,5]=>[4,1,1,1,1]
[1,1,2,1,1,1,1]=>[3,5]
[1,1,2,1,1,2]=>[3,4,1]
[1,1,2,1,2,1]=>[3,3,2]
[1,1,2,1,3]=>[3,3,1,1]
[1,1,2,2,1,1]=>[3,2,3]
[1,1,2,2,2]=>[3,2,2,1]
[1,1,2,3,1]=>[3,2,1,2]
[1,1,2,4]=>[3,2,1,1,1]
[1,1,3,1,1,1]=>[3,1,4]
[1,1,3,1,2]=>[3,1,3,1]
[1,1,3,2,1]=>[3,1,2,2]
[1,1,3,3]=>[3,1,2,1,1]
[1,1,4,1,1]=>[3,1,1,3]
[1,1,4,2]=>[3,1,1,2,1]
[1,1,5,1]=>[3,1,1,1,2]
[1,1,6]=>[3,1,1,1,1,1]
[1,2,1,1,1,1,1]=>[2,6]
[1,2,1,1,1,2]=>[2,5,1]
[1,2,1,1,2,1]=>[2,4,2]
[1,2,1,1,3]=>[2,4,1,1]
[1,2,1,2,1,1]=>[2,3,3]
[1,2,1,2,2]=>[2,3,2,1]
[1,2,1,3,1]=>[2,3,1,2]
[1,2,1,4]=>[2,3,1,1,1]
[1,2,2,1,1,1]=>[2,2,4]
[1,2,2,1,2]=>[2,2,3,1]
[1,2,2,2,1]=>[2,2,2,2]
[1,2,2,3]=>[2,2,2,1,1]
[1,2,3,1,1]=>[2,2,1,3]
[1,2,3,2]=>[2,2,1,2,1]
[1,2,4,1]=>[2,2,1,1,2]
[1,2,5]=>[2,2,1,1,1,1]
[1,3,1,1,1,1]=>[2,1,5]
[1,3,1,1,2]=>[2,1,4,1]
[1,3,1,2,1]=>[2,1,3,2]
[1,3,1,3]=>[2,1,3,1,1]
[1,3,2,1,1]=>[2,1,2,3]
[1,3,2,2]=>[2,1,2,2,1]
[1,3,3,1]=>[2,1,2,1,2]
[1,3,4]=>[2,1,2,1,1,1]
[1,4,1,1,1]=>[2,1,1,4]
[1,4,1,2]=>[2,1,1,3,1]
[1,4,2,1]=>[2,1,1,2,2]
[1,4,3]=>[2,1,1,2,1,1]
[1,5,1,1]=>[2,1,1,1,3]
[1,5,2]=>[2,1,1,1,2,1]
[1,6,1]=>[2,1,1,1,1,2]
[1,7]=>[2,1,1,1,1,1,1]
[2,1,1,1,1,1,1]=>[1,7]
[2,1,1,1,1,2]=>[1,6,1]
[2,1,1,1,2,1]=>[1,5,2]
[2,1,1,1,3]=>[1,5,1,1]
[2,1,1,2,1,1]=>[1,4,3]
[2,1,1,2,2]=>[1,4,2,1]
[2,1,1,3,1]=>[1,4,1,2]
[2,1,1,4]=>[1,4,1,1,1]
[2,1,2,1,1,1]=>[1,3,4]
[2,1,2,1,2]=>[1,3,3,1]
[2,1,2,2,1]=>[1,3,2,2]
[2,1,2,3]=>[1,3,2,1,1]
[2,1,3,1,1]=>[1,3,1,3]
[2,1,3,2]=>[1,3,1,2,1]
[2,1,4,1]=>[1,3,1,1,2]
[2,1,5]=>[1,3,1,1,1,1]
[2,2,1,1,1,1]=>[1,2,5]
[2,2,1,1,2]=>[1,2,4,1]
[2,2,1,2,1]=>[1,2,3,2]
[2,2,1,3]=>[1,2,3,1,1]
[2,2,2,1,1]=>[1,2,2,3]
[2,2,2,2]=>[1,2,2,2,1]
[2,2,3,1]=>[1,2,2,1,2]
[2,2,4]=>[1,2,2,1,1,1]
[2,3,1,1,1]=>[1,2,1,4]
[2,3,1,2]=>[1,2,1,3,1]
[2,3,2,1]=>[1,2,1,2,2]
[2,3,3]=>[1,2,1,2,1,1]
[2,4,1,1]=>[1,2,1,1,3]
[2,4,2]=>[1,2,1,1,2,1]
[2,5,1]=>[1,2,1,1,1,2]
[2,6]=>[1,2,1,1,1,1,1]
[3,1,1,1,1,1]=>[1,1,6]
[3,1,1,1,2]=>[1,1,5,1]
[3,1,1,2,1]=>[1,1,4,2]
[3,1,1,3]=>[1,1,4,1,1]
[3,1,2,1,1]=>[1,1,3,3]
[3,1,2,2]=>[1,1,3,2,1]
[3,1,3,1]=>[1,1,3,1,2]
[3,1,4]=>[1,1,3,1,1,1]
[3,2,1,1,1]=>[1,1,2,4]
[3,2,1,2]=>[1,1,2,3,1]
[3,2,2,1]=>[1,1,2,2,2]
[3,2,3]=>[1,1,2,2,1,1]
[3,3,1,1]=>[1,1,2,1,3]
[3,3,2]=>[1,1,2,1,2,1]
[3,4,1]=>[1,1,2,1,1,2]
[3,5]=>[1,1,2,1,1,1,1]
[4,1,1,1,1]=>[1,1,1,5]
[4,1,1,2]=>[1,1,1,4,1]
[4,1,2,1]=>[1,1,1,3,2]
[4,1,3]=>[1,1,1,3,1,1]
[4,2,1,1]=>[1,1,1,2,3]
[4,2,2]=>[1,1,1,2,2,1]
[4,3,1]=>[1,1,1,2,1,2]
[4,4]=>[1,1,1,2,1,1,1]
[5,1,1,1]=>[1,1,1,1,4]
[5,1,2]=>[1,1,1,1,3,1]
[5,2,1]=>[1,1,1,1,2,2]
[5,3]=>[1,1,1,1,2,1,1]
[6,1,1]=>[1,1,1,1,1,3]
[6,2]=>[1,1,1,1,1,2,1]
[7,1]=>[1,1,1,1,1,1,2]
[8]=>[1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1]=>[9]
[1,1,1,1,1,1,1,2]=>[8,1]
[1,1,1,1,1,1,2,1]=>[7,2]
[1,1,1,1,1,1,3]=>[7,1,1]
[1,1,1,1,1,2,1,1]=>[6,3]
[1,1,1,1,1,2,2]=>[6,2,1]
[1,1,1,1,1,3,1]=>[6,1,2]
[1,1,1,1,1,4]=>[6,1,1,1]
[1,1,1,1,2,1,1,1]=>[5,4]
[1,1,1,1,2,1,2]=>[5,3,1]
[1,1,1,1,2,2,1]=>[5,2,2]
[1,1,1,1,2,3]=>[5,2,1,1]
[1,1,1,1,3,1,1]=>[5,1,3]
[1,1,1,1,3,2]=>[5,1,2,1]
[1,1,1,1,4,1]=>[5,1,1,2]
[1,1,1,1,5]=>[5,1,1,1,1]
[1,1,1,2,1,1,1,1]=>[4,5]
[1,1,1,2,1,1,2]=>[4,4,1]
[1,1,1,2,1,2,1]=>[4,3,2]
[1,1,1,2,1,3]=>[4,3,1,1]
[1,1,1,2,2,1,1]=>[4,2,3]
[1,1,1,2,2,2]=>[4,2,2,1]
[1,1,1,2,3,1]=>[4,2,1,2]
[1,1,1,2,4]=>[4,2,1,1,1]
[1,1,1,3,1,1,1]=>[4,1,4]
[1,1,1,3,1,2]=>[4,1,3,1]
[1,1,1,3,2,1]=>[4,1,2,2]
[1,1,1,3,3]=>[4,1,2,1,1]
[1,1,1,4,1,1]=>[4,1,1,3]
[1,1,1,4,2]=>[4,1,1,2,1]
[1,1,1,5,1]=>[4,1,1,1,2]
[1,1,1,6]=>[4,1,1,1,1,1]
[1,1,2,1,1,1,1,1]=>[3,6]
[1,1,2,1,1,1,2]=>[3,5,1]
[1,1,2,1,1,2,1]=>[3,4,2]
[1,1,2,1,1,3]=>[3,4,1,1]
[1,1,2,1,2,1,1]=>[3,3,3]
[1,1,2,1,2,2]=>[3,3,2,1]
[1,1,2,1,3,1]=>[3,3,1,2]
[1,1,2,1,4]=>[3,3,1,1,1]
[1,1,2,2,1,1,1]=>[3,2,4]
[1,1,2,2,1,2]=>[3,2,3,1]
[1,1,2,2,2,1]=>[3,2,2,2]
[1,1,2,2,3]=>[3,2,2,1,1]
[1,1,2,3,1,1]=>[3,2,1,3]
[1,1,2,3,2]=>[3,2,1,2,1]
[1,1,2,4,1]=>[3,2,1,1,2]
[1,1,2,5]=>[3,2,1,1,1,1]
[1,1,3,1,1,1,1]=>[3,1,5]
[1,1,3,1,1,2]=>[3,1,4,1]
[1,1,3,1,2,1]=>[3,1,3,2]
[1,1,3,1,3]=>[3,1,3,1,1]
[1,1,3,2,1,1]=>[3,1,2,3]
[1,1,3,2,2]=>[3,1,2,2,1]
[1,1,3,3,1]=>[3,1,2,1,2]
[1,1,3,4]=>[3,1,2,1,1,1]
[1,1,4,1,1,1]=>[3,1,1,4]
[1,1,4,1,2]=>[3,1,1,3,1]
[1,1,4,2,1]=>[3,1,1,2,2]
[1,1,4,3]=>[3,1,1,2,1,1]
[1,1,5,1,1]=>[3,1,1,1,3]
[1,1,5,2]=>[3,1,1,1,2,1]
[1,1,6,1]=>[3,1,1,1,1,2]
[1,1,7]=>[3,1,1,1,1,1,1]
[1,2,1,1,1,1,1,1]=>[2,7]
[1,2,1,1,1,1,2]=>[2,6,1]
[1,2,1,1,1,2,1]=>[2,5,2]
[1,2,1,1,1,3]=>[2,5,1,1]
[1,2,1,1,2,1,1]=>[2,4,3]
[1,2,1,1,2,2]=>[2,4,2,1]
[1,2,1,1,3,1]=>[2,4,1,2]
[1,2,1,1,4]=>[2,4,1,1,1]
[1,2,1,2,1,1,1]=>[2,3,4]
[1,2,1,2,1,2]=>[2,3,3,1]
[1,2,1,2,2,1]=>[2,3,2,2]
[1,2,1,2,3]=>[2,3,2,1,1]
[1,2,1,3,1,1]=>[2,3,1,3]
[1,2,1,3,2]=>[2,3,1,2,1]
[1,2,1,4,1]=>[2,3,1,1,2]
[1,2,1,5]=>[2,3,1,1,1,1]
[1,2,2,1,1,1,1]=>[2,2,5]
[1,2,2,1,1,2]=>[2,2,4,1]
[1,2,2,1,2,1]=>[2,2,3,2]
[1,2,2,1,3]=>[2,2,3,1,1]
[1,2,2,2,1,1]=>[2,2,2,3]
[1,2,2,2,2]=>[2,2,2,2,1]
[1,2,2,3,1]=>[2,2,2,1,2]
[1,2,2,4]=>[2,2,2,1,1,1]
[1,2,3,1,1,1]=>[2,2,1,4]
[1,2,3,1,2]=>[2,2,1,3,1]
[1,2,3,2,1]=>[2,2,1,2,2]
[1,2,3,3]=>[2,2,1,2,1,1]
[1,2,4,1,1]=>[2,2,1,1,3]
[1,2,4,2]=>[2,2,1,1,2,1]
[1,2,5,1]=>[2,2,1,1,1,2]
[1,2,6]=>[2,2,1,1,1,1,1]
[1,3,1,1,1,1,1]=>[2,1,6]
[1,3,1,1,1,2]=>[2,1,5,1]
[1,3,1,1,2,1]=>[2,1,4,2]
[1,3,1,1,3]=>[2,1,4,1,1]
[1,3,1,2,1,1]=>[2,1,3,3]
[1,3,1,2,2]=>[2,1,3,2,1]
[1,3,1,3,1]=>[2,1,3,1,2]
[1,3,1,4]=>[2,1,3,1,1,1]
[1,3,2,1,1,1]=>[2,1,2,4]
[1,3,2,1,2]=>[2,1,2,3,1]
[1,3,2,2,1]=>[2,1,2,2,2]
[1,3,2,3]=>[2,1,2,2,1,1]
[1,3,3,1,1]=>[2,1,2,1,3]
[1,3,3,2]=>[2,1,2,1,2,1]
[1,3,4,1]=>[2,1,2,1,1,2]
[1,3,5]=>[2,1,2,1,1,1,1]
[1,4,1,1,1,1]=>[2,1,1,5]
[1,4,1,1,2]=>[2,1,1,4,1]
[1,4,1,2,1]=>[2,1,1,3,2]
[1,4,1,3]=>[2,1,1,3,1,1]
[1,4,2,1,1]=>[2,1,1,2,3]
[1,4,2,2]=>[2,1,1,2,2,1]
[1,4,3,1]=>[2,1,1,2,1,2]
[1,4,4]=>[2,1,1,2,1,1,1]
[1,5,1,1,1]=>[2,1,1,1,4]
[1,5,1,2]=>[2,1,1,1,3,1]
[1,5,2,1]=>[2,1,1,1,2,2]
[1,5,3]=>[2,1,1,1,2,1,1]
[1,6,1,1]=>[2,1,1,1,1,3]
[1,6,2]=>[2,1,1,1,1,2,1]
[1,7,1]=>[2,1,1,1,1,1,2]
[1,8]=>[2,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1]=>[1,8]
[2,1,1,1,1,1,2]=>[1,7,1]
[2,1,1,1,1,2,1]=>[1,6,2]
[2,1,1,1,1,3]=>[1,6,1,1]
[2,1,1,1,2,1,1]=>[1,5,3]
[2,1,1,1,2,2]=>[1,5,2,1]
[2,1,1,1,3,1]=>[1,5,1,2]
[2,1,1,1,4]=>[1,5,1,1,1]
[2,1,1,2,1,1,1]=>[1,4,4]
[2,1,1,2,1,2]=>[1,4,3,1]
[2,1,1,2,2,1]=>[1,4,2,2]
[2,1,1,2,3]=>[1,4,2,1,1]
[2,1,1,3,1,1]=>[1,4,1,3]
[2,1,1,3,2]=>[1,4,1,2,1]
[2,1,1,4,1]=>[1,4,1,1,2]
[2,1,1,5]=>[1,4,1,1,1,1]
[2,1,2,1,1,1,1]=>[1,3,5]
[2,1,2,1,1,2]=>[1,3,4,1]
[2,1,2,1,2,1]=>[1,3,3,2]
[2,1,2,1,3]=>[1,3,3,1,1]
[2,1,2,2,1,1]=>[1,3,2,3]
[2,1,2,2,2]=>[1,3,2,2,1]
[2,1,2,3,1]=>[1,3,2,1,2]
[2,1,2,4]=>[1,3,2,1,1,1]
[2,1,3,1,1,1]=>[1,3,1,4]
[2,1,3,1,2]=>[1,3,1,3,1]
[2,1,3,2,1]=>[1,3,1,2,2]
[2,1,3,3]=>[1,3,1,2,1,1]
[2,1,4,1,1]=>[1,3,1,1,3]
[2,1,4,2]=>[1,3,1,1,2,1]
[2,1,5,1]=>[1,3,1,1,1,2]
[2,1,6]=>[1,3,1,1,1,1,1]
[2,2,1,1,1,1,1]=>[1,2,6]
[2,2,1,1,1,2]=>[1,2,5,1]
[2,2,1,1,2,1]=>[1,2,4,2]
[2,2,1,1,3]=>[1,2,4,1,1]
[2,2,1,2,1,1]=>[1,2,3,3]
[2,2,1,2,2]=>[1,2,3,2,1]
[2,2,1,3,1]=>[1,2,3,1,2]
[2,2,1,4]=>[1,2,3,1,1,1]
[2,2,2,1,1,1]=>[1,2,2,4]
[2,2,2,1,2]=>[1,2,2,3,1]
[2,2,2,2,1]=>[1,2,2,2,2]
[2,2,2,3]=>[1,2,2,2,1,1]
[2,2,3,1,1]=>[1,2,2,1,3]
[2,2,3,2]=>[1,2,2,1,2,1]
[2,2,4,1]=>[1,2,2,1,1,2]
[2,2,5]=>[1,2,2,1,1,1,1]
[2,3,1,1,1,1]=>[1,2,1,5]
[2,3,1,1,2]=>[1,2,1,4,1]
[2,3,1,2,1]=>[1,2,1,3,2]
[2,3,1,3]=>[1,2,1,3,1,1]
[2,3,2,1,1]=>[1,2,1,2,3]
[2,3,2,2]=>[1,2,1,2,2,1]
[2,3,3,1]=>[1,2,1,2,1,2]
[2,3,4]=>[1,2,1,2,1,1,1]
[2,4,1,1,1]=>[1,2,1,1,4]
[2,4,1,2]=>[1,2,1,1,3,1]
[2,4,2,1]=>[1,2,1,1,2,2]
[2,4,3]=>[1,2,1,1,2,1,1]
[2,5,1,1]=>[1,2,1,1,1,3]
[2,5,2]=>[1,2,1,1,1,2,1]
[2,6,1]=>[1,2,1,1,1,1,2]
[2,7]=>[1,2,1,1,1,1,1,1]
[3,1,1,1,1,1,1]=>[1,1,7]
[3,1,1,1,1,2]=>[1,1,6,1]
[3,1,1,1,2,1]=>[1,1,5,2]
[3,1,1,1,3]=>[1,1,5,1,1]
[3,1,1,2,1,1]=>[1,1,4,3]
[3,1,1,2,2]=>[1,1,4,2,1]
[3,1,1,3,1]=>[1,1,4,1,2]
[3,1,1,4]=>[1,1,4,1,1,1]
[3,1,2,1,1,1]=>[1,1,3,4]
[3,1,2,1,2]=>[1,1,3,3,1]
[3,1,2,2,1]=>[1,1,3,2,2]
[3,1,2,3]=>[1,1,3,2,1,1]
[3,1,3,1,1]=>[1,1,3,1,3]
[3,1,3,2]=>[1,1,3,1,2,1]
[3,1,4,1]=>[1,1,3,1,1,2]
[3,1,5]=>[1,1,3,1,1,1,1]
[3,2,1,1,1,1]=>[1,1,2,5]
[3,2,1,1,2]=>[1,1,2,4,1]
[3,2,1,2,1]=>[1,1,2,3,2]
[3,2,1,3]=>[1,1,2,3,1,1]
[3,2,2,1,1]=>[1,1,2,2,3]
[3,2,2,2]=>[1,1,2,2,2,1]
[3,2,3,1]=>[1,1,2,2,1,2]
[3,2,4]=>[1,1,2,2,1,1,1]
[3,3,1,1,1]=>[1,1,2,1,4]
[3,3,1,2]=>[1,1,2,1,3,1]
[3,3,2,1]=>[1,1,2,1,2,2]
[3,3,3]=>[1,1,2,1,2,1,1]
[3,4,1,1]=>[1,1,2,1,1,3]
[3,4,2]=>[1,1,2,1,1,2,1]
[3,5,1]=>[1,1,2,1,1,1,2]
[3,6]=>[1,1,2,1,1,1,1,1]
[4,1,1,1,1,1]=>[1,1,1,6]
[4,1,1,1,2]=>[1,1,1,5,1]
[4,1,1,2,1]=>[1,1,1,4,2]
[4,1,1,3]=>[1,1,1,4,1,1]
[4,1,2,1,1]=>[1,1,1,3,3]
[4,1,2,2]=>[1,1,1,3,2,1]
[4,1,3,1]=>[1,1,1,3,1,2]
[4,1,4]=>[1,1,1,3,1,1,1]
[4,2,1,1,1]=>[1,1,1,2,4]
[4,2,1,2]=>[1,1,1,2,3,1]
[4,2,2,1]=>[1,1,1,2,2,2]
[4,2,3]=>[1,1,1,2,2,1,1]
[4,3,1,1]=>[1,1,1,2,1,3]
[4,3,2]=>[1,1,1,2,1,2,1]
[4,4,1]=>[1,1,1,2,1,1,2]
[4,5]=>[1,1,1,2,1,1,1,1]
[5,1,1,1,1]=>[1,1,1,1,5]
[5,1,1,2]=>[1,1,1,1,4,1]
[5,1,2,1]=>[1,1,1,1,3,2]
[5,1,3]=>[1,1,1,1,3,1,1]
[5,2,1,1]=>[1,1,1,1,2,3]
[5,2,2]=>[1,1,1,1,2,2,1]
[5,3,1]=>[1,1,1,1,2,1,2]
[5,4]=>[1,1,1,1,2,1,1,1]
[6,1,1,1]=>[1,1,1,1,1,4]
[6,1,2]=>[1,1,1,1,1,3,1]
[6,2,1]=>[1,1,1,1,1,2,2]
[6,3]=>[1,1,1,1,1,2,1,1]
[7,1,1]=>[1,1,1,1,1,1,3]
[7,2]=>[1,1,1,1,1,1,2,1]
[8,1]=>[1,1,1,1,1,1,1,2]
[9]=>[1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1]=>[10]
[1,1,1,1,1,1,1,1,2]=>[9,1]
[1,1,1,1,1,1,1,2,1]=>[8,2]
[1,1,1,1,1,1,1,3]=>[8,1,1]
[1,1,1,1,1,1,2,1,1]=>[7,3]
[1,1,1,1,1,1,2,2]=>[7,2,1]
[1,1,1,1,1,1,3,1]=>[7,1,2]
[1,1,1,1,1,1,4]=>[7,1,1,1]
[1,1,1,1,1,2,1,1,1]=>[6,4]
[1,1,1,1,1,2,1,2]=>[6,3,1]
[1,1,1,1,1,2,2,1]=>[6,2,2]
[1,1,1,1,1,2,3]=>[6,2,1,1]
[1,1,1,1,1,3,1,1]=>[6,1,3]
[1,1,1,1,1,3,2]=>[6,1,2,1]
[1,1,1,1,1,4,1]=>[6,1,1,2]
[1,1,1,1,1,5]=>[6,1,1,1,1]
[1,1,1,1,2,1,1,1,1]=>[5,5]
[1,1,1,1,2,1,1,2]=>[5,4,1]
[1,1,1,1,2,1,2,1]=>[5,3,2]
[1,1,1,1,2,1,3]=>[5,3,1,1]
[1,1,1,1,2,2,1,1]=>[5,2,3]
[1,1,1,1,2,2,2]=>[5,2,2,1]
[1,1,1,1,2,3,1]=>[5,2,1,2]
[1,1,1,1,2,4]=>[5,2,1,1,1]
[1,1,1,1,3,1,1,1]=>[5,1,4]
[1,1,1,1,3,1,2]=>[5,1,3,1]
[1,1,1,1,3,2,1]=>[5,1,2,2]
[1,1,1,1,3,3]=>[5,1,2,1,1]
[1,1,1,1,4,1,1]=>[5,1,1,3]
[1,1,1,1,4,2]=>[5,1,1,2,1]
[1,1,1,1,5,1]=>[5,1,1,1,2]
[1,1,1,1,6]=>[5,1,1,1,1,1]
[1,1,1,2,1,1,1,1,1]=>[4,6]
[1,1,1,2,1,1,1,2]=>[4,5,1]
[1,1,1,2,1,1,2,1]=>[4,4,2]
[1,1,1,2,1,1,3]=>[4,4,1,1]
[1,1,1,2,1,2,1,1]=>[4,3,3]
[1,1,1,2,1,2,2]=>[4,3,2,1]
[1,1,1,2,1,3,1]=>[4,3,1,2]
[1,1,1,2,1,4]=>[4,3,1,1,1]
[1,1,1,2,2,1,1,1]=>[4,2,4]
[1,1,1,2,2,1,2]=>[4,2,3,1]
[1,1,1,2,2,2,1]=>[4,2,2,2]
[1,1,1,2,2,3]=>[4,2,2,1,1]
[1,1,1,2,3,1,1]=>[4,2,1,3]
[1,1,1,2,3,2]=>[4,2,1,2,1]
[1,1,1,2,4,1]=>[4,2,1,1,2]
[1,1,1,2,5]=>[4,2,1,1,1,1]
[1,1,1,3,1,1,1,1]=>[4,1,5]
[1,1,1,3,1,1,2]=>[4,1,4,1]
[1,1,1,3,1,2,1]=>[4,1,3,2]
[1,1,1,3,1,3]=>[4,1,3,1,1]
[1,1,1,3,2,1,1]=>[4,1,2,3]
[1,1,1,3,2,2]=>[4,1,2,2,1]
[1,1,1,3,3,1]=>[4,1,2,1,2]
[1,1,1,3,4]=>[4,1,2,1,1,1]
[1,1,1,4,1,1,1]=>[4,1,1,4]
[1,1,1,4,1,2]=>[4,1,1,3,1]
[1,1,1,4,2,1]=>[4,1,1,2,2]
[1,1,1,4,3]=>[4,1,1,2,1,1]
[1,1,1,5,1,1]=>[4,1,1,1,3]
[1,1,1,5,2]=>[4,1,1,1,2,1]
[1,1,1,6,1]=>[4,1,1,1,1,2]
[1,1,1,7]=>[4,1,1,1,1,1,1]
[1,1,2,1,1,1,1,1,1]=>[3,7]
[1,1,2,1,1,1,1,2]=>[3,6,1]
[1,1,2,1,1,1,2,1]=>[3,5,2]
[1,1,2,1,1,1,3]=>[3,5,1,1]
[1,1,2,1,1,2,1,1]=>[3,4,3]
[1,1,2,1,1,2,2]=>[3,4,2,1]
[1,1,2,1,1,3,1]=>[3,4,1,2]
[1,1,2,1,1,4]=>[3,4,1,1,1]
[1,1,2,1,2,1,1,1]=>[3,3,4]
[1,1,2,1,2,1,2]=>[3,3,3,1]
[1,1,2,1,2,2,1]=>[3,3,2,2]
[1,1,2,1,2,3]=>[3,3,2,1,1]
[1,1,2,1,3,1,1]=>[3,3,1,3]
[1,1,2,1,3,2]=>[3,3,1,2,1]
[1,1,2,1,4,1]=>[3,3,1,1,2]
[1,1,2,1,5]=>[3,3,1,1,1,1]
[1,1,2,2,1,1,1,1]=>[3,2,5]
[1,1,2,2,1,1,2]=>[3,2,4,1]
[1,1,2,2,1,2,1]=>[3,2,3,2]
[1,1,2,2,1,3]=>[3,2,3,1,1]
[1,1,2,2,2,1,1]=>[3,2,2,3]
[1,1,2,2,2,2]=>[3,2,2,2,1]
[1,1,2,2,3,1]=>[3,2,2,1,2]
[1,1,2,2,4]=>[3,2,2,1,1,1]
[1,1,2,3,1,1,1]=>[3,2,1,4]
[1,1,2,3,1,2]=>[3,2,1,3,1]
[1,1,2,3,2,1]=>[3,2,1,2,2]
[1,1,2,3,3]=>[3,2,1,2,1,1]
[1,1,2,4,1,1]=>[3,2,1,1,3]
[1,1,2,4,2]=>[3,2,1,1,2,1]
[1,1,2,5,1]=>[3,2,1,1,1,2]
[1,1,2,6]=>[3,2,1,1,1,1,1]
[1,1,3,1,1,1,1,1]=>[3,1,6]
[1,1,3,1,1,1,2]=>[3,1,5,1]
[1,1,3,1,1,2,1]=>[3,1,4,2]
[1,1,3,1,1,3]=>[3,1,4,1,1]
[1,1,3,1,2,1,1]=>[3,1,3,3]
[1,1,3,1,2,2]=>[3,1,3,2,1]
[1,1,3,1,3,1]=>[3,1,3,1,2]
[1,1,3,1,4]=>[3,1,3,1,1,1]
[1,1,3,2,1,1,1]=>[3,1,2,4]
[1,1,3,2,1,2]=>[3,1,2,3,1]
[1,1,3,2,2,1]=>[3,1,2,2,2]
[1,1,3,2,3]=>[3,1,2,2,1,1]
[1,1,3,3,1,1]=>[3,1,2,1,3]
[1,1,3,3,2]=>[3,1,2,1,2,1]
[1,1,3,4,1]=>[3,1,2,1,1,2]
[1,1,3,5]=>[3,1,2,1,1,1,1]
[1,1,4,1,1,1,1]=>[3,1,1,5]
[1,1,4,1,1,2]=>[3,1,1,4,1]
[1,1,4,1,2,1]=>[3,1,1,3,2]
[1,1,4,1,3]=>[3,1,1,3,1,1]
[1,1,4,2,1,1]=>[3,1,1,2,3]
[1,1,4,2,2]=>[3,1,1,2,2,1]
[1,1,4,3,1]=>[3,1,1,2,1,2]
[1,1,4,4]=>[3,1,1,2,1,1,1]
[1,1,5,1,1,1]=>[3,1,1,1,4]
[1,1,5,1,2]=>[3,1,1,1,3,1]
[1,1,5,2,1]=>[3,1,1,1,2,2]
[1,1,5,3]=>[3,1,1,1,2,1,1]
[1,1,6,1,1]=>[3,1,1,1,1,3]
[1,1,6,2]=>[3,1,1,1,1,2,1]
[1,1,7,1]=>[3,1,1,1,1,1,2]
[1,1,8]=>[3,1,1,1,1,1,1,1]
[1,2,1,1,1,1,1,1,1]=>[2,8]
[1,2,1,1,1,1,1,2]=>[2,7,1]
[1,2,1,1,1,1,2,1]=>[2,6,2]
[1,2,1,1,1,1,3]=>[2,6,1,1]
[1,2,1,1,1,2,1,1]=>[2,5,3]
[1,2,1,1,1,2,2]=>[2,5,2,1]
[1,2,1,1,1,3,1]=>[2,5,1,2]
[1,2,1,1,1,4]=>[2,5,1,1,1]
[1,2,1,1,2,1,1,1]=>[2,4,4]
[1,2,1,1,2,1,2]=>[2,4,3,1]
[1,2,1,1,2,2,1]=>[2,4,2,2]
[1,2,1,1,2,3]=>[2,4,2,1,1]
[1,2,1,1,3,1,1]=>[2,4,1,3]
[1,2,1,1,3,2]=>[2,4,1,2,1]
[1,2,1,1,4,1]=>[2,4,1,1,2]
[1,2,1,1,5]=>[2,4,1,1,1,1]
[1,2,1,2,1,1,1,1]=>[2,3,5]
[1,2,1,2,1,1,2]=>[2,3,4,1]
[1,2,1,2,1,2,1]=>[2,3,3,2]
[1,2,1,2,1,3]=>[2,3,3,1,1]
[1,2,1,2,2,1,1]=>[2,3,2,3]
[1,2,1,2,2,2]=>[2,3,2,2,1]
[1,2,1,2,3,1]=>[2,3,2,1,2]
[1,2,1,2,4]=>[2,3,2,1,1,1]
[1,2,1,3,1,1,1]=>[2,3,1,4]
[1,2,1,3,1,2]=>[2,3,1,3,1]
[1,2,1,3,2,1]=>[2,3,1,2,2]
[1,2,1,3,3]=>[2,3,1,2,1,1]
[1,2,1,4,1,1]=>[2,3,1,1,3]
[1,2,1,4,2]=>[2,3,1,1,2,1]
[1,2,1,5,1]=>[2,3,1,1,1,2]
[1,2,1,6]=>[2,3,1,1,1,1,1]
[1,2,2,1,1,1,1,1]=>[2,2,6]
[1,2,2,1,1,1,2]=>[2,2,5,1]
[1,2,2,1,1,2,1]=>[2,2,4,2]
[1,2,2,1,1,3]=>[2,2,4,1,1]
[1,2,2,1,2,1,1]=>[2,2,3,3]
[1,2,2,1,2,2]=>[2,2,3,2,1]
[1,2,2,1,3,1]=>[2,2,3,1,2]
[1,2,2,1,4]=>[2,2,3,1,1,1]
[1,2,2,2,1,1,1]=>[2,2,2,4]
[1,2,2,2,1,2]=>[2,2,2,3,1]
[1,2,2,2,2,1]=>[2,2,2,2,2]
[1,2,2,2,3]=>[2,2,2,2,1,1]
[1,2,2,3,1,1]=>[2,2,2,1,3]
[1,2,2,3,2]=>[2,2,2,1,2,1]
[1,2,2,4,1]=>[2,2,2,1,1,2]
[1,2,2,5]=>[2,2,2,1,1,1,1]
[1,2,3,1,1,1,1]=>[2,2,1,5]
[1,2,3,1,1,2]=>[2,2,1,4,1]
[1,2,3,1,2,1]=>[2,2,1,3,2]
[1,2,3,1,3]=>[2,2,1,3,1,1]
[1,2,3,2,1,1]=>[2,2,1,2,3]
[1,2,3,2,2]=>[2,2,1,2,2,1]
[1,2,3,3,1]=>[2,2,1,2,1,2]
[1,2,3,4]=>[2,2,1,2,1,1,1]
[1,2,4,1,1,1]=>[2,2,1,1,4]
[1,2,4,1,2]=>[2,2,1,1,3,1]
[1,2,4,2,1]=>[2,2,1,1,2,2]
[1,2,4,3]=>[2,2,1,1,2,1,1]
[1,2,5,1,1]=>[2,2,1,1,1,3]
[1,2,5,2]=>[2,2,1,1,1,2,1]
[1,2,6,1]=>[2,2,1,1,1,1,2]
[1,2,7]=>[2,2,1,1,1,1,1,1]
[1,3,1,1,1,1,1,1]=>[2,1,7]
[1,3,1,1,1,1,2]=>[2,1,6,1]
[1,3,1,1,1,2,1]=>[2,1,5,2]
[1,3,1,1,1,3]=>[2,1,5,1,1]
[1,3,1,1,2,1,1]=>[2,1,4,3]
[1,3,1,1,2,2]=>[2,1,4,2,1]
[1,3,1,1,3,1]=>[2,1,4,1,2]
[1,3,1,1,4]=>[2,1,4,1,1,1]
[1,3,1,2,1,1,1]=>[2,1,3,4]
[1,3,1,2,1,2]=>[2,1,3,3,1]
[1,3,1,2,2,1]=>[2,1,3,2,2]
[1,3,1,2,3]=>[2,1,3,2,1,1]
[1,3,1,3,1,1]=>[2,1,3,1,3]
[1,3,1,3,2]=>[2,1,3,1,2,1]
[1,3,1,4,1]=>[2,1,3,1,1,2]
[1,3,1,5]=>[2,1,3,1,1,1,1]
[1,3,2,1,1,1,1]=>[2,1,2,5]
[1,3,2,1,1,2]=>[2,1,2,4,1]
[1,3,2,1,2,1]=>[2,1,2,3,2]
[1,3,2,1,3]=>[2,1,2,3,1,1]
[1,3,2,2,1,1]=>[2,1,2,2,3]
[1,3,2,2,2]=>[2,1,2,2,2,1]
[1,3,2,3,1]=>[2,1,2,2,1,2]
[1,3,2,4]=>[2,1,2,2,1,1,1]
[1,3,3,1,1,1]=>[2,1,2,1,4]
[1,3,3,1,2]=>[2,1,2,1,3,1]
[1,3,3,2,1]=>[2,1,2,1,2,2]
[1,3,3,3]=>[2,1,2,1,2,1,1]
[1,3,4,1,1]=>[2,1,2,1,1,3]
[1,3,4,2]=>[2,1,2,1,1,2,1]
[1,3,5,1]=>[2,1,2,1,1,1,2]
[1,3,6]=>[2,1,2,1,1,1,1,1]
[1,4,1,1,1,1,1]=>[2,1,1,6]
[1,4,1,1,1,2]=>[2,1,1,5,1]
[1,4,1,1,2,1]=>[2,1,1,4,2]
[1,4,1,1,3]=>[2,1,1,4,1,1]
[1,4,1,2,1,1]=>[2,1,1,3,3]
[1,4,1,2,2]=>[2,1,1,3,2,1]
[1,4,1,3,1]=>[2,1,1,3,1,2]
[1,4,1,4]=>[2,1,1,3,1,1,1]
[1,4,2,1,1,1]=>[2,1,1,2,4]
[1,4,2,1,2]=>[2,1,1,2,3,1]
[1,4,2,2,1]=>[2,1,1,2,2,2]
[1,4,2,3]=>[2,1,1,2,2,1,1]
[1,4,3,1,1]=>[2,1,1,2,1,3]
[1,4,3,2]=>[2,1,1,2,1,2,1]
[1,4,4,1]=>[2,1,1,2,1,1,2]
[1,4,5]=>[2,1,1,2,1,1,1,1]
[1,5,1,1,1,1]=>[2,1,1,1,5]
[1,5,1,1,2]=>[2,1,1,1,4,1]
[1,5,1,2,1]=>[2,1,1,1,3,2]
[1,5,1,3]=>[2,1,1,1,3,1,1]
[1,5,2,1,1]=>[2,1,1,1,2,3]
[1,5,2,2]=>[2,1,1,1,2,2,1]
[1,5,3,1]=>[2,1,1,1,2,1,2]
[1,5,4]=>[2,1,1,1,2,1,1,1]
[1,6,1,1,1]=>[2,1,1,1,1,4]
[1,6,1,2]=>[2,1,1,1,1,3,1]
[1,6,2,1]=>[2,1,1,1,1,2,2]
[1,6,3]=>[2,1,1,1,1,2,1,1]
[1,7,1,1]=>[2,1,1,1,1,1,3]
[1,7,2]=>[2,1,1,1,1,1,2,1]
[1,8,1]=>[2,1,1,1,1,1,1,2]
[1,9]=>[2,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1]=>[1,9]
[2,1,1,1,1,1,1,2]=>[1,8,1]
[2,1,1,1,1,1,2,1]=>[1,7,2]
[2,1,1,1,1,1,3]=>[1,7,1,1]
[2,1,1,1,1,2,1,1]=>[1,6,3]
[2,1,1,1,1,2,2]=>[1,6,2,1]
[2,1,1,1,1,3,1]=>[1,6,1,2]
[2,1,1,1,1,4]=>[1,6,1,1,1]
[2,1,1,1,2,1,1,1]=>[1,5,4]
[2,1,1,1,2,1,2]=>[1,5,3,1]
[2,1,1,1,2,2,1]=>[1,5,2,2]
[2,1,1,1,2,3]=>[1,5,2,1,1]
[2,1,1,1,3,1,1]=>[1,5,1,3]
[2,1,1,1,3,2]=>[1,5,1,2,1]
[2,1,1,1,4,1]=>[1,5,1,1,2]
[2,1,1,1,5]=>[1,5,1,1,1,1]
[2,1,1,2,1,1,1,1]=>[1,4,5]
[2,1,1,2,1,1,2]=>[1,4,4,1]
[2,1,1,2,1,2,1]=>[1,4,3,2]
[2,1,1,2,1,3]=>[1,4,3,1,1]
[2,1,1,2,2,1,1]=>[1,4,2,3]
[2,1,1,2,2,2]=>[1,4,2,2,1]
[2,1,1,2,3,1]=>[1,4,2,1,2]
[2,1,1,2,4]=>[1,4,2,1,1,1]
[2,1,1,3,1,1,1]=>[1,4,1,4]
[2,1,1,3,1,2]=>[1,4,1,3,1]
[2,1,1,3,2,1]=>[1,4,1,2,2]
[2,1,1,3,3]=>[1,4,1,2,1,1]
[2,1,1,4,1,1]=>[1,4,1,1,3]
[2,1,1,4,2]=>[1,4,1,1,2,1]
[2,1,1,5,1]=>[1,4,1,1,1,2]
[2,1,1,6]=>[1,4,1,1,1,1,1]
[2,1,2,1,1,1,1,1]=>[1,3,6]
[2,1,2,1,1,1,2]=>[1,3,5,1]
[2,1,2,1,1,2,1]=>[1,3,4,2]
[2,1,2,1,1,3]=>[1,3,4,1,1]
[2,1,2,1,2,1,1]=>[1,3,3,3]
[2,1,2,1,2,2]=>[1,3,3,2,1]
[2,1,2,1,3,1]=>[1,3,3,1,2]
[2,1,2,1,4]=>[1,3,3,1,1,1]
[2,1,2,2,1,1,1]=>[1,3,2,4]
[2,1,2,2,1,2]=>[1,3,2,3,1]
[2,1,2,2,2,1]=>[1,3,2,2,2]
[2,1,2,2,3]=>[1,3,2,2,1,1]
[2,1,2,3,1,1]=>[1,3,2,1,3]
[2,1,2,3,2]=>[1,3,2,1,2,1]
[2,1,2,4,1]=>[1,3,2,1,1,2]
[2,1,2,5]=>[1,3,2,1,1,1,1]
[2,1,3,1,1,1,1]=>[1,3,1,5]
[2,1,3,1,1,2]=>[1,3,1,4,1]
[2,1,3,1,2,1]=>[1,3,1,3,2]
[2,1,3,1,3]=>[1,3,1,3,1,1]
[2,1,3,2,1,1]=>[1,3,1,2,3]
[2,1,3,2,2]=>[1,3,1,2,2,1]
[2,1,3,3,1]=>[1,3,1,2,1,2]
[2,1,3,4]=>[1,3,1,2,1,1,1]
[2,1,4,1,1,1]=>[1,3,1,1,4]
[2,1,4,1,2]=>[1,3,1,1,3,1]
[2,1,4,2,1]=>[1,3,1,1,2,2]
[2,1,4,3]=>[1,3,1,1,2,1,1]
[2,1,5,1,1]=>[1,3,1,1,1,3]
[2,1,5,2]=>[1,3,1,1,1,2,1]
[2,1,6,1]=>[1,3,1,1,1,1,2]
[2,1,7]=>[1,3,1,1,1,1,1,1]
[2,2,1,1,1,1,1,1]=>[1,2,7]
[2,2,1,1,1,1,2]=>[1,2,6,1]
[2,2,1,1,1,2,1]=>[1,2,5,2]
[2,2,1,1,1,3]=>[1,2,5,1,1]
[2,2,1,1,2,1,1]=>[1,2,4,3]
[2,2,1,1,2,2]=>[1,2,4,2,1]
[2,2,1,1,3,1]=>[1,2,4,1,2]
[2,2,1,1,4]=>[1,2,4,1,1,1]
[2,2,1,2,1,1,1]=>[1,2,3,4]
[2,2,1,2,1,2]=>[1,2,3,3,1]
[2,2,1,2,2,1]=>[1,2,3,2,2]
[2,2,1,2,3]=>[1,2,3,2,1,1]
[2,2,1,3,1,1]=>[1,2,3,1,3]
[2,2,1,3,2]=>[1,2,3,1,2,1]
[2,2,1,4,1]=>[1,2,3,1,1,2]
[2,2,1,5]=>[1,2,3,1,1,1,1]
[2,2,2,1,1,1,1]=>[1,2,2,5]
[2,2,2,1,1,2]=>[1,2,2,4,1]
[2,2,2,1,2,1]=>[1,2,2,3,2]
[2,2,2,1,3]=>[1,2,2,3,1,1]
[2,2,2,2,1,1]=>[1,2,2,2,3]
[2,2,2,2,2]=>[1,2,2,2,2,1]
[2,2,2,3,1]=>[1,2,2,2,1,2]
[2,2,2,4]=>[1,2,2,2,1,1,1]
[2,2,3,1,1,1]=>[1,2,2,1,4]
[2,2,3,1,2]=>[1,2,2,1,3,1]
[2,2,3,2,1]=>[1,2,2,1,2,2]
[2,2,3,3]=>[1,2,2,1,2,1,1]
[2,2,4,1,1]=>[1,2,2,1,1,3]
[2,2,4,2]=>[1,2,2,1,1,2,1]
[2,2,5,1]=>[1,2,2,1,1,1,2]
[2,2,6]=>[1,2,2,1,1,1,1,1]
[2,3,1,1,1,1,1]=>[1,2,1,6]
[2,3,1,1,1,2]=>[1,2,1,5,1]
[2,3,1,1,2,1]=>[1,2,1,4,2]
[2,3,1,1,3]=>[1,2,1,4,1,1]
[2,3,1,2,1,1]=>[1,2,1,3,3]
[2,3,1,2,2]=>[1,2,1,3,2,1]
[2,3,1,3,1]=>[1,2,1,3,1,2]
[2,3,1,4]=>[1,2,1,3,1,1,1]
[2,3,2,1,1,1]=>[1,2,1,2,4]
[2,3,2,1,2]=>[1,2,1,2,3,1]
[2,3,2,2,1]=>[1,2,1,2,2,2]
[2,3,2,3]=>[1,2,1,2,2,1,1]
[2,3,3,1,1]=>[1,2,1,2,1,3]
[2,3,3,2]=>[1,2,1,2,1,2,1]
[2,3,4,1]=>[1,2,1,2,1,1,2]
[2,3,5]=>[1,2,1,2,1,1,1,1]
[2,4,1,1,1,1]=>[1,2,1,1,5]
[2,4,1,1,2]=>[1,2,1,1,4,1]
[2,4,1,2,1]=>[1,2,1,1,3,2]
[2,4,1,3]=>[1,2,1,1,3,1,1]
[2,4,2,1,1]=>[1,2,1,1,2,3]
[2,4,2,2]=>[1,2,1,1,2,2,1]
[2,4,3,1]=>[1,2,1,1,2,1,2]
[2,4,4]=>[1,2,1,1,2,1,1,1]
[2,5,1,1,1]=>[1,2,1,1,1,4]
[2,5,1,2]=>[1,2,1,1,1,3,1]
[2,5,2,1]=>[1,2,1,1,1,2,2]
[2,5,3]=>[1,2,1,1,1,2,1,1]
[2,6,1,1]=>[1,2,1,1,1,1,3]
[2,6,2]=>[1,2,1,1,1,1,2,1]
[2,7,1]=>[1,2,1,1,1,1,1,2]
[2,8]=>[1,2,1,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1]=>[1,1,8]
[3,1,1,1,1,1,2]=>[1,1,7,1]
[3,1,1,1,1,2,1]=>[1,1,6,2]
[3,1,1,1,1,3]=>[1,1,6,1,1]
[3,1,1,1,2,1,1]=>[1,1,5,3]
[3,1,1,1,2,2]=>[1,1,5,2,1]
[3,1,1,1,3,1]=>[1,1,5,1,2]
[3,1,1,1,4]=>[1,1,5,1,1,1]
[3,1,1,2,1,1,1]=>[1,1,4,4]
[3,1,1,2,1,2]=>[1,1,4,3,1]
[3,1,1,2,2,1]=>[1,1,4,2,2]
[3,1,1,2,3]=>[1,1,4,2,1,1]
[3,1,1,3,1,1]=>[1,1,4,1,3]
[3,1,1,3,2]=>[1,1,4,1,2,1]
[3,1,1,4,1]=>[1,1,4,1,1,2]
[3,1,1,5]=>[1,1,4,1,1,1,1]
[3,1,2,1,1,1,1]=>[1,1,3,5]
[3,1,2,1,1,2]=>[1,1,3,4,1]
[3,1,2,1,2,1]=>[1,1,3,3,2]
[3,1,2,1,3]=>[1,1,3,3,1,1]
[3,1,2,2,1,1]=>[1,1,3,2,3]
[3,1,2,2,2]=>[1,1,3,2,2,1]
[3,1,2,3,1]=>[1,1,3,2,1,2]
[3,1,2,4]=>[1,1,3,2,1,1,1]
[3,1,3,1,1,1]=>[1,1,3,1,4]
[3,1,3,1,2]=>[1,1,3,1,3,1]
[3,1,3,2,1]=>[1,1,3,1,2,2]
[3,1,3,3]=>[1,1,3,1,2,1,1]
[3,1,4,1,1]=>[1,1,3,1,1,3]
[3,1,4,2]=>[1,1,3,1,1,2,1]
[3,1,5,1]=>[1,1,3,1,1,1,2]
[3,1,6]=>[1,1,3,1,1,1,1,1]
[3,2,1,1,1,1,1]=>[1,1,2,6]
[3,2,1,1,1,2]=>[1,1,2,5,1]
[3,2,1,1,2,1]=>[1,1,2,4,2]
[3,2,1,1,3]=>[1,1,2,4,1,1]
[3,2,1,2,1,1]=>[1,1,2,3,3]
[3,2,1,2,2]=>[1,1,2,3,2,1]
[3,2,1,3,1]=>[1,1,2,3,1,2]
[3,2,1,4]=>[1,1,2,3,1,1,1]
[3,2,2,1,1,1]=>[1,1,2,2,4]
[3,2,2,1,2]=>[1,1,2,2,3,1]
[3,2,2,2,1]=>[1,1,2,2,2,2]
[3,2,2,3]=>[1,1,2,2,2,1,1]
[3,2,3,1,1]=>[1,1,2,2,1,3]
[3,2,3,2]=>[1,1,2,2,1,2,1]
[3,2,4,1]=>[1,1,2,2,1,1,2]
[3,2,5]=>[1,1,2,2,1,1,1,1]
[3,3,1,1,1,1]=>[1,1,2,1,5]
[3,3,1,1,2]=>[1,1,2,1,4,1]
[3,3,1,2,1]=>[1,1,2,1,3,2]
[3,3,1,3]=>[1,1,2,1,3,1,1]
[3,3,2,1,1]=>[1,1,2,1,2,3]
[3,3,2,2]=>[1,1,2,1,2,2,1]
[3,3,3,1]=>[1,1,2,1,2,1,2]
[3,3,4]=>[1,1,2,1,2,1,1,1]
[3,4,1,1,1]=>[1,1,2,1,1,4]
[3,4,1,2]=>[1,1,2,1,1,3,1]
[3,4,2,1]=>[1,1,2,1,1,2,2]
[3,4,3]=>[1,1,2,1,1,2,1,1]
[3,5,1,1]=>[1,1,2,1,1,1,3]
[3,5,2]=>[1,1,2,1,1,1,2,1]
[3,6,1]=>[1,1,2,1,1,1,1,2]
[3,7]=>[1,1,2,1,1,1,1,1,1]
[4,1,1,1,1,1,1]=>[1,1,1,7]
[4,1,1,1,1,2]=>[1,1,1,6,1]
[4,1,1,1,2,1]=>[1,1,1,5,2]
[4,1,1,1,3]=>[1,1,1,5,1,1]
[4,1,1,2,1,1]=>[1,1,1,4,3]
[4,1,1,2,2]=>[1,1,1,4,2,1]
[4,1,1,3,1]=>[1,1,1,4,1,2]
[4,1,1,4]=>[1,1,1,4,1,1,1]
[4,1,2,1,1,1]=>[1,1,1,3,4]
[4,1,2,1,2]=>[1,1,1,3,3,1]
[4,1,2,2,1]=>[1,1,1,3,2,2]
[4,1,2,3]=>[1,1,1,3,2,1,1]
[4,1,3,1,1]=>[1,1,1,3,1,3]
[4,1,3,2]=>[1,1,1,3,1,2,1]
[4,1,4,1]=>[1,1,1,3,1,1,2]
[4,1,5]=>[1,1,1,3,1,1,1,1]
[4,2,1,1,1,1]=>[1,1,1,2,5]
[4,2,1,1,2]=>[1,1,1,2,4,1]
[4,2,1,2,1]=>[1,1,1,2,3,2]
[4,2,1,3]=>[1,1,1,2,3,1,1]
[4,2,2,1,1]=>[1,1,1,2,2,3]
[4,2,2,2]=>[1,1,1,2,2,2,1]
[4,2,3,1]=>[1,1,1,2,2,1,2]
[4,2,4]=>[1,1,1,2,2,1,1,1]
[4,3,1,1,1]=>[1,1,1,2,1,4]
[4,3,1,2]=>[1,1,1,2,1,3,1]
[4,3,2,1]=>[1,1,1,2,1,2,2]
[4,3,3]=>[1,1,1,2,1,2,1,1]
[4,4,1,1]=>[1,1,1,2,1,1,3]
[4,4,2]=>[1,1,1,2,1,1,2,1]
[4,5,1]=>[1,1,1,2,1,1,1,2]
[4,6]=>[1,1,1,2,1,1,1,1,1]
[5,1,1,1,1,1]=>[1,1,1,1,6]
[5,1,1,1,2]=>[1,1,1,1,5,1]
[5,1,1,2,1]=>[1,1,1,1,4,2]
[5,1,1,3]=>[1,1,1,1,4,1,1]
[5,1,2,1,1]=>[1,1,1,1,3,3]
[5,1,2,2]=>[1,1,1,1,3,2,1]
[5,1,3,1]=>[1,1,1,1,3,1,2]
[5,1,4]=>[1,1,1,1,3,1,1,1]
[5,2,1,1,1]=>[1,1,1,1,2,4]
[5,2,1,2]=>[1,1,1,1,2,3,1]
[5,2,2,1]=>[1,1,1,1,2,2,2]
[5,2,3]=>[1,1,1,1,2,2,1,1]
[5,3,1,1]=>[1,1,1,1,2,1,3]
[5,3,2]=>[1,1,1,1,2,1,2,1]
[5,4,1]=>[1,1,1,1,2,1,1,2]
[5,5]=>[1,1,1,1,2,1,1,1,1]
[6,1,1,1,1]=>[1,1,1,1,1,5]
[6,1,1,2]=>[1,1,1,1,1,4,1]
[6,1,2,1]=>[1,1,1,1,1,3,2]
[6,1,3]=>[1,1,1,1,1,3,1,1]
[6,2,1,1]=>[1,1,1,1,1,2,3]
[6,2,2]=>[1,1,1,1,1,2,2,1]
[6,3,1]=>[1,1,1,1,1,2,1,2]
[6,4]=>[1,1,1,1,1,2,1,1,1]
[7,1,1,1]=>[1,1,1,1,1,1,4]
[7,1,2]=>[1,1,1,1,1,1,3,1]
[7,2,1]=>[1,1,1,1,1,1,2,2]
[7,3]=>[1,1,1,1,1,1,2,1,1]
[8,1,1]=>[1,1,1,1,1,1,1,3]
[8,2]=>[1,1,1,1,1,1,1,2,1]
[9,1]=>[1,1,1,1,1,1,1,1,2]
[10]=>[1,1,1,1,1,1,1,1,1,1]
[1,10]=>[2,1,1,1,1,1,1,1,1,1]
[1,8,1,1]=>[2,1,1,1,1,1,1,3]
[1,7,2,1]=>[2,1,1,1,1,1,2,2]
[1,6,3,1]=>[2,1,1,1,1,2,1,2]
[1,5,4,1]=>[2,1,1,1,2,1,1,2]
[1,4,5,1]=>[2,1,1,2,1,1,1,2]
[1,3,6,1]=>[2,1,2,1,1,1,1,2]
[1,2,7,1]=>[2,2,1,1,1,1,1,2]
[1,1,8,1]=>[3,1,1,1,1,1,1,2]
[10,1]=>[1,1,1,1,1,1,1,1,1,2]
[1,7,1,2]=>[2,1,1,1,1,1,3,1]
[1,3,1,1,1,1,1,2]=>[2,1,7,1]
[1,1,1,1,1,1,1,1,1,2]=>[10,1]
[1,1,2,1,1,1,1,1,2]=>[3,7,1]
[1,2,2,2,1,3]=>[2,2,2,3,1,1]
[1,2,2,1,1,4]=>[2,2,4,1,1,1]
[1,2,1,3,1,3]=>[2,3,1,3,1,1]
[1,2,1,2,3,2]=>[2,3,2,1,2,1]
[1,2,1,2,1,4]=>[2,3,3,1,1,1]
[1,2,1,1,1,5]=>[2,5,1,1,1,1]
[1,1,3,1,1,4]=>[3,1,4,1,1,1]
[1,1,2,3,2,2]=>[3,2,1,2,2,1]
[1,1,2,2,1,4]=>[3,2,3,1,1,1]
[1,1,2,1,1,5]=>[3,4,1,1,1,1]
[1,1,1,4,1,3]=>[4,1,1,3,1,1]
[1,1,1,2,3,3]=>[4,2,1,2,1,1]
[1,1,1,2,2,4]=>[4,2,2,1,1,1]
[1,1,1,2,1,5]=>[4,3,1,1,1,1]
[1,1,1,1,2,5]=>[5,2,1,1,1,1]
[1,1,1,1,1,6]=>[6,1,1,1,1,1]
[3,3,3,2]=>[1,1,2,1,2,1,2,1]
[3,4,4]=>[1,1,2,1,1,2,1,1,1]
[2,3,3,3]=>[1,2,1,2,1,2,1,1]
[4,4,3]=>[1,1,1,2,1,1,2,1,1]
[2,1,1,1,1,1,1,1,1,1]=>[1,10]
[2,8,1]=>[1,2,1,1,1,1,1,1,2]
[2,1,7,1]=>[1,3,1,1,1,1,1,2]
[2,1,1,1,1,1,3,1]=>[1,7,1,2]
[2,1,1,1,1,1,1,2,1]=>[1,8,2]
[3,7,1]=>[1,1,2,1,1,1,1,1,2]
[2,1,1,1,1,1,2,1,1]=>[1,7,3]
[3,1,2,2,2,1]=>[1,1,3,2,2,2]
[3,2,1,2,2,1]=>[1,1,2,3,2,2]
[4,1,1,2,2,1]=>[1,1,1,4,2,2]
[3,1,3,1,2,1]=>[1,1,3,1,3,2]
[4,1,2,1,2,1]=>[1,1,1,3,3,2]
[5,1,1,1,2,1]=>[1,1,1,1,5,2]
[4,1,1,3,1,1]=>[1,1,1,4,1,3]
[4,1,2,2,1,1]=>[1,1,1,3,2,3]
[5,1,1,2,1,1]=>[1,1,1,1,4,3]
[3,1,4,1,1,1]=>[1,1,3,1,1,4]
[5,1,2,1,1,1]=>[1,1,1,1,3,4]
[6,1,1,1,1,1]=>[1,1,1,1,1,6]
[2,1,1,1,1,1,2,2]=>[1,7,2,1]
[2,2,1,1,1,1,1,2]=>[1,2,7,1]
[9,2]=>[1,1,1,1,1,1,1,1,2,1]
[1,9,1]=>[2,1,1,1,1,1,1,1,2]
[11]=>[1,1,1,1,1,1,1,1,1,1,1]
[1,1,2,1,2,1,2,1]=>[3,3,3,2]
[1,2,1,2,1,2,1,1]=>[2,3,3,3]
[2,9]=>[1,2,1,1,1,1,1,1,1,1]
[3,3,2,2,1]=>[1,1,2,1,2,2,2]
[4,2,2,2,1]=>[1,1,1,2,2,2,2]
[3,3,3,1,1]=>[1,1,2,1,2,1,3]
[4,3,2,1,1]=>[1,1,1,2,1,2,3]
[5,2,2,1,1]=>[1,1,1,1,2,2,3]
[4,4,1,1,1]=>[1,1,1,2,1,1,4]
[5,3,1,1,1]=>[1,1,1,1,2,1,4]
[4,3,2,2]=>[1,1,1,2,1,2,2,1]
[5,2,2,2]=>[1,1,1,1,2,2,2,1]
[4,3,3,1]=>[1,1,1,2,1,2,1,2]
[4,4,2,1]=>[1,1,1,2,1,1,2,2]
[5,3,2,1]=>[1,1,1,1,2,1,2,2]
[5,4,1,1]=>[1,1,1,1,2,1,1,3]
[5,3,3]=>[1,1,1,1,2,1,2,1,1]
[5,4,2]=>[1,1,1,1,2,1,1,2,1]
[2,1,3,1,3,1]=>[1,3,1,3,1,2]
[2,1,2,3,2,1]=>[1,3,2,1,2,2]
[2,1,2,1,4,1]=>[1,3,3,1,1,2]
[1,3,1,1,4,1]=>[2,1,4,1,1,2]
[1,2,1,1,5,1]=>[2,4,1,1,1,2]
[1,1,4,1,3,1]=>[3,1,1,3,1,2]
[1,1,3,1,4,1]=>[3,1,3,1,1,2]
[1,1,2,3,3,1]=>[3,2,1,2,1,2]
[1,1,1,1,6,1]=>[5,1,1,1,1,2]
[2,2,2,2,1,2]=>[1,2,2,2,3,1]
[2,2,2,1,2,2]=>[1,2,2,3,2,1]
[2,2,2,1,1,3]=>[1,2,2,4,1,1]
[2,2,1,2,1,3]=>[1,2,3,3,1,1]
[2,2,1,1,1,4]=>[1,2,5,1,1,1]
[2,1,3,1,1,3]=>[1,3,1,4,1,1]
[2,1,2,2,2,2]=>[1,3,2,2,2,1]
[2,1,2,2,1,3]=>[1,3,2,3,1,1]
[2,1,2,1,3,2]=>[1,3,3,1,2,1]
[2,1,2,1,2,3]=>[1,3,3,2,1,1]
[2,1,2,1,1,4]=>[1,3,4,1,1,1]
[2,1,1,3,2,2]=>[1,4,1,2,2,1]
[2,1,1,3,1,3]=>[1,4,1,3,1,1]
[2,1,1,2,3,2]=>[1,4,2,1,2,1]
[2,1,1,2,2,3]=>[1,4,2,2,1,1]
[2,1,1,2,1,4]=>[1,4,3,1,1,1]
[2,1,1,1,4,2]=>[1,5,1,1,2,1]
[2,1,1,1,3,3]=>[1,5,1,2,1,1]
[2,1,1,1,2,4]=>[1,5,2,1,1,1]
[2,1,1,1,1,5]=>[1,6,1,1,1,1]
[3,1,1,3,1,2]=>[1,1,4,1,3,1]
[3,1,1,2,2,2]=>[1,1,4,2,2,1]
[1,3,1,2,1,3]=>[2,1,3,3,1,1]
[3,1,1,2,1,3]=>[1,1,4,3,1,1]
[4,1,2,1,1,2]=>[1,1,1,3,4,1]
[3,2,1,2,1,2]=>[1,1,2,3,3,1]
[3,1,1,1,3,2]=>[1,1,5,1,2,1]
[3,1,1,1,2,3]=>[1,1,5,2,1,1]
[4,1,1,2,1,2]=>[1,1,1,4,3,1]
[1,3,1,1,1,4]=>[2,1,5,1,1,1]
[3,1,1,1,1,4]=>[1,1,6,1,1,1]
[4,1,1,1,2,2]=>[1,1,1,5,2,1]
[1,4,1,1,1,3]=>[2,1,1,5,1,1]
[2,3,1,1,1,3]=>[1,2,1,5,1,1]
[3,2,1,1,1,3]=>[1,1,2,5,1,1]
[4,1,1,1,1,3]=>[1,1,1,6,1,1]
[5,1,1,1,1,2]=>[1,1,1,1,6,1]
[2,7,1,1]=>[1,2,1,1,1,1,1,3]
[2,3,1,1,1,1,1,1]=>[1,2,1,7]
[2,2,1,1,1,1,1,1,1]=>[1,2,8]
[2,2,2,1,1,1,1,1]=>[1,2,2,6]
[2,1,2,1,1,1,1,1,1]=>[1,3,7]
[8,2,1]=>[1,1,1,1,1,1,1,2,2]
[7,1,2,1]=>[1,1,1,1,1,1,3,2]
[1,1,1,1,1,1,1,1,2,1]=>[9,2]
[7,3,1]=>[1,1,1,1,1,1,2,1,2]
[2,2,1,1,1,1,2,1]=>[1,2,6,2]
[1,2,1,1,1,1,1,2,1]=>[2,7,2]
[1,1,1,1,1,1,1,1,1,1,1]=>[11]
[1,1,1,1,1,3,1,1,1]=>[6,1,4]
[1,1,1,1,1,2,1,2,1]=>[6,3,2]
[1,1,1,3,1,3,1]=>[4,1,3,1,2]
[1,1,1,2,1,2,1,1,1]=>[4,3,4]
[1,1,1,2,1,1,1,2,1]=>[4,5,2]
[1,1,1,2,3,2,1]=>[4,2,1,2,2]
[1,3,1,1,1,3,1]=>[2,1,5,1,2]
[1,3,1,3,1,1,1]=>[2,1,3,1,4]
[1,3,1,2,1,2,1]=>[2,1,3,3,2]
[1,4,1,4,1]=>[2,1,1,3,1,1,2]
[1,2,1,2,1,1,1,1,1]=>[2,3,6]
[1,2,1,2,1,3,1]=>[2,3,3,1,2]
[1,2,1,3,1,2,1]=>[2,3,1,3,2]
[1,2,1,1,1,2,1,1,1]=>[2,5,4]
[1,2,2,1,2,2,1]=>[2,2,3,2,2]
[1,1,9]=>[3,1,1,1,1,1,1,1,1]
[1,1,7,2]=>[3,1,1,1,1,1,2,1]
[1,1,6,3]=>[3,1,1,1,1,2,1,1]
[1,1,5,4]=>[3,1,1,1,2,1,1,1]
[1,1,4,5]=>[3,1,1,2,1,1,1,1]
[1,1,3,6]=>[3,1,2,1,1,1,1,1]
[1,1,2,7]=>[3,2,1,1,1,1,1,1]
[1,1,1,8]=>[4,1,1,1,1,1,1,1]
[1,1,1,1,1,2,1,1,1,1]=>[6,5]
[1,1,1,3,1,1,1,2]=>[4,1,5,1]
[9,1,1]=>[1,1,1,1,1,1,1,1,3]
[1,6,1,1,1,1]=>[2,1,1,1,1,5]
[1,5,1,1,2,1]=>[2,1,1,1,4,2]
[1,4,1,1,3,1]=>[2,1,1,4,1,2]
[1,3,1,3,1,2]=>[2,1,3,1,3,1]
[1,4,1,2,1,2]=>[2,1,1,3,3,1]
[1,1,1,1,1,1,1,1,3]=>[9,1,1]
[3,1,3,1,3]=>[1,1,3,1,3,1,1]
[3,1,2,3,2]=>[1,1,3,2,1,2,1]
[3,1,2,1,4]=>[1,1,3,3,1,1,1]
[2,1,4,1,3]=>[1,3,1,1,3,1,1]
[2,1,3,1,4]=>[1,3,1,3,1,1,1]
[1,1,2,3,4]=>[3,2,1,2,1,1,1]
[2,1,8]=>[1,3,1,1,1,1,1,1,1]
[2,1,6,1,1]=>[1,3,1,1,1,1,3]
[2,1,5,1,1,1]=>[1,3,1,1,1,4]
[2,1,4,1,1,1,1]=>[1,3,1,1,5]
[2,1,3,1,1,1,1,1]=>[1,3,1,6]
[3,1,7]=>[1,1,3,1,1,1,1,1,1]
[2,1,6,2]=>[1,3,1,1,1,1,2,1]
[2,1,5,2,1]=>[1,3,1,1,1,2,2]
[2,1,4,2,1,1]=>[1,3,1,1,2,3]
[2,1,3,2,1,1,1]=>[1,3,1,2,4]
[2,1,2,2,1,1,1,1]=>[1,3,2,5]
[2,1,1,2,1,1,1,1,1]=>[1,4,6]
[8,1,1,1]=>[1,1,1,1,1,1,1,4]
[7,2,1,1]=>[1,1,1,1,1,1,2,3]
[6,3,1,1]=>[1,1,1,1,1,2,1,3]
[4,5,1,1]=>[1,1,1,2,1,1,1,3]
[3,6,1,1]=>[1,1,2,1,1,1,1,3]
[2,1,1,1,1,1,1,1,2]=>[1,9,1]
[2,1,1,1,1,2,1,1,1]=>[1,6,4]
[2,1,1,1,2,1,1,1,1]=>[1,5,5]
[3,1,1,1,1,1,1,1,1]=>[1,1,9]
[1,1,1,1,1,1,1,2,1,1]=>[8,3]
[1,1,1,1,1,3,1,2]=>[6,1,3,1]
[1,1,1,2,1,3,1,1]=>[4,3,1,3]
[1,1,1,2,1,1,1,1,1,1]=>[4,7]
[1,1,1,2,1,2,1,2]=>[4,3,3,1]
[1,1,1,3,1,2,1,1]=>[4,1,3,3]
[1,2,1,3,1,1,1,1]=>[2,3,1,5]
[1,2,1,4,1,2]=>[2,3,1,1,3,1]
[1,2,1,1,1,3,1,1]=>[2,5,1,3]
[1,2,1,1,1,1,1,1,1,1]=>[2,9]
[1,2,1,1,1,2,1,2]=>[2,5,3,1]
[1,2,1,2,1,1,1,2]=>[2,3,5,1]
[1,3,1,4,1,1]=>[2,1,3,1,1,3]
[1,3,1,2,1,1,1,1]=>[2,1,3,5]
[1,3,1,1,1,2,1,1]=>[2,1,5,3]
[1,4,1,3,1,1]=>[2,1,1,3,1,3]
[1,5,1,4]=>[2,1,1,1,3,1,1,1]
[1,1,2,1,1,1,1,1,1,1]=>[3,8]
[1,1,2,1,1,1,2,1,1]=>[3,5,3]
[1,1,2,1,2,1,1,1,1]=>[3,3,5]
[1,1,2,1,3,1,2]=>[3,3,1,3,1]
[1,1,3,1,2,1,1,1]=>[3,1,3,4]
[1,1,3,1,3,1,1]=>[3,1,3,1,3]
[1,1,3,1,1,1,2,1]=>[3,1,5,2]
[1,1,3,1,1,1,1,1,1]=>[3,1,7]
[1,1,3,1,2,1,2]=>[3,1,3,3,1]
[1,1,4,1,2,1,1]=>[3,1,1,3,3]
[1,1,4,1,1,1,2]=>[3,1,1,5,1]
[1,1,5,1,3]=>[3,1,1,1,3,1,1]
[1,1,1,1,2,1,1,1,1,1]=>[5,6]
[1,1,1,1,2,1,2,1,1]=>[5,3,3]
[1,1,1,1,3,1,2,1]=>[5,1,3,2]
[1,1,1,1,3,1,1,1,1]=>[5,1,5]
[1,1,1,1,4,1,2]=>[5,1,1,3,1]
[1,1,1,1,1,1,2,1,1,1]=>[7,4]
[1,1,1,1,1,1,3,1,1]=>[7,1,3]
[1,1,1,1,1,1,2,1,2]=>[7,3,1]
[1,1,1,1,2,1,3,1]=>[5,3,1,2]
[1,1,1,1,2,1,1,1,2]=>[5,5,1]
[1,1,1,1,3,1,3]=>[5,1,3,1,1]
[1,1,2,1,3,1,1,1]=>[3,3,1,4]
[1,1,2,1,4,1,1]=>[3,3,1,1,3]
[1,1,2,1,1,1,3,1]=>[3,5,1,2]
[1,1,2,1,2,1,3]=>[3,3,3,1,1]
[1,1,3,1,1,1,3]=>[3,1,5,1,1]
[1,1,4,1,4]=>[3,1,1,3,1,1,1]
[2,1,3,1,2,1,1]=>[1,3,1,3,3]
[2,1,4,1,2,1]=>[1,3,1,1,3,2]
[2,1,5,1,2]=>[1,3,1,1,1,3,1]
[2,1,2,1,2,1,1,1]=>[1,3,3,4]
[2,1,2,1,3,1,1]=>[1,3,3,1,3]
[2,1,2,1,1,1,2,1]=>[1,3,5,2]
[2,1,2,1,2,1,2]=>[1,3,3,3,1]
[2,1,3,1,1,1,2]=>[1,3,1,5,1]
[2,1,1,1,3,1,1,1]=>[1,5,1,4]
[2,1,1,1,4,1,1]=>[1,5,1,1,3]
[2,1,1,1,2,1,2,1]=>[1,5,3,2]
[2,1,1,1,3,1,2]=>[1,5,1,3,1]
[2,1,1,1,2,1,3]=>[1,5,3,1,1]
[2,1,2,1,1,1,3]=>[1,3,5,1,1]
[3,1,5,1,1]=>[1,1,3,1,1,1,3]
[3,1,3,1,1,1,1]=>[1,1,3,1,5]
[3,1,4,1,2]=>[1,1,3,1,1,3,1]
[3,1,2,1,3,1]=>[1,1,3,3,1,2]
[3,1,2,1,2,1,1]=>[1,1,3,3,3]
[3,1,2,1,1,1,2]=>[1,1,3,5,1]
[3,1,1,1,4,1]=>[1,1,5,1,1,2]
[3,1,1,1,3,1,1]=>[1,1,5,1,3]
[3,1,1,1,2,1,2]=>[1,1,5,3,1]
[3,1,1,1,1,1,3]=>[1,1,7,1,1]
[4,1,5,1]=>[1,1,1,3,1,1,1,2]
[4,1,4,1,1]=>[1,1,1,3,1,1,3]
[4,1,3,1,2]=>[1,1,1,3,1,3,1]
[4,1,2,1,3]=>[1,1,1,3,3,1,1]
[4,1,1,1,4]=>[1,1,1,5,1,1,1]
[5,1,5]=>[1,1,1,1,3,1,1,1,1]
[1,1,2,2,2,2,1]=>[3,2,2,2,2]
[1,1,2,3,2,1,1]=>[3,2,1,2,3]
[8,1,2]=>[1,1,1,1,1,1,1,3,1]
[4,2,1,1,1,2]=>[1,1,1,2,5,1]
[3,1,2,2,1,2]=>[1,1,3,2,3,1]
[3,1,2,1,2,2]=>[1,1,3,3,2,1]
[3,1,2,1,1,3]=>[1,1,3,4,1,1]
[3,1,1,3,2,1]=>[1,1,4,1,2,2]
[3,1,1,2,3,1]=>[1,1,4,2,1,2]
[4,1,1,1,3,1]=>[1,1,1,5,1,2]
[6,4,1]=>[1,1,1,1,1,2,1,1,2]
[5,5,1]=>[1,1,1,1,2,1,1,1,2]
[4,6,1]=>[1,1,1,2,1,1,1,1,2]
[1,1,1,1,1,1,3,2]=>[7,1,2,1]
[1,1,1,1,1,2,2,2]=>[6,2,2,1]
[1,1,1,1,2,1,2,2]=>[5,3,2,1]
[1,1,1,2,1,1,2,2]=>[4,4,2,1]
[1,1,2,1,1,1,2,2]=>[3,5,2,1]
[1,2,1,1,1,1,2,2]=>[2,6,2,1]
[1,1,1,1,1,1,2,3]=>[7,2,1,1]
[1,1,1,1,2,3,2]=>[5,2,1,2,1]
[1,1,1,1,2,2,2,1]=>[5,2,2,2]
[1,1,1,2,2,2,2]=>[4,2,2,2,1]
[1,1,1,1,2,2,3]=>[5,2,2,1,1]
[2,4,1,1,1,2]=>[1,2,1,1,5,1]
[1,1,1,1,1,2,1,1,2]=>[6,4,1]
[2,3,1,2,1,2]=>[1,2,1,3,3,1]
[2,2,3,1,1,2]=>[1,2,2,1,4,1]
[3,1,3,1,1,2]=>[1,1,3,1,4,1]
[2,3,2,1,1,2]=>[1,2,1,2,4,1]
[3,2,2,1,1,2]=>[1,1,2,2,4,1]
[3,3,1,1,1,2]=>[1,1,2,1,5,1]
[2,1,1,5,1,1]=>[1,4,1,1,1,3]
[1,1,1,6,1,1]=>[4,1,1,1,1,3]
[2,2,2,2,1,1,1]=>[1,2,2,2,4]
[3,2,2,1,1,1,1]=>[1,1,2,2,5]
[1,2,2,2,1,1,1,1]=>[2,2,2,5]
[2,2,1,1,2,2,1]=>[1,2,4,2,2]
[2,2,1,2,2,1,1]=>[1,2,3,2,3]
[3,1,1,2,2,1,1]=>[1,1,4,2,3]
[1,2,1,1,2,2,1,1]=>[2,4,2,3]
[1,2,3,1,1,3]=>[2,2,1,4,1,1]
[1,3,2,1,1,3]=>[2,1,2,4,1,1]
[3,2,1,1,1,1,1,1]=>[1,1,2,7]
[1,1,1,5,1,2]=>[4,1,1,1,3,1]
[2,2,1,2,1,1,1,1]=>[1,2,3,5]
[2,2,1,1,2,1,1,1]=>[1,2,4,4]
[2,2,1,1,1,2,1,1]=>[1,2,5,3]
[1,1,2,4,1,2]=>[3,2,1,1,3,1]
[7,1,3]=>[1,1,1,1,1,1,3,1,1]
[1,1,7,1,1]=>[3,1,1,1,1,1,3]
[1,1,6,1,2]=>[3,1,1,1,1,3,1]
[1,1,1,1,2,2,1,2]=>[5,2,3,1]
[1,1,1,2,3,1,2]=>[4,2,1,3,1]
[1,2,5,1,2]=>[2,2,1,1,1,3,1]
[2,6,1,2]=>[1,2,1,1,1,1,3,1]
[3,1,1,4,1,1]=>[1,1,4,1,1,3]
[1,1,1,1,1,1,1,1,1,1,1,1]=>[12]
[1,1,1,1,1,1,1,1,2,2]=>[9,2,1]
[1,1,1,1,1,1,2,2,1,1]=>[7,2,3]
[1,1,1,1,1,1,2,1,1,2]=>[7,4,1]
[1,1,1,1,1,1,3,3]=>[7,1,2,1,1]
[1,1,1,1,2,2,1,1,1,1]=>[5,2,5]
[1,1,1,1,2,2,2,2]=>[5,2,2,2,1]
[1,1,1,1,2,1,1,2,1,1]=>[5,4,3]
[1,1,1,1,2,1,1,1,1,2]=>[5,6,1]
[1,1,1,1,2,1,2,3]=>[5,3,2,1,1]
[1,1,1,1,3,3,1,1]=>[5,1,2,1,3]
[1,1,1,1,3,2,1,2]=>[5,1,2,3,1]
[1,1,1,1,3,1,1,3]=>[5,1,4,1,1]
[1,1,1,1,4,4]=>[5,1,1,2,1,1,1]
[1,1,2,2,1,1,1,1,1,1]=>[3,2,7]
[1,1,2,2,1,1,2,2]=>[3,2,4,2,1]
[1,1,2,2,2,2,1,1]=>[3,2,2,2,3]
[1,1,2,2,2,1,1,2]=>[3,2,2,4,1]
[1,1,2,2,3,3]=>[3,2,2,1,2,1,1]
[1,1,2,1,1,2,1,1,1,1]=>[3,4,5]
[1,1,2,1,1,2,2,2]=>[3,4,2,2,1]
[1,1,2,1,1,1,1,2,1,1]=>[3,6,3]
[1,1,2,1,1,1,1,1,1,2]=>[3,8,1]
[1,1,2,1,1,1,2,3]=>[3,5,2,1,1]
[1,1,2,1,2,3,1,1]=>[3,3,2,1,3]
[1,1,2,1,2,2,1,2]=>[3,3,2,3,1]
[1,1,2,1,2,1,1,3]=>[3,3,4,1,1]
[1,1,2,1,3,4]=>[3,3,1,2,1,1,1]
[1,1,3,3,1,1,1,1]=>[3,1,2,1,5]
[1,1,3,3,2,2]=>[3,1,2,1,2,2,1]
[1,1,3,2,1,2,1,1]=>[3,1,2,3,3]
[1,1,3,2,1,1,1,2]=>[3,1,2,5,1]
[1,1,3,2,2,3]=>[3,1,2,2,2,1,1]
[1,1,3,1,1,3,1,1]=>[3,1,4,1,3]
[1,1,3,1,1,2,1,2]=>[3,1,4,3,1]
[1,1,3,1,1,1,1,3]=>[3,1,6,1,1]
[1,1,3,1,2,4]=>[3,1,3,2,1,1,1]
[1,1,4,4,1,1]=>[3,1,1,2,1,1,3]
[1,1,4,3,1,2]=>[3,1,1,2,1,3,1]
[1,1,4,2,1,3]=>[3,1,1,2,3,1,1]
[1,1,4,1,1,4]=>[3,1,1,4,1,1,1]
[1,1,5,5]=>[3,1,1,1,2,1,1,1,1]
[2,2,1,1,1,1,1,1,1,1]=>[1,2,9]
[2,2,1,1,1,1,2,2]=>[1,2,6,2,1]
[2,2,1,1,2,2,1,1]=>[1,2,4,2,3]
[2,2,1,1,2,1,1,2]=>[1,2,4,4,1]
[2,2,1,1,3,3]=>[1,2,4,1,2,1,1]
[2,2,2,2,1,1,1,1]=>[1,2,2,2,5]
[2,2,2,2,2,2]=>[1,2,2,2,2,2,1]
[2,2,2,1,1,2,1,1]=>[1,2,2,4,3]
[2,2,2,1,1,1,1,2]=>[1,2,2,6,1]
[2,2,2,1,2,3]=>[1,2,2,3,2,1,1]
[2,2,3,3,1,1]=>[1,2,2,1,2,1,3]
[2,2,3,2,1,2]=>[1,2,2,1,2,3,1]
[2,2,3,1,1,3]=>[1,2,2,1,4,1,1]
[2,2,4,4]=>[1,2,2,1,1,2,1,1,1]
[2,1,1,2,1,1,1,1,1,1]=>[1,4,7]
[2,1,1,2,1,1,2,2]=>[1,4,4,2,1]
[2,1,1,2,2,2,1,1]=>[1,4,2,2,3]
[2,1,1,2,2,1,1,2]=>[1,4,2,4,1]
[2,1,1,2,3,3]=>[1,4,2,1,2,1,1]
[2,1,1,1,1,2,1,1,1,1]=>[1,6,5]
[2,1,1,1,1,2,2,2]=>[1,6,2,2,1]
[2,1,1,1,1,1,1,2,1,1]=>[1,8,3]
[2,1,1,1,1,1,1,1,1,2]=>[1,10,1]
[2,1,1,1,1,1,2,3]=>[1,7,2,1,1]
[2,1,1,1,2,3,1,1]=>[1,5,2,1,3]
[2,1,1,1,2,2,1,2]=>[1,5,2,3,1]
[2,1,1,1,2,1,1,3]=>[1,5,4,1,1]
[2,1,1,1,3,4]=>[1,5,1,2,1,1,1]
[2,1,2,3,1,1,1,1]=>[1,3,2,1,5]
[2,1,2,3,2,2]=>[1,3,2,1,2,2,1]
[2,1,2,2,1,2,1,1]=>[1,3,2,3,3]
[2,1,2,2,1,1,1,2]=>[1,3,2,5,1]
[2,1,2,2,2,3]=>[1,3,2,2,2,1,1]
[2,1,2,1,1,3,1,1]=>[1,3,4,1,3]
[2,1,2,1,1,2,1,2]=>[1,3,4,3,1]
[2,1,2,1,1,1,1,3]=>[1,3,6,1,1]
[2,1,2,1,2,4]=>[1,3,3,2,1,1,1]
[2,1,3,4,1,1]=>[1,3,1,2,1,1,3]
[2,1,3,3,1,2]=>[1,3,1,2,1,3,1]
[2,1,3,2,1,3]=>[1,3,1,2,3,1,1]
[2,1,3,1,1,4]=>[1,3,1,4,1,1,1]
[2,1,4,5]=>[1,3,1,1,2,1,1,1,1]
[3,3,1,1,1,1,1,1]=>[1,1,2,1,7]
[3,3,1,1,2,2]=>[1,1,2,1,4,2,1]
[3,3,2,2,1,1]=>[1,1,2,1,2,2,3]
[3,3,2,1,1,2]=>[1,1,2,1,2,4,1]
[3,3,3,3]=>[1,1,2,1,2,1,2,1,1]
[3,2,1,2,1,1,1,1]=>[1,1,2,3,5]
[3,2,1,2,2,2]=>[1,1,2,3,2,2,1]
[3,2,1,1,1,2,1,1]=>[1,1,2,5,3]
[3,2,1,1,1,1,1,2]=>[1,1,2,7,1]
[3,2,1,1,2,3]=>[1,1,2,4,2,1,1]
[3,2,2,3,1,1]=>[1,1,2,2,2,1,3]
[3,2,2,2,1,2]=>[1,1,2,2,2,3,1]
[3,2,2,1,1,3]=>[1,1,2,2,4,1,1]
[3,2,3,4]=>[1,1,2,2,1,2,1,1,1]
[3,1,1,3,1,1,1,1]=>[1,1,4,1,5]
[3,1,1,3,2,2]=>[1,1,4,1,2,2,1]
[3,1,1,2,1,2,1,1]=>[1,1,4,3,3]
[3,1,1,2,1,1,1,2]=>[1,1,4,5,1]
[3,1,1,2,2,3]=>[1,1,4,2,2,1,1]
[3,1,1,1,1,3,1,1]=>[1,1,6,1,3]
[3,1,1,1,1,2,1,2]=>[1,1,6,3,1]
[3,1,1,1,1,1,1,3]=>[1,1,8,1,1]
[3,1,1,1,2,4]=>[1,1,5,2,1,1,1]
[3,1,2,4,1,1]=>[1,1,3,2,1,1,3]
[3,1,2,3,1,2]=>[1,1,3,2,1,3,1]
[3,1,2,2,1,3]=>[1,1,3,2,3,1,1]
[3,1,2,1,1,4]=>[1,1,3,4,1,1,1]
[3,1,3,5]=>[1,1,3,1,2,1,1,1,1]
[4,4,1,1,1,1]=>[1,1,1,2,1,1,5]
[4,4,2,2]=>[1,1,1,2,1,1,2,2,1]
[4,3,1,2,1,1]=>[1,1,1,2,1,3,3]
[4,3,1,1,1,2]=>[1,1,1,2,1,5,1]
[4,3,2,3]=>[1,1,1,2,1,2,2,1,1]
[4,2,1,3,1,1]=>[1,1,1,2,3,1,3]
[4,2,1,2,1,2]=>[1,1,1,2,3,3,1]
[4,2,1,1,1,3]=>[1,1,1,2,5,1,1]
[4,2,2,4]=>[1,1,1,2,2,2,1,1,1]
[4,1,1,4,1,1]=>[1,1,1,4,1,1,3]
[4,1,1,3,1,2]=>[1,1,1,4,1,3,1]
[4,1,1,2,1,3]=>[1,1,1,4,3,1,1]
[4,1,1,1,1,4]=>[1,1,1,6,1,1,1]
[4,1,2,5]=>[1,1,1,3,2,1,1,1,1]
[5,5,1,1]=>[1,1,1,1,2,1,1,1,3]
[5,4,1,2]=>[1,1,1,1,2,1,1,3,1]
[5,3,1,3]=>[1,1,1,1,2,1,3,1,1]
[5,2,1,4]=>[1,1,1,1,2,3,1,1,1]
[5,1,1,5]=>[1,1,1,1,4,1,1,1,1]
[6,6]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,2,2,2,2,1]=>[2,2,2,2,2,2]
[1,2,2,2,3,2]=>[2,2,2,2,1,2,1]
[1,2,2,3,3,1]=>[2,2,2,1,2,1,2]
[1,2,2,3,2,2]=>[2,2,2,1,2,2,1]
[1,2,2,4,3]=>[2,2,2,1,1,2,1,1]
[1,2,3,3,2,1]=>[2,2,1,2,1,2,2]
[1,2,3,4,2]=>[2,2,1,2,1,1,2,1]
[1,2,3,2,3,1]=>[2,2,1,2,2,1,2]
[1,2,3,2,2,2]=>[2,2,1,2,2,2,1]
[1,2,3,3,3]=>[2,2,1,2,1,2,1,1]
[1,2,4,4,1]=>[2,2,1,1,2,1,1,2]
[1,2,4,3,2]=>[2,2,1,1,2,1,2,1]
[1,2,4,2,3]=>[2,2,1,1,2,2,1,1]
[1,2,5,4]=>[2,2,1,1,1,2,1,1,1]
[1,3,3,2,2,1]=>[2,1,2,1,2,2,2]
[1,3,3,3,2]=>[2,1,2,1,2,1,2,1]
[1,3,4,3,1]=>[2,1,2,1,1,2,1,2]
[1,3,4,2,2]=>[2,1,2,1,1,2,2,1]
[1,3,5,3]=>[2,1,2,1,1,1,2,1,1]
[1,3,2,3,2,1]=>[2,1,2,2,1,2,2]
[1,3,2,4,2]=>[2,1,2,2,1,1,2,1]
[1,3,2,2,3,1]=>[2,1,2,2,2,1,2]
[1,3,2,2,2,2]=>[2,1,2,2,2,2,1]
[1,3,2,3,3]=>[2,1,2,2,1,2,1,1]
[1,3,3,4,1]=>[2,1,2,1,2,1,1,2]
[1,3,3,2,3]=>[2,1,2,1,2,2,1,1]
[1,3,4,4]=>[2,1,2,1,1,2,1,1,1]
[1,4,4,2,1]=>[2,1,1,2,1,1,2,2]
[1,4,5,2]=>[2,1,1,2,1,1,1,2,1]
[1,4,3,3,1]=>[2,1,1,2,1,2,1,2]
[1,4,3,2,2]=>[2,1,1,2,1,2,2,1]
[1,4,4,3]=>[2,1,1,2,1,1,2,1,1]
[1,4,2,4,1]=>[2,1,1,2,2,1,1,2]
[1,4,2,3,2]=>[2,1,1,2,2,1,2,1]
[1,4,2,2,3]=>[2,1,1,2,2,2,1,1]
[1,4,3,4]=>[2,1,1,2,1,2,1,1,1]
[1,5,5,1]=>[2,1,1,1,2,1,1,1,2]
[1,5,4,2]=>[2,1,1,1,2,1,1,2,1]
[1,5,3,3]=>[2,1,1,1,2,1,2,1,1]
[1,5,2,4]=>[2,1,1,1,2,2,1,1,1]
[1,6,5]=>[2,1,1,1,1,2,1,1,1,1]
[2,3,2,2,2,1]=>[1,2,1,2,2,2,2]
[2,3,2,3,2]=>[1,2,1,2,2,1,2,1]
[2,3,3,3,1]=>[1,2,1,2,1,2,1,2]
[2,3,3,2,2]=>[1,2,1,2,1,2,2,1]
[2,3,4,3]=>[1,2,1,2,1,1,2,1,1]
[2,4,3,2,1]=>[1,2,1,1,2,1,2,2]
[2,4,4,2]=>[1,2,1,1,2,1,1,2,1]
[2,4,2,3,1]=>[1,2,1,1,2,2,1,2]
[2,4,2,2,2]=>[1,2,1,1,2,2,2,1]
[2,4,3,3]=>[1,2,1,1,2,1,2,1,1]
[2,5,4,1]=>[1,2,1,1,1,2,1,1,2]
[2,5,3,2]=>[1,2,1,1,1,2,1,2,1]
[2,5,2,3]=>[1,2,1,1,1,2,2,1,1]
[2,6,4]=>[1,2,1,1,1,1,2,1,1,1]
[2,2,3,2,2,1]=>[1,2,2,1,2,2,2]
[2,2,3,3,2]=>[1,2,2,1,2,1,2,1]
[2,2,4,3,1]=>[1,2,2,1,1,2,1,2]
[2,2,4,2,2]=>[1,2,2,1,1,2,2,1]
[2,2,5,3]=>[1,2,2,1,1,1,2,1,1]
[2,2,2,3,2,1]=>[1,2,2,2,1,2,2]
[2,2,2,4,2]=>[1,2,2,2,1,1,2,1]
[2,2,2,2,3,1]=>[1,2,2,2,2,1,2]
[2,2,2,3,3]=>[1,2,2,2,1,2,1,1]
[2,2,3,4,1]=>[1,2,2,1,2,1,1,2]
[2,2,3,2,3]=>[1,2,2,1,2,2,1,1]
[2,3,4,2,1]=>[1,2,1,2,1,1,2,2]
[2,3,5,2]=>[1,2,1,2,1,1,1,2,1]
[2,3,2,4,1]=>[1,2,1,2,2,1,1,2]
[2,3,2,2,3]=>[1,2,1,2,2,2,1,1]
[2,3,3,4]=>[1,2,1,2,1,2,1,1,1]
[2,4,5,1]=>[1,2,1,1,2,1,1,1,2]
[2,4,2,4]=>[1,2,1,1,2,2,1,1,1]
[2,5,5]=>[1,2,1,1,1,2,1,1,1,1]
[3,4,2,2,1]=>[1,1,2,1,1,2,2,2]
[3,4,3,2]=>[1,1,2,1,1,2,1,2,1]
[3,5,3,1]=>[1,1,2,1,1,1,2,1,2]
[3,5,2,2]=>[1,1,2,1,1,1,2,2,1]
[3,6,3]=>[1,1,2,1,1,1,1,2,1,1]
[3,3,3,2,1]=>[1,1,2,1,2,1,2,2]
[3,3,4,2]=>[1,1,2,1,2,1,1,2,1]
[3,3,2,3,1]=>[1,1,2,1,2,2,1,2]
[3,3,2,2,2]=>[1,1,2,1,2,2,2,1]
[3,4,4,1]=>[1,1,2,1,1,2,1,1,2]
[3,4,2,3]=>[1,1,2,1,1,2,2,1,1]
[3,5,4]=>[1,1,2,1,1,1,2,1,1,1]
[3,2,4,2,1]=>[1,1,2,2,1,1,2,2]
[3,2,5,2]=>[1,1,2,2,1,1,1,2,1]
[3,2,3,3,1]=>[1,1,2,2,1,2,1,2]
[3,2,3,2,2]=>[1,1,2,2,1,2,2,1]
[3,2,4,3]=>[1,1,2,2,1,1,2,1,1]
[3,2,2,4,1]=>[1,1,2,2,2,1,1,2]
[3,2,2,3,2]=>[1,1,2,2,2,1,2,1]
[3,2,2,2,3]=>[1,1,2,2,2,2,1,1]
[3,3,5,1]=>[1,1,2,1,2,1,1,1,2]
[3,3,2,4]=>[1,1,2,1,2,2,1,1,1]
[3,4,5]=>[1,1,2,1,1,2,1,1,1,1]
[4,5,2,1]=>[1,1,1,2,1,1,1,2,2]
[4,6,2]=>[1,1,1,2,1,1,1,1,2,1]
[4,4,3,1]=>[1,1,1,2,1,1,2,1,2]
[4,5,3]=>[1,1,1,2,1,1,1,2,1,1]
[4,3,4,1]=>[1,1,1,2,1,2,1,1,2]
[4,3,3,2]=>[1,1,1,2,1,2,1,2,1]
[4,4,4]=>[1,1,1,2,1,1,2,1,1,1]
[4,2,5,1]=>[1,1,1,2,2,1,1,1,2]
[4,2,4,2]=>[1,1,1,2,2,1,1,2,1]
[4,2,3,3]=>[1,1,1,2,2,1,2,1,1]
[4,3,5]=>[1,1,1,2,1,2,1,1,1,1]
[5,6,1]=>[1,1,1,1,2,1,1,1,1,2]
[5,5,2]=>[1,1,1,1,2,1,1,1,2,1]
[5,4,3]=>[1,1,1,1,2,1,1,2,1,1]
[5,3,4]=>[1,1,1,1,2,1,2,1,1,1]
[5,2,5]=>[1,1,1,1,2,2,1,1,1,1]
[1,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,9,2]=>[2,1,1,1,1,1,1,1,2,1]
[1,8,1,2]=>[2,1,1,1,1,1,1,3,1]
[1,3,1,1,1,1,1,1,2]=>[2,1,8,1]
[1,1,1,1,1,1,1,1,1,1,2]=>[11,1]
[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]
[3,2,7]=>[1,1,2,2,1,1,1,1,1,1]
[7,2,3]=>[1,1,1,1,1,1,2,2,1,1]
[1,1,2,5,3]=>[3,2,1,1,1,2,1,1]
[3,1,2,3,3]=>[1,1,3,2,1,2,1,1]
[1,1,4,3,3]=>[3,1,1,2,1,2,1,1]
[1,1,1,2,1,3,3]=>[4,3,1,2,1,1]
[3,3,2,1,3]=>[1,1,2,1,2,3,1,1]
[1,5,2,1,3]=>[2,1,1,1,2,3,1,1]
[1,3,1,2,1,1,3]=>[2,1,3,4,1,1]
[1,1,1,4,1,1,3]=>[4,1,1,4,1,1]
[5,2,2,2,1]=>[1,1,1,1,2,2,2,2]
[1,1,2,3,2,2,1]=>[3,2,1,2,2,2]
[3,1,2,1,2,2,1]=>[1,1,3,3,2,2]
[1,3,2,1,2,2,1]=>[2,1,2,3,2,2]
[1,1,1,2,1,1,2,2,1]=>[4,4,2,2]
[1,1,2,1,2,4,1]=>[3,3,2,1,1,2]
[3,1,2,5,1]=>[1,1,3,2,1,1,1,2]
[1,1,4,5,1]=>[3,1,1,2,1,1,1,2]
[1,2,2,1,2,3,1]=>[2,2,3,2,1,2]
[1,1,2,2,2,3,1]=>[3,2,2,2,1,2]
[1,1,1,2,3,3,1]=>[4,2,1,2,1,2]
[3,1,1,2,1,3,1]=>[1,1,4,3,1,2]
[1,1,3,2,1,3,1]=>[3,1,2,3,1,2]
[1,1,1,1,2,1,1,3,1]=>[5,4,1,2]
[1,2,4,1,2,1,1]=>[2,2,1,1,3,3]
[3,2,2,1,2,1,1]=>[1,1,2,2,3,3]
[1,4,2,1,2,1,1]=>[2,1,1,2,3,3]
[1,1,2,1,2,1,2,1,1]=>[3,3,3,3]
[5,3,2,1,1]=>[1,1,1,1,2,1,2,3]
[1,2,2,3,2,1,1]=>[2,2,2,1,2,3]
[3,5,2,1,1]=>[1,1,2,1,1,1,2,3]
[1,1,2,4,2,1,1]=>[3,2,1,1,2,3]
[3,1,2,2,2,1,1]=>[1,1,3,2,2,3]
[1,3,2,2,2,1,1]=>[2,1,2,2,2,3]
[1,1,1,2,1,2,2,1,1]=>[4,3,2,3]
[3,3,4,1,1]=>[1,1,2,1,2,1,1,3]
[1,5,4,1,1]=>[2,1,1,1,2,1,1,3]
[3,1,1,2,3,1,1]=>[1,1,4,2,1,3]
[1,3,1,2,3,1,1]=>[2,1,3,2,1,3]
[1,1,1,4,3,1,1]=>[4,1,1,2,1,3]
[5,1,1,2,1,1,1]=>[1,1,1,1,4,4]
[1,2,2,1,1,2,1,1,1]=>[2,2,4,4]
[3,3,1,2,1,1,1]=>[1,1,2,1,3,4]
[1,5,1,2,1,1,1]=>[2,1,1,1,3,4]
[1,1,2,2,1,2,1,1,1]=>[3,2,3,4]
[3,1,3,2,1,1,1]=>[1,1,3,1,2,4]
[1,3,3,2,1,1,1]=>[2,1,2,1,2,4]
[1,1,1,2,2,2,1,1,1]=>[4,2,2,4]
[3,1,1,4,1,1,1]=>[1,1,4,1,1,4]
[1,3,1,4,1,1,1]=>[2,1,3,1,1,4]
[1,1,3,4,1,1,1]=>[3,1,2,1,1,4]
[1,1,1,1,2,3,1,1,1]=>[5,2,1,4]
[1,3,1,1,2,1,1,1,1]=>[2,1,4,5]
[1,1,1,3,2,1,1,1,1]=>[4,1,2,5]
[1,1,1,1,1,2,1,1,1,1,1]=>[6,6]
[2,2,2,2,1,2,1]=>[1,2,2,2,3,2]
[2,2,2,1,2,1,2]=>[1,2,2,3,3,1]
[2,2,2,1,2,2,1]=>[1,2,2,3,2,2]
[2,2,2,1,1,2,2]=>[1,2,2,4,2,1]
[2,2,1,2,1,2,2]=>[1,2,3,3,2,1]
[2,2,1,2,1,1,2,1]=>[1,2,3,4,2]
[2,2,1,2,2,1,2]=>[1,2,3,2,3,1]
[2,2,1,2,2,2,1]=>[1,2,3,2,2,2]
[2,2,1,1,2,2,2]=>[1,2,4,2,2,1]
[2,2,1,1,2,1,2,1]=>[1,2,4,3,2]
[2,2,1,1,1,2,2,1]=>[1,2,5,2,2]
[2,1,2,1,2,2,2]=>[1,3,3,2,2,1]
[2,1,2,1,2,1,2,1]=>[1,3,3,3,2]
[2,1,2,1,1,2,2,1]=>[1,3,4,2,2]
[2,1,2,1,1,1,2,2]=>[1,3,5,2,1]
[2,1,2,2,1,2,2]=>[1,3,2,3,2,1]
[2,1,2,2,1,1,2,1]=>[1,3,2,4,2]
[2,1,2,2,2,1,2]=>[1,3,2,2,3,1]
[2,1,2,2,2,2,1]=>[1,3,2,2,2,2]
[2,1,1,2,2,2,2]=>[1,4,2,2,2,1]
[2,1,1,2,2,1,2,1]=>[1,4,2,3,2]
[2,1,1,2,1,2,1,2]=>[1,4,3,3,1]
[2,1,1,2,1,2,2,1]=>[1,4,3,2,2]
[2,1,1,1,2,2,2,1]=>[1,5,2,2,2]
[2,1,1,1,2,1,2,2]=>[1,5,3,2,1]
[1,2,1,2,2,2,2]=>[2,3,2,2,2,1]
[1,2,1,2,2,1,2,1]=>[2,3,2,3,2]
[1,2,1,2,1,2,1,2]=>[2,3,3,3,1]
[1,2,1,2,1,2,2,1]=>[2,3,3,2,2]
[1,2,1,2,1,1,2,2]=>[2,3,4,2,1]
[1,2,1,1,2,1,2,2]=>[2,4,3,2,1]
[1,2,1,1,2,1,1,2,1]=>[2,4,4,2]
[1,2,1,1,2,2,1,2]=>[2,4,2,3,1]
[1,2,1,1,2,2,2,1]=>[2,4,2,2,2]
[1,2,1,1,1,2,2,2]=>[2,5,2,2,1]
[1,2,1,1,1,2,1,2,1]=>[2,5,3,2]
[1,2,1,1,1,1,2,2,1]=>[2,6,2,2]
[1,2,2,1,2,2,2]=>[2,2,3,2,2,1]
[1,2,2,1,2,1,2,1]=>[2,2,3,3,2]
[1,2,2,1,1,2,1,2]=>[2,2,4,3,1]
[1,2,2,1,1,2,2,1]=>[2,2,4,2,2]
[1,2,2,1,1,1,2,2]=>[2,2,5,2,1]
[1,2,2,2,1,2,2]=>[2,2,2,3,2,1]
[1,2,2,2,1,1,2,1]=>[2,2,2,4,2]
[1,2,2,2,2,1,2]=>[2,2,2,2,3,1]
[1,1,2,2,2,2,2]=>[3,2,2,2,2,1]
[1,1,2,2,2,1,2,1]=>[3,2,2,3,2]
[1,1,2,2,1,2,1,2]=>[3,2,3,3,1]
[1,1,2,2,1,2,2,1]=>[3,2,3,2,2]
[1,1,2,1,2,1,2,2]=>[3,3,3,2,1]
[1,1,2,1,2,1,1,2,1]=>[3,3,4,2]
[1,1,2,1,2,2,2,1]=>[3,3,2,2,2]
[1,1,2,1,1,2,1,2,1]=>[3,4,3,2]
[1,1,2,1,1,1,2,2,1]=>[3,5,2,2]
[1,1,1,2,2,1,2,2]=>[4,2,3,2,1]
[1,1,1,2,2,1,1,2,1]=>[4,2,4,2]
[1,1,1,2,2,2,1,2]=>[4,2,2,3,1]
[1,1,1,2,2,2,2,1]=>[4,2,2,2,2]
[1,1,1,2,1,2,2,2]=>[4,3,2,2,1]
[1,1,1,2,1,2,1,2,1]=>[4,3,3,2]
[1,1,1,1,2,2,1,2,1]=>[5,2,3,2]
[1,1,1,1,2,1,2,2,1]=>[5,3,2,2]
[1,1,1,1,1,2,2,2,1]=>[6,2,2,2]
[3,2,2,2,2,1]=>[1,1,2,2,2,2,2]
[4,3,2,2,1]=>[1,1,1,2,1,2,2,2]
[4,2,3,2,1]=>[1,1,1,2,2,1,2,2]
[4,2,2,3,1]=>[1,1,1,2,2,2,1,2]
[4,2,2,2,2]=>[1,1,1,2,2,2,2,1]
[5,4,2,1]=>[1,1,1,1,2,1,1,2,2]
[5,3,3,1]=>[1,1,1,1,2,1,2,1,2]
[5,3,2,2]=>[1,1,1,1,2,1,2,2,1]
[5,2,4,1]=>[1,1,1,1,2,2,1,1,2]
[5,2,3,2]=>[1,1,1,1,2,2,1,2,1]
[5,2,2,3]=>[1,1,1,1,2,2,2,1,1]
[6,5,1]=>[1,1,1,1,1,2,1,1,1,2]
[6,4,2]=>[1,1,1,1,1,2,1,1,2,1]
[6,3,3]=>[1,1,1,1,1,2,1,2,1,1]
[6,2,4]=>[1,1,1,1,1,2,2,1,1,1]
[7,5]=>[1,1,1,1,1,1,2,1,1,1,1]
[11,1]=>[1,1,1,1,1,1,1,1,1,1,2]
[2,9,1]=>[1,2,1,1,1,1,1,1,1,2]
[2,1,8,1]=>[1,3,1,1,1,1,1,1,2]
[2,1,1,1,1,1,1,3,1]=>[1,8,1,2]
[2,1,1,1,1,1,1,1,1,1,1]=>[1,11]
[2,2,1,2,1,2,1,1]=>[1,2,3,3,3]
[2,2,1,1,1,2,1,1,1]=>[1,2,5,4]
[2,1,2,1,1,1,2,1,1]=>[1,3,5,3]
[2,1,2,1,2,1,1,2]=>[1,3,3,4,1]
[2,1,2,1,2,2,1,1]=>[1,3,3,2,3]
[2,1,2,1,1,2,1,1,1]=>[1,3,4,4]
[2,1,1,2,1,1,1,2,1]=>[1,4,5,2]
[2,1,1,2,1,1,2,1,1]=>[1,4,4,3]
[2,1,1,2,1,2,1,1,1]=>[1,4,3,4]
[2,1,1,1,2,1,1,1,2]=>[1,5,5,1]
[2,1,1,1,2,1,1,2,1]=>[1,5,4,2]
[2,1,1,1,2,1,2,1,1]=>[1,5,3,3]
[2,1,1,1,2,2,1,1,1]=>[1,5,2,4]
[1,2,1,2,1,1,2,1,1]=>[2,3,4,3]
[1,2,1,1,2,1,2,1,1]=>[2,4,3,3]
[1,2,1,1,1,2,1,1,2]=>[2,5,4,1]
[1,2,1,1,1,2,2,1,1]=>[2,5,2,3]
[1,2,1,1,1,1,2,1,1,1]=>[2,6,4]
[1,2,2,1,1,1,2,1,1]=>[2,2,5,3]
[1,2,2,2,1,2,1,1]=>[2,2,2,3,3]
[1,2,2,1,2,1,1,2]=>[2,2,3,4,1]
[1,2,2,1,2,2,1,1]=>[2,2,3,2,3]
[1,2,1,2,1,1,1,2,1]=>[2,3,5,2]
[1,2,1,2,2,1,1,2]=>[2,3,2,4,1]
[1,2,1,2,2,2,1,1]=>[2,3,2,2,3]
[1,2,1,2,1,2,1,1,1]=>[2,3,3,4]
[1,2,1,1,2,1,1,1,2]=>[2,4,5,1]
[1,2,1,1,2,2,1,1,1]=>[2,4,2,4]
[1,2,1,1,1,2,1,1,1,1]=>[2,5,5]
[1,1,2,1,1,1,2,1,2]=>[3,5,3,1]
[1,1,2,1,1,2,1,1,2]=>[3,4,4,1]
[1,1,2,1,1,2,2,1,1]=>[3,4,2,3]
[1,1,2,1,1,1,2,1,1,1]=>[3,5,4]
[1,1,2,2,1,1,1,2,1]=>[3,2,5,2]
[1,1,2,2,1,1,2,1,1]=>[3,2,4,3]
[1,1,2,1,2,1,1,1,2]=>[3,3,5,1]
[1,1,2,1,2,2,1,1,1]=>[3,3,2,4]
[1,1,1,2,1,1,1,2,2]=>[4,5,2,1]
[1,1,1,2,1,1,1,1,2,1]=>[4,6,2]
[1,1,1,2,1,1,2,1,2]=>[4,4,3,1]
[1,1,1,2,1,1,1,2,1,1]=>[4,5,3]
[1,1,1,2,1,2,1,1,2]=>[4,3,4,1]
[1,1,1,2,1,1,2,1,1,1]=>[4,4,4]
[1,1,1,2,2,1,1,1,2]=>[4,2,5,1]
[1,1,1,2,2,1,2,1,1]=>[4,2,3,3]
[1,1,1,2,1,2,1,1,1,1]=>[4,3,5]
[1,1,1,1,2,1,1,1,2,1]=>[5,5,2]
[1,1,1,1,2,1,2,1,1,1]=>[5,3,4]
[1,3,5,2,1]=>[2,1,2,1,1,1,2,2]
[1,5,2,2,2]=>[2,1,1,1,2,2,2,1]
[1,5,3,2,1]=>[2,1,1,1,2,1,2,2]
[2,6,2,2]=>[1,2,1,1,1,1,2,2,1]
[6,2,2,2]=>[1,1,1,1,1,2,2,2,1]
[2,2,2,2,2,1,1]=>[1,2,2,2,2,3]
[2,2,2,1,2,1,1,1]=>[1,2,2,3,4]
[2,2,1,2,2,1,1,1]=>[1,2,3,2,4]
[2,1,2,2,2,1,1,1]=>[1,3,2,2,4]
[1,2,2,2,2,1,1,1]=>[2,2,2,2,4]
[2,2,1,1,2,1,1,1,1]=>[1,2,4,5]
[2,1,2,1,2,1,1,1,1]=>[1,3,3,5]
[1,2,2,1,2,1,1,1,1]=>[2,2,3,5]
[2,1,1,2,2,1,1,1,1]=>[1,4,2,5]
[1,2,1,2,2,1,1,1,1]=>[2,3,2,5]
[1,1,2,2,2,1,1,1,1]=>[3,2,2,5]
[2,1,1,1,2,1,1,1,1,1]=>[1,5,6]
[1,2,1,1,2,1,1,1,1,1]=>[2,4,6]
[1,1,2,1,2,1,1,1,1,1]=>[3,3,6]
[1,1,1,2,2,1,1,1,1,1]=>[4,2,6]
[1,1,1,1,2,1,1,1,1,1,1]=>[5,7]
[10,2]=>[1,1,1,1,1,1,1,1,1,2,1]
[1,1,1,1,1,1,1,2,2,1]=>[8,2,2]
[1,1,1,1,1,2,2,1,1,1]=>[6,2,4]
[1,1,1,1,1,2,1,1,2,1]=>[6,4,2]
[1,1,1,1,1,3,3,1]=>[6,1,2,1,2]
[1,1,1,2,1,2,3,1]=>[4,3,2,1,2]
[1,1,1,3,3,1,1,1]=>[4,1,2,1,4]
[1,1,1,3,2,1,2,1]=>[4,1,2,3,2]
[1,1,1,3,1,1,3,1]=>[4,1,4,1,2]
[1,1,1,4,4,1]=>[4,1,1,2,1,1,2]
[1,2,2,1,1,1,1,1,1,1]=>[2,2,8]
[1,2,1,1,1,1,1,1,2,1]=>[2,8,2]
[1,2,1,1,1,2,3,1]=>[2,5,2,1,2]
[1,2,1,2,3,1,1,1]=>[2,3,2,1,4]
[1,2,1,2,1,1,3,1]=>[2,3,4,1,2]
[1,2,1,3,4,1]=>[2,3,1,2,1,1,2]
[1,3,3,1,1,1,1,1]=>[2,1,2,1,6]
[1,3,2,1,2,1,1,1]=>[2,1,2,3,4]
[1,3,2,1,1,1,2,1]=>[2,1,2,5,2]
[1,3,1,1,3,1,1,1]=>[2,1,4,1,4]
[1,3,1,1,2,1,2,1]=>[2,1,4,3,2]
[1,3,1,1,1,1,3,1]=>[2,1,6,1,2]
[1,3,1,2,4,1]=>[2,1,3,2,1,1,2]
[1,4,4,1,1,1]=>[2,1,1,2,1,1,4]
[1,4,3,1,2,1]=>[2,1,1,2,1,3,2]
[1,4,2,1,3,1]=>[2,1,1,2,3,1,2]
[1,4,1,1,4,1]=>[2,1,1,4,1,1,2]
[2,1,1,3,3,2]=>[1,4,1,2,1,2,1]
[2,2,1,2,3,2]=>[1,2,3,2,1,2,1]
[2,3,3,1,1,2]=>[1,2,1,2,1,4,1]
[2,3,2,1,2,2]=>[1,2,1,2,3,2,1]
[2,3,1,1,3,2]=>[1,2,1,4,1,2,1]
[1,1,2,3,3,2]=>[3,2,1,2,1,2,1]
[1,1,1,1,1,2,3,2]=>[6,2,1,2,1]
[1,1,1,2,3,1,1,2]=>[4,2,1,4,1]
[1,1,1,2,1,1,3,2]=>[4,4,1,2,1]
[1,1,1,3,4,2]=>[4,1,2,1,1,2,1]
[1,2,3,1,1,1,1,2]=>[2,2,1,6,1]
[1,2,1,1,3,1,1,2]=>[2,4,1,4,1]
[1,2,1,1,1,1,3,2]=>[2,6,1,2,1]
[1,2,1,2,4,2]=>[2,3,2,1,1,2,1]
[1,3,4,1,1,2]=>[2,1,2,1,1,4,1]
[1,3,3,1,2,2]=>[2,1,2,1,3,2,1]
[1,3,2,1,3,2]=>[2,1,2,3,1,2,1]
[1,3,1,1,4,2]=>[2,1,4,1,1,2,1]
[1,1,1,2,4,3]=>[4,2,1,1,2,1,1]
[1,2,4,1,1,3]=>[2,2,1,1,4,1,1]
[1,2,3,1,2,3]=>[2,2,1,3,2,1,1]
[1,2,2,1,3,3]=>[2,2,3,1,2,1,1]
[1,2,1,1,4,3]=>[2,4,1,1,2,1,1]
[1,2,2,2,3,1,1]=>[2,2,2,2,1,3]
[1,2,2,3,1,2,1]=>[2,2,2,1,3,2]
[1,2,2,4,1,1,1]=>[2,2,2,1,1,4]
[1,2,3,1,2,2,1]=>[2,2,1,3,2,2]
[1,2,3,1,3,1,1]=>[2,2,1,3,1,3]
[1,2,3,2,1,2,1]=>[2,2,1,2,3,2]
[1,2,4,1,1,2,1]=>[2,2,1,1,4,2]
[1,2,3,2,2,1,1]=>[2,2,1,2,2,3]
[1,2,3,3,1,1,1]=>[2,2,1,2,1,4]
[1,2,4,2,1,1,1]=>[2,2,1,1,2,4]
[1,2,5,1,1,1,1]=>[2,2,1,1,1,5]
[1,3,1,2,2,2,1]=>[2,1,3,2,2,2]
[1,3,1,3,1,2,1]=>[2,1,3,1,3,2]
[1,3,1,3,2,1,1]=>[2,1,3,1,2,3]
[1,3,2,1,3,1,1]=>[2,1,2,3,1,3]
[1,4,1,1,2,2,1]=>[2,1,1,4,2,2]
[1,4,1,1,3,1,1]=>[2,1,1,4,1,3]
[1,3,2,2,1,2,1]=>[2,1,2,2,3,2]
[1,3,3,1,1,2,1]=>[2,1,2,1,4,2]
[1,4,1,2,1,2,1]=>[2,1,1,3,3,2]
[1,4,2,1,1,2,1]=>[2,1,1,2,4,2]
[1,5,1,1,1,2,1]=>[2,1,1,1,5,2]
[1,3,2,3,1,1,1]=>[2,1,2,2,1,4]
[1,3,3,1,2,1,1]=>[2,1,2,1,3,3]
[1,3,4,1,1,1,1]=>[2,1,2,1,1,5]
[1,4,1,2,2,1,1]=>[2,1,1,3,2,3]
[1,4,1,3,1,1,1]=>[2,1,1,3,1,4]
[1,5,1,1,2,1,1]=>[2,1,1,1,4,3]
[1,4,2,2,1,1,1]=>[2,1,1,2,2,4]
[1,4,3,1,1,1,1]=>[2,1,1,2,1,5]
[1,5,2,1,1,1,1]=>[2,1,1,1,2,5]
[1,6,1,1,1,1,1]=>[2,1,1,1,1,6]
[2,1,2,2,3,1,1]=>[1,3,2,2,1,3]
[2,1,2,3,1,2,1]=>[1,3,2,1,3,2]
[2,1,2,3,2,1,1]=>[1,3,2,1,2,3]
[2,1,2,4,1,1,1]=>[1,3,2,1,1,4]
[2,1,3,1,2,2,1]=>[1,3,1,3,2,2]
[2,1,3,1,3,1,1]=>[1,3,1,3,1,3]
[2,1,3,2,1,2,1]=>[1,3,1,2,3,2]
[2,1,4,1,1,2,1]=>[1,3,1,1,4,2]
[2,1,3,2,2,1,1]=>[1,3,1,2,2,3]
[2,1,3,3,1,1,1]=>[1,3,1,2,1,4]
[2,1,4,1,2,1,1]=>[1,3,1,1,3,3]
[2,1,4,2,1,1,1]=>[1,3,1,1,2,4]
[2,1,5,1,1,1,1]=>[1,3,1,1,1,5]
[2,2,1,2,3,1,1]=>[1,2,3,2,1,3]
[2,2,1,3,1,2,1]=>[1,2,3,1,3,2]
[2,2,1,3,2,1,1]=>[1,2,3,1,2,3]
[2,2,1,4,1,1,1]=>[1,2,3,1,1,4]
[3,1,1,2,2,2,1]=>[1,1,4,2,2,2]
[3,1,1,3,1,2,1]=>[1,1,4,1,3,2]
[3,1,1,3,2,1,1]=>[1,1,4,1,2,3]
[2,2,2,1,3,1,1]=>[1,2,2,3,1,3]
[2,3,1,1,2,2,1]=>[1,2,1,4,2,2]
[2,3,1,1,3,1,1]=>[1,2,1,4,1,3]
[3,1,2,1,3,1,1]=>[1,1,3,3,1,3]
[3,2,1,1,2,2,1]=>[1,1,2,4,2,2]
[3,2,1,1,3,1,1]=>[1,1,2,4,1,3]
[4,1,1,1,2,2,1]=>[1,1,1,5,2,2]
[4,1,1,1,3,1,1]=>[1,1,1,5,1,3]
[2,2,3,1,1,2,1]=>[1,2,2,1,4,2]
[2,3,1,2,1,2,1]=>[1,2,1,3,3,2]
[2,3,2,1,1,2,1]=>[1,2,1,2,4,2]
[2,4,1,1,1,2,1]=>[1,2,1,1,5,2]
[3,1,2,2,1,2,1]=>[1,1,3,2,3,2]
[3,1,3,1,1,2,1]=>[1,1,3,1,4,2]
[3,2,1,2,1,2,1]=>[1,1,2,3,3,2]
[4,1,1,2,1,2,1]=>[1,1,1,4,3,2]
[3,2,2,1,1,2,1]=>[1,1,2,2,4,2]
[3,3,1,1,1,2,1]=>[1,1,2,1,5,2]
[4,1,2,1,1,2,1]=>[1,1,1,3,4,2]
[4,2,1,1,1,2,1]=>[1,1,1,2,5,2]
[5,1,1,1,1,2,1]=>[1,1,1,1,6,2]
[2,2,2,3,1,1,1]=>[1,2,2,2,1,4]
[2,2,3,1,2,1,1]=>[1,2,2,1,3,3]
[2,2,3,2,1,1,1]=>[1,2,2,1,2,4]
[2,2,4,1,1,1,1]=>[1,2,2,1,1,5]
[2,3,1,2,2,1,1]=>[1,2,1,3,2,3]
[2,3,1,3,1,1,1]=>[1,2,1,3,1,4]
[2,3,2,1,2,1,1]=>[1,2,1,2,3,3]
[2,4,1,1,2,1,1]=>[1,2,1,1,4,3]
[2,3,2,2,1,1,1]=>[1,2,1,2,2,4]
[2,3,3,1,1,1,1]=>[1,2,1,2,1,5]
[2,4,1,2,1,1,1]=>[1,2,1,1,3,4]
[2,4,2,1,1,1,1]=>[1,2,1,1,2,5]
[2,5,1,1,1,1,1]=>[1,2,1,1,1,6]
[3,1,2,3,1,1,1]=>[1,1,3,2,1,4]
[3,1,3,1,2,1,1]=>[1,1,3,1,3,3]
[3,1,4,1,1,1,1]=>[1,1,3,1,1,5]
[3,2,1,2,2,1,1]=>[1,1,2,3,2,3]
[3,2,1,3,1,1,1]=>[1,1,2,3,1,4]
[4,1,1,2,2,1,1]=>[1,1,1,4,2,3]
[4,1,1,3,1,1,1]=>[1,1,1,4,1,4]
[3,3,1,1,2,1,1]=>[1,1,2,1,4,3]
[4,1,2,1,2,1,1]=>[1,1,1,3,3,3]
[4,2,1,1,2,1,1]=>[1,1,1,2,4,3]
[5,1,1,1,2,1,1]=>[1,1,1,1,5,3]
[3,2,2,2,1,1,1]=>[1,1,2,2,2,4]
[3,2,3,1,1,1,1]=>[1,1,2,2,1,5]
[3,3,2,1,1,1,1]=>[1,1,2,1,2,5]
[3,4,1,1,1,1,1]=>[1,1,2,1,1,6]
[4,1,2,2,1,1,1]=>[1,1,1,3,2,4]
[4,1,3,1,1,1,1]=>[1,1,1,3,1,5]
[4,2,1,2,1,1,1]=>[1,1,1,2,3,4]
[4,2,2,1,1,1,1]=>[1,1,1,2,2,5]
[4,3,1,1,1,1,1]=>[1,1,1,2,1,6]
[5,1,2,1,1,1,1]=>[1,1,1,1,3,5]
[5,2,1,1,1,1,1]=>[1,1,1,1,2,6]
[6,1,1,1,1,1,1]=>[1,1,1,1,1,7]
[4,3,3,1,1]=>[1,1,1,2,1,2,1,3]
[4,4,2,1,1]=>[1,1,1,2,1,1,2,3]
[5,4,1,1,1]=>[1,1,1,1,2,1,1,4]
[1,2,1,1,1,1,1,1,1,1,1]=>[2,10]
[1,2,1,1,3,3,1]=>[2,4,1,2,1,2]
[1,2,2,2,1,1,1,1,1]=>[2,2,2,6]
[1,2,2,1,1,1,1,2,1]=>[2,2,6,2]
[1,2,3,1,1,3,1]=>[2,2,1,4,1,2]
[1,1,1,2,1,1,1,1,1,1,1]=>[4,8]
[1,1,1,1,1,1,1,2,1,1,1]=>[8,4]
[1,1,1,1,1,1,1,1,1,2,1]=>[10,2]
[1,1,1,1,1,1,2,3,1]=>[7,2,1,2]
[1,1,1,1,3,4,1]=>[5,1,2,1,1,2]
[1,1,2,3,1,1,1,1,1]=>[3,2,1,6]
[1,1,2,1,1,3,1,1,1]=>[3,4,1,4]
[1,1,2,1,1,1,1,3,1]=>[3,6,1,2]
[1,1,3,3,1,2,1]=>[3,1,2,1,3,2]
[1,1,3,1,1,4,1]=>[3,1,4,1,1,2]
[2,3,1,1,1,1,1,1,1]=>[1,2,1,8]
[2,2,1,2,1,1,1,1,1]=>[1,2,3,6]
[2,2,1,1,1,1,1,2,1]=>[1,2,7,2]
[2,2,1,1,2,3,1]=>[1,2,4,2,1,2]
[2,2,2,1,1,3,1]=>[1,2,2,4,1,2]
[2,1,1,3,1,1,1,1,1]=>[1,4,1,6]
[2,1,1,3,2,2,1]=>[1,4,1,2,2,2]
[2,1,1,2,2,3,1]=>[1,4,2,2,1,2]
[2,1,1,1,1,3,1,1,1]=>[1,6,1,4]
[2,1,1,1,1,2,1,2,1]=>[1,6,3,2]
[2,1,1,1,2,4,1]=>[1,5,2,1,1,2]
[2,1,2,2,1,3,1]=>[1,3,2,3,1,2]
[2,1,2,1,1,4,1]=>[1,3,4,1,1,2]
[2,1,3,5,1]=>[1,3,1,2,1,1,1,2]
[3,2,1,1,1,3,1]=>[1,1,2,5,1,2]
[3,1,1,1,1,4,1]=>[1,1,6,1,1,2]
[4,5,1,1,1]=>[1,1,1,2,1,1,1,4]
[4,4,1,2,1]=>[1,1,1,2,1,1,3,2]
[4,3,1,3,1]=>[1,1,1,2,1,3,1,2]
[4,2,1,4,1]=>[1,1,1,2,3,1,1,2]
[4,1,1,5,1]=>[1,1,1,4,1,1,1,2]
[2,1,2,2,3,2]=>[1,3,2,2,1,2,1]
[3,1,2,2,4]=>[1,1,3,2,2,1,1,1]
[2,1,2,3,4]=>[1,3,2,1,2,1,1,1]
[1,1,2,3,2,3]=>[3,2,1,2,2,1,1]
[1,1,2,4,4]=>[3,2,1,1,2,1,1,1]
[2,1,2,4,3]=>[1,3,2,1,1,2,1,1]
[3,1,2,4,2]=>[1,1,3,2,1,1,2,1]
[2,1,3,3,3]=>[1,3,1,2,1,2,1,1]
[1,1,3,4,3]=>[3,1,2,1,1,2,1,1]
[2,1,3,4,2]=>[1,3,1,2,1,1,2,1]
[1,1,3,2,3,2]=>[3,1,2,2,1,2,1]
[2,1,3,2,4]=>[1,3,1,2,2,1,1,1]
[2,1,3,2,2,2]=>[1,3,1,2,2,2,1]
[3,1,3,2,3]=>[1,1,3,1,2,2,1,1]
[1,1,3,3,4]=>[3,1,2,1,2,1,1,1]
[3,1,3,3,2]=>[1,1,3,1,2,1,2,1]
[4,1,3,4]=>[1,1,1,3,1,2,1,1,1]
[1,1,4,4,2]=>[3,1,1,2,1,1,2,1]
[2,1,4,3,2]=>[1,3,1,1,2,1,2,1]
[3,1,4,4]=>[1,1,3,1,1,2,1,1,1]
[1,1,4,2,4]=>[3,1,1,2,2,1,1,1]
[2,1,4,2,3]=>[1,3,1,1,2,2,1,1]
[3,1,4,2,2]=>[1,1,3,1,1,2,2,1]
[4,1,4,3]=>[1,1,1,3,1,1,2,1,1]
[2,1,5,4]=>[1,3,1,1,1,2,1,1,1]
[3,1,5,3]=>[1,1,3,1,1,1,2,1,1]
[4,1,5,2]=>[1,1,1,3,1,1,1,2,1]
[5,1,6]=>[1,1,1,1,3,1,1,1,1,1]
[4,2,6]=>[1,1,1,2,2,1,1,1,1,1]
[3,2,2,5]=>[1,1,2,2,2,1,1,1,1]
[2,2,2,2,4]=>[1,2,2,2,2,1,1,1]
[1,2,2,2,2,3]=>[2,2,2,2,2,1,1]
[1,2,2,3,4]=>[2,2,2,1,2,1,1,1]
[2,2,3,5]=>[1,2,2,1,2,1,1,1,1]
[1,2,3,2,4]=>[2,2,1,2,2,1,1,1]
[1,2,4,5]=>[2,2,1,1,2,1,1,1,1]
[3,3,6]=>[1,1,2,1,2,1,1,1,1,1]
[2,3,2,5]=>[1,2,1,2,2,1,1,1,1]
[1,3,2,2,4]=>[2,1,2,2,2,1,1,1]
[1,3,3,5]=>[2,1,2,1,2,1,1,1,1]
[2,4,6]=>[1,2,1,1,2,1,1,1,1,1]
[1,4,2,5]=>[2,1,1,2,2,1,1,1,1]
[1,5,6]=>[2,1,1,1,2,1,1,1,1,1]
[1,1,1,1,1,1,1,3,2]=>[8,1,2,1]
[1,1,1,1,1,2,1,2,2]=>[6,3,2,1]
[1,1,1,1,1,3,2,1,1]=>[6,1,2,3]
[1,1,1,1,1,3,1,1,2]=>[6,1,4,1]
[1,1,1,1,1,4,3]=>[6,1,1,2,1,1]
[1,1,1,2,2,3,2]=>[4,2,2,1,2,1]
[1,1,1,3,3,2,1]=>[4,1,2,1,2,2]
[1,1,1,3,2,2,2]=>[4,1,2,2,2,1]
[1,1,1,3,1,1,2,1,1]=>[4,1,4,3]
[1,1,1,3,1,1,1,1,2]=>[4,1,6,1]
[1,1,1,3,1,2,3]=>[4,1,3,2,1,1]
[1,1,1,4,2,1,2]=>[4,1,1,2,3,1]
[1,1,1,5,4]=>[4,1,1,1,2,1,1,1]
[1,2,2,1,1,3,2]=>[2,2,4,1,2,1]
[1,2,2,3,1,1,2]=>[2,2,2,1,4,1]
[1,2,1,1,2,3,2]=>[2,4,2,1,2,1]
[1,2,1,1,1,1,1,2,2]=>[2,7,2,1]
[1,2,1,1,1,3,3]=>[2,5,1,2,1,1]
[1,2,1,2,3,2,1]=>[2,3,2,1,2,2]
[1,2,1,2,1,1,1,1,2]=>[2,3,6,1]
[1,2,1,2,1,2,3]=>[2,3,3,2,1,1]
[1,2,1,3,3,1,1]=>[2,3,1,2,1,3]
[1,2,1,3,2,1,2]=>[2,3,1,2,3,1]
[1,2,1,3,1,1,3]=>[2,3,1,4,1,1]
[1,2,1,4,4]=>[2,3,1,1,2,1,1,1]
[1,3,2,1,1,1,1,1,1]=>[2,1,2,7]
[1,3,2,1,1,2,2]=>[2,1,2,4,2,1]
[1,3,2,2,1,1,2]=>[2,1,2,2,4,1]
[1,3,1,1,3,2,1]=>[2,1,4,1,2,2]
[1,3,1,1,2,2,2]=>[2,1,4,2,2,1]
[1,3,1,1,1,1,2,1,1]=>[2,1,6,3]
[1,3,1,1,1,2,3]=>[2,1,5,2,1,1]
[1,3,1,2,2,1,2]=>[2,1,3,2,3,1]
[1,3,1,3,4]=>[2,1,3,1,2,1,1,1]
[1,4,2,1,1,1,2]=>[2,1,1,2,5,1]
[1,4,1,1,2,1,2]=>[2,1,1,4,3,1]
[1,4,1,1,1,1,3]=>[2,1,1,6,1,1]
[1,4,1,2,4]=>[2,1,1,3,2,1,1,1]
[1,5,3,1,2]=>[2,1,1,1,2,1,3,1]
[1,5,1,1,4]=>[2,1,1,1,4,1,1,1]
[2,10]=>[1,2,1,1,1,1,1,1,1,1,1]
[2,4,1,1,1,1,2]=>[1,2,1,1,6,1]
[2,4,1,2,3]=>[1,2,1,1,3,2,1,1]
[1,1,2,2,1,3,2]=>[3,2,3,1,2,1]
[2,1,1,2,1,3,2]=>[1,4,3,1,2,1]
[3,3,1,3,2]=>[1,1,2,1,3,1,2,1]
[2,5,3,1,1]=>[1,2,1,1,1,2,1,3]
[1,2,4,2,1,2]=>[2,2,1,1,2,3,1]
[2,5,2,1,2]=>[1,2,1,1,1,2,3,1]
[2,5,1,1,3]=>[1,2,1,1,1,4,1,1]
[1,1,2,3,1,2,2]=>[3,2,1,3,2,1]
[2,1,1,3,1,2,2]=>[1,4,1,3,2,1]
[3,4,1,2,2]=>[1,1,2,1,1,3,2,1]
[2,2,1,3,1,1,2]=>[1,2,3,1,4,1]
[2,1,1,4,2,1,1]=>[1,4,1,1,2,3]
[1,1,2,4,1,1,2]=>[3,2,1,1,4,1]
[2,1,1,4,1,1,2]=>[1,4,1,1,4,1]
[3,5,1,1,2]=>[1,1,2,1,1,1,4,1]
[2,2,1,4,3]=>[1,2,3,1,1,2,1,1]
[2,1,1,5,3]=>[1,4,1,1,1,2,1,1]
[1,1,3,5,2]=>[3,1,2,1,1,1,2,1]
[2,1,2,5,2]=>[1,3,2,1,1,1,2,1]
[3,1,1,5,2]=>[1,1,4,1,1,1,2,1]
[7,1,1,2,1]=>[1,1,1,1,1,1,4,2]
[1,2,2,1,1,1,1,1,2]=>[2,2,7,1]
[5,7]=>[1,1,1,1,2,1,1,1,1,1,1]
[2,1,1,1,1,1,1,2,2]=>[1,8,2,1]
[2,1,1,1,1,2,2,1,1]=>[1,6,2,3]
[2,1,1,1,1,2,1,1,2]=>[1,6,4,1]
[2,1,1,1,1,3,3]=>[1,6,1,2,1,1]
[2,1,1,2,1,1,1,1,2]=>[1,4,6,1]
[2,1,1,2,1,2,3]=>[1,4,3,2,1,1]
[2,1,1,3,3,1,1]=>[1,4,1,2,1,3]
[2,1,1,3,2,1,2]=>[1,4,1,2,3,1]
[2,1,1,3,1,1,3]=>[1,4,1,4,1,1]
[2,1,1,4,4]=>[1,4,1,1,2,1,1,1]
[2,2,2,1,1,1,1,1,1]=>[1,2,2,7]
[2,2,2,2,1,1,2]=>[1,2,2,2,4,1]
[2,2,1,1,1,1,2,1,1]=>[1,2,6,3]
[2,2,1,1,1,1,1,1,2]=>[1,2,8,1]
[2,2,1,1,1,2,3]=>[1,2,5,2,1,1]
[2,2,1,2,1,1,3]=>[1,2,3,4,1,1]
[2,2,1,3,4]=>[1,2,3,1,2,1,1,1]
[2,3,2,1,1,1,2]=>[1,2,1,2,5,1]
[2,3,1,1,2,1,2]=>[1,2,1,4,3,1]
[2,3,1,1,1,1,3]=>[1,2,1,6,1,1]
[2,3,1,2,4]=>[1,2,1,3,2,1,1,1]
[2,4,4,1,1]=>[1,2,1,1,2,1,1,3]
[2,4,3,1,2]=>[1,2,1,1,2,1,3,1]
[2,4,2,1,3]=>[1,2,1,1,2,3,1,1]
[2,4,1,1,4]=>[1,2,1,1,4,1,1,1]
[1,1,2,1,1,1,1,1,1,1,1]=>[3,9]
[1,1,2,1,1,1,1,2,2]=>[3,6,2,1]
[1,1,2,1,1,3,3]=>[3,4,1,2,1,1]
[1,1,2,2,1,1,1,1,2]=>[3,2,6,1]
[1,1,2,2,1,2,3]=>[3,2,3,2,1,1]
[1,1,2,3,3,1,1]=>[3,2,1,2,1,3]
[1,1,2,3,2,1,2]=>[3,2,1,2,3,1]
[1,1,2,3,1,1,3]=>[3,2,1,4,1,1]
[1,1,1,1,2,1,1,2,2]=>[5,4,2,1]
[1,1,1,1,2,2,2,1,1]=>[5,2,2,3]
[1,1,1,1,2,2,1,1,2]=>[5,2,4,1]
[1,1,1,1,2,3,3]=>[5,2,1,2,1,1]
[1,1,1,1,1,1,2,1,1,1,1]=>[7,5]
[1,1,1,1,1,1,2,2,2]=>[7,2,2,1]
[1,1,1,1,1,1,1,1,2,1,1]=>[9,3]
[1,1,1,1,1,1,1,2,3]=>[8,2,1,1]
[1,1,1,1,1,2,3,1,1]=>[6,2,1,3]
[1,1,1,1,1,2,2,1,2]=>[6,2,3,1]
[1,1,1,1,1,2,1,1,3]=>[6,4,1,1]
[1,1,1,1,1,3,4]=>[6,1,2,1,1,1]
[1,1,1,2,3,1,1,1,1]=>[4,2,1,5]
[1,1,1,2,3,2,2]=>[4,2,1,2,2,1]
[1,1,1,2,2,2,3]=>[4,2,2,2,1,1]
[1,1,1,2,1,1,3,1,1]=>[4,4,1,3]
[1,1,1,2,1,1,1,1,3]=>[4,6,1,1]
[1,1,1,2,1,2,4]=>[4,3,2,1,1,1]
[1,1,1,3,4,1,1]=>[4,1,2,1,1,3]
[1,1,1,3,3,1,2]=>[4,1,2,1,3,1]
[1,1,1,3,2,1,3]=>[4,1,2,3,1,1]
[1,1,1,3,1,1,4]=>[4,1,4,1,1,1]
[1,1,1,4,5]=>[4,1,1,2,1,1,1,1]
[1,2,3,1,1,1,1,1,1]=>[2,2,1,7]
[1,2,3,1,1,2,2]=>[2,2,1,4,2,1]
[1,2,3,2,1,1,2]=>[2,2,1,2,4,1]
[1,2,2,1,1,2,3]=>[2,2,4,2,1,1]
[1,2,2,2,1,1,3]=>[2,2,2,4,1,1]
[1,2,1,1,3,1,1,1,1]=>[2,4,1,5]
[1,2,1,1,3,2,2]=>[2,4,1,2,2,1]
[1,2,1,1,2,2,3]=>[2,4,2,2,1,1]
[1,2,1,1,1,1,3,1,1]=>[2,6,1,3]
[1,2,1,1,1,1,2,1,2]=>[2,6,3,1]
[1,2,1,1,1,1,1,1,3]=>[2,8,1,1]
[1,2,1,1,1,2,4]=>[2,5,2,1,1,1]
[1,2,1,2,4,1,1]=>[2,3,2,1,1,3]
[1,2,1,2,3,1,2]=>[2,3,2,1,3,1]
[1,2,1,2,2,1,3]=>[2,3,2,3,1,1]
[1,2,1,2,1,1,4]=>[2,3,4,1,1,1]
[1,2,1,3,5]=>[2,3,1,2,1,1,1,1]
[1,3,3,1,1,1,2]=>[2,1,2,1,5,1]
[1,3,2,1,2,1,2]=>[2,1,2,3,3,1]
[1,3,2,1,1,1,3]=>[2,1,2,5,1,1]
[1,3,1,1,4,1,1]=>[2,1,4,1,1,3]
[1,3,1,1,3,1,2]=>[2,1,4,1,3,1]
[1,3,1,1,2,1,3]=>[2,1,4,3,1,1]
[1,3,1,1,1,1,4]=>[2,1,6,1,1,1]
[1,3,1,2,5]=>[2,1,3,2,1,1,1,1]
[1,4,5,1,1]=>[2,1,1,2,1,1,1,3]
[1,4,4,1,2]=>[2,1,1,2,1,1,3,1]
[1,4,3,1,3]=>[2,1,1,2,1,3,1,1]
[1,4,2,1,4]=>[2,1,1,2,3,1,1,1]
[1,4,1,1,5]=>[2,1,1,4,1,1,1,1]
[2,2,2,6]=>[1,2,2,2,1,1,1,1,1]
[2,2,6,2]=>[1,2,2,1,1,1,1,2,1]
[2,2,8]=>[1,2,2,1,1,1,1,1,1,1]
[2,3,7]=>[1,2,1,2,1,1,1,1,1,1]
[2,8,2]=>[1,2,1,1,1,1,1,1,2,1]
[2,7,3]=>[1,2,1,1,1,1,1,2,1,1]
[4,8]=>[1,1,1,2,1,1,1,1,1,1,1]
[3,7,2]=>[1,1,2,1,1,1,1,1,2,1]
[3,9]=>[1,1,2,1,1,1,1,1,1,1,1]
[8,2,2]=>[1,1,1,1,1,1,1,2,2,1]
[8,4]=>[1,1,1,1,1,1,1,2,1,1,1]
[7,3,2]=>[1,1,1,1,1,1,2,1,2,1]
[9,3]=>[1,1,1,1,1,1,1,1,2,1,1]
[1,3,3,1,3,1]=>[2,1,2,1,3,1,2]
[2,1,9]=>[1,3,1,1,1,1,1,1,1,1]
[2,1,7,1,1]=>[1,3,1,1,1,1,1,3]
[2,1,6,1,1,1]=>[1,3,1,1,1,1,4]
[2,1,4,1,1,1,1,1]=>[1,3,1,1,6]
[2,1,3,1,1,1,1,1,1]=>[1,3,1,7]
[2,1,2,1,1,1,1,1,1,1]=>[1,3,8]
[2,1,2,2,1,1,3]=>[1,3,2,4,1,1]
[1,2,1,2,1,1,1,1,1,1]=>[2,3,7]
[1,2,1,1,1,1,1,2,1,1]=>[2,7,3]
[1,1,2,1,1,1,1,1,2,1]=>[3,7,2]
[1,1,1,1,1,2,1,2,1,1]=>[6,3,3]
[1,1,1,1,1,1,2,1,2,1]=>[7,3,2]
[1,2,5,3,1]=>[2,2,1,1,1,2,1,2]
[2,2,2,5,1]=>[1,2,2,2,1,1,1,2]
[1,2,3,5,1]=>[2,2,1,2,1,1,1,2]
[2,3,3,2,1,1]=>[1,2,1,2,1,2,3]
[2,3,2,3,1,1]=>[1,2,1,2,2,1,3]
[3,4,3,1,1]=>[1,1,2,1,1,2,1,3]
[3,2,3,2,1,1]=>[1,1,2,2,1,2,3]
[4,2,4,1,1]=>[1,1,1,2,2,1,1,3]
[3,3,3,1,2]=>[1,1,2,1,2,1,3,1]
[4,3,2,1,2]=>[1,1,1,2,1,2,3,1]
[4,2,3,1,2]=>[1,1,1,2,2,1,3,1]
[2,3,2,2,1,2]=>[1,2,1,2,2,3,1]
[2,2,2,3,1,2]=>[1,2,2,2,1,3,1]
[2,3,4,1,2]=>[1,2,1,2,1,1,3,1]
[3,4,2,1,2]=>[1,1,2,1,1,2,3,1]
[3,2,4,1,2]=>[1,1,2,2,1,1,3,1]
[4,5,1,2]=>[1,1,1,2,1,1,1,3,1]
[4,2,2,1,3]=>[1,1,1,2,2,3,1,1]
[3,2,3,1,3]=>[1,1,2,2,1,3,1,1]
[4,4,1,3]=>[1,1,1,2,1,1,3,1,1]
[2,3,3,1,3]=>[1,2,1,2,1,3,1,1]
[2,2,4,1,3]=>[1,2,2,1,1,3,1,1]
[3,5,1,3]=>[1,1,2,1,1,1,3,1,1]
[4,3,1,4]=>[1,1,1,2,1,3,1,1,1]
[3,4,1,4]=>[1,1,2,1,1,3,1,1,1]
[2,5,1,4]=>[1,2,1,1,1,3,1,1,1]
[6,1,5]=>[1,1,1,1,1,3,1,1,1,1]
[9,1,2]=>[1,1,1,1,1,1,1,1,3,1]
[1,1,1,1,2,1,2,1,2]=>[5,3,3,1]
[1,1,1,1,1,2,1,1,1,2]=>[6,5,1]
[2,2,1,1,1,2,1,2]=>[1,2,5,3,1]
[2,2,1,2,1,1,1,2]=>[1,2,3,5,1]
[2,1,1,1,1,3,2,1]=>[1,6,1,2,2]
[2,1,1,3,2,1,1,1]=>[1,4,1,2,4]
[2,1,1,3,1,1,2,1]=>[1,4,1,4,2]
[2,1,1,4,3,1]=>[1,4,1,1,2,1,2]
[3,1,1,4,2,1]=>[1,1,4,1,1,2,2]
[2,2,1,3,3,1]=>[1,2,3,1,2,1,2]
[3,2,1,3,2,1]=>[1,1,2,3,1,2,2]
[2,3,2,1,1,1,1,1]=>[1,2,1,2,6]
[2,3,1,1,2,1,1,1]=>[1,2,1,4,4]
[2,3,1,1,1,1,2,1]=>[1,2,1,6,2]
[2,3,1,2,3,1]=>[1,2,1,3,2,1,2]
[3,3,1,2,2,1]=>[1,1,2,1,3,2,2]
[2,4,3,1,1,1]=>[1,2,1,1,2,1,4]
[2,4,2,1,2,1]=>[1,2,1,1,2,3,2]
[3,4,2,1,1,1]=>[1,1,2,1,1,2,4]
[2,4,1,1,3,1]=>[1,2,1,1,4,1,2]
[3,4,1,1,2,1]=>[1,1,2,1,1,4,2]
[2,1,1,2,3,1,2]=>[1,4,2,1,3,1]
[3,2,1,1,1,2,2]=>[1,1,2,5,2,1]
[1,1,3,2,1,2,2]=>[3,1,2,3,2,1]
[3,1,1,2,1,2,2]=>[1,1,4,3,2,1]
[2,1,1,1,2,3,2]=>[1,5,2,1,2,1]
[1,1,3,3,2,1,1]=>[3,1,2,1,2,3]
[1,1,3,2,1,1,1,1,1]=>[3,1,2,6]
[3,1,1,2,1,1,1,1,1]=>[1,1,4,6]
[1,1,1,1,3,2,1,1,1]=>[5,1,2,4]
[1,1,3,1,1,2,1,1,1]=>[3,1,4,4]
[3,1,1,1,1,2,1,1,1]=>[1,1,6,4]
[1,1,4,3,1,1,1]=>[3,1,1,2,1,4]
[1,1,2,2,3,2,1]=>[3,2,2,1,2,2]
[2,1,1,2,3,2,1]=>[1,4,2,1,2,2]
[1,1,3,2,2,2,1]=>[3,1,2,2,2,2]
[1,1,4,2,1,2,1]=>[3,1,1,2,3,2]
[5,3,1,2,1]=>[1,1,1,1,2,1,3,2]
[1,1,1,1,4,3,1]=>[5,1,1,2,1,2]
[1,1,2,1,3,3,1]=>[3,3,1,2,1,2]
[1,1,3,1,2,3,1]=>[3,1,3,2,1,2]
[3,1,1,1,2,3,1]=>[1,1,5,2,1,2]
[1,1,4,1,1,3,1]=>[3,1,1,4,1,2]
[3,1,2,1,1,3,1]=>[1,1,3,4,1,2]
[5,2,1,3,1]=>[1,1,1,1,2,3,1,2]
[1,1,5,4,1]=>[3,1,1,1,2,1,1,2]
[3,1,3,4,1]=>[1,1,3,1,2,1,1,2]
[5,1,1,4,1]=>[1,1,1,1,4,1,1,2]
[1,2,1,1,7]=>[2,4,1,1,1,1,1,1]
[8,3,1]=>[1,1,1,1,1,1,1,2,1,2]
[4,1,2,1,2,2]=>[1,1,1,3,3,2,1]
[4,2,2,1,2,1]=>[1,1,1,2,2,3,2]
[4,1,2,2,2,1]=>[1,1,1,3,2,2,2]
[3,1,2,3,2,1]=>[1,1,3,2,1,2,2]
[7,1,4]=>[1,1,1,1,1,1,3,1,1,1]
[5,1,2,2,2]=>[1,1,1,1,3,2,2,1]
[5,1,1,2,3]=>[1,1,1,1,4,2,1,1]
[5,1,3,2,1]=>[1,1,1,1,3,1,2,2]
[3,1,8]=>[1,1,3,1,1,1,1,1,1,1]
[3,1,1,2,5]=>[1,1,4,2,1,1,1,1]
[3,3,1,2,3]=>[1,1,2,1,3,2,1,1]
[3,1,1,4,3]=>[1,1,4,1,1,2,1,1]
[3,1,1,1,2,1,3]=>[1,1,5,3,1,1]
[3,5,1,2,1]=>[1,1,2,1,1,1,3,2]
[3,1,5,2,1]=>[1,1,3,1,1,1,2,2]
[3,3,1,4,1]=>[1,1,2,1,3,1,1,2]
[3,1,1,6,1]=>[1,1,4,1,1,1,1,2]
[3,1,1,1,4,1,1]=>[1,1,5,1,1,3]
[1,1,2,6,2]=>[3,2,1,1,1,1,2,1]
[1,1,1,2,1,4,2]=>[4,3,1,1,2,1]
[1,1,6,2,2]=>[3,1,1,1,1,2,2,1]
[1,3,1,2,1,2,2]=>[2,1,3,3,2,1]
[1,1,1,4,1,2,2]=>[4,1,1,3,2,1]
[1,7,4]=>[2,1,1,1,1,1,2,1,1,1]
[1,1,2,2,6]=>[3,2,2,1,1,1,1,1]
[1,3,8]=>[2,1,2,1,1,1,1,1,1,1]
[1,1,10]=>[3,1,1,1,1,1,1,1,1,1]
[1,1,1,2,7]=>[4,2,1,1,1,1,1,1]
[1,1,3,2,5]=>[3,1,2,2,1,1,1,1]
[1,1,1,1,2,1,5]=>[5,3,1,1,1,1]
[1,5,1,2,3]=>[2,1,1,1,3,2,1,1]
[1,1,5,2,3]=>[3,1,1,1,2,2,1,1]
[1,3,1,4,3]=>[2,1,3,1,1,2,1,1]
[1,1,1,6,3]=>[4,1,1,1,1,2,1,1]
[1,1,3,1,2,1,3]=>[3,1,3,3,1,1]
[1,1,1,1,4,1,3]=>[5,1,1,3,1,1]
[1,7,1,2,1]=>[2,1,1,1,1,1,3,2]
[1,1,2,4,1,2,1]=>[3,2,1,1,3,2]
[1,1,7,2,1]=>[3,1,1,1,1,1,2,2]
[1,1,1,2,4,2,1]=>[4,2,1,1,2,2]
[1,1,1,4,2,2,1]=>[4,1,1,2,2,2]
[1,5,1,4,1]=>[2,1,1,1,3,1,1,2]
[1,1,2,2,1,4,1]=>[3,2,3,1,1,2]
[1,1,1,2,2,4,1]=>[4,2,2,1,1,2]
[1,3,1,6,1]=>[2,1,3,1,1,1,1,2]
[1,1,3,6,1]=>[3,1,2,1,1,1,1,2]
[1,1,1,8,1]=>[4,1,1,1,1,1,1,2]
[1,1,1,1,2,5,1]=>[5,2,1,1,1,2]
[1,3,1,1,2,3,1]=>[2,1,4,2,1,2]
[1,1,1,3,2,3,1]=>[4,1,2,2,1,2]
[1,1,1,1,1,2,1,3,1]=>[6,3,1,2]
[1,1,5,1,2,1,1]=>[3,1,1,1,3,3]
[1,1,1,5,2,1,1]=>[4,1,1,1,2,3]
[1,1,3,1,4,1,1]=>[3,1,3,1,1,3]
[1,1,1,1,6,1,1]=>[5,1,1,1,1,3]
[1,3,1,1,1,2,1,1,1]=>[2,1,5,4]
[1,1,1,3,1,2,1,1,1]=>[4,1,3,4]
[1,1,1,1,1,4,1,1,1]=>[6,1,1,4]
[4,1,7]=>[1,1,1,3,1,1,1,1,1,1]
[2,2,2,1,5]=>[1,2,2,3,1,1,1,1]
[3,2,1,1,5]=>[1,1,2,4,1,1,1,1]
[1,2,3,1,5]=>[2,2,1,3,1,1,1,1]
[1,1,2,1,1,1,5]=>[3,5,1,1,1,1]
[8,1,3]=>[1,1,1,1,1,1,1,3,1,1]
[5,2,1,1,3]=>[1,1,1,1,2,4,1,1]
[3,2,1,3,3]=>[1,1,2,3,1,2,1,1]
[3,4,1,1,3]=>[1,1,2,1,1,4,1,1]
[3,1,2,1,1,1,3]=>[1,1,3,5,1,1]
[1,2,1,5,3]=>[2,3,1,1,1,2,1,1]
[1,2,5,1,3]=>[2,2,1,1,1,3,1,1]
[1,4,1,3,3]=>[2,1,1,3,1,2,1,1]
[1,6,1,1,3]=>[2,1,1,1,1,4,1,1]
[1,1,2,1,3,1,3]=>[3,3,1,3,1,1]
[1,1,4,1,1,1,3]=>[3,1,1,5,1,1]
[2,6,2,1,1]=>[1,2,1,1,1,1,2,3]
[2,2,6,1,1]=>[1,2,2,1,1,1,1,3]
[2,2,1,2,1,3,1]=>[1,2,3,3,1,2]
[4,7,1]=>[1,1,1,2,1,1,1,1,1,2]
[6,2,2,1,1]=>[1,1,1,1,1,2,2,3]
[10,1,1]=>[1,1,1,1,1,1,1,1,1,3]
[7,2,1,1,1]=>[1,1,1,1,1,1,2,4]
[5,2,3,1,1]=>[1,1,1,1,2,2,1,3]
[3,2,1,5,1]=>[1,1,2,3,1,1,1,2]
[3,2,5,1,1]=>[1,1,2,2,1,1,1,3]
[3,4,1,3,1]=>[1,1,2,1,1,3,1,2]
[3,6,1,1,1]=>[1,1,2,1,1,1,1,4]
[1,2,1,7,1]=>[2,3,1,1,1,1,1,2]
[1,2,1,4,2,1,1]=>[2,3,1,1,2,3]
[1,2,1,2,2,3,1]=>[2,3,2,2,1,2]
[1,2,7,1,1]=>[2,2,1,1,1,1,1,3]
[1,2,2,2,1,3,1]=>[2,2,2,3,1,2]
[1,4,1,5,1]=>[2,1,1,3,1,1,1,2]
[1,6,1,3,1]=>[2,1,1,1,1,3,1,2]
[1,6,3,1,1]=>[2,1,1,1,1,2,1,3]
[1,8,1,1,1]=>[2,1,1,1,1,1,1,4]
[1,3,2,1,1,3,1]=>[2,1,2,4,1,2]
[1,3,1,2,1,1,1,1,1]=>[2,1,3,6]
[1,1,2,1,1,5,1]=>[3,4,1,1,1,2]
[1,1,2,1,5,1,1]=>[3,3,1,1,1,3]
[1,1,2,3,1,3,1]=>[3,2,1,3,1,2]
[1,1,2,5,1,1,1]=>[3,2,1,1,1,4]
[1,1,4,1,3,1,1]=>[3,1,1,3,1,3]
[1,1,6,1,1,1,1]=>[3,1,1,1,1,5]
[1,1,1,2,1,1,1,3,1]=>[4,5,1,2]
[1,1,1,2,1,3,1,1,1]=>[4,3,1,4]
[1,1,1,4,1,1,1,1,1]=>[4,1,1,6]
[4,2,1,2,2,1]=>[1,1,1,2,3,2,2]
[3,2,2,1,2,2]=>[1,1,2,2,3,2,1]
[1,1,1,2,3,4]=>[4,2,1,2,1,1,1]
[3,1,2,2,2,2]=>[1,1,3,2,2,2,1]
[2,3,1,2,2,2]=>[1,2,1,3,2,2,1]
[4,1,1,2,2,2]=>[1,1,1,4,2,2,1]
[4,2,1,1,2,2]=>[1,1,1,2,4,2,1]
[4,1,2,2,1,2]=>[1,1,1,3,2,3,1]
[3,2,1,1,2,1,2]=>[1,1,2,4,3,1]
[3,1,2,1,2,1,2]=>[1,1,3,3,3,1]
[3,1,2,1,1,2,2]=>[1,1,3,4,2,1]
[3,1,1,2,2,1,2]=>[1,1,4,2,3,1]
[3,1,1,1,2,2,2]=>[1,1,5,2,2,1]
[2,3,1,1,1,2,2]=>[1,2,1,5,2,1]
[2,1,3,1,2,1,2]=>[1,3,1,3,3,1]
[2,1,3,1,1,2,2]=>[1,3,1,4,2,1]
[2,1,1,1,2,2,3]=>[1,5,2,2,1,1]
[2,1,1,1,3,2,2]=>[1,5,1,2,2,1]
[1,1,1,1,2,2,4]=>[5,2,2,1,1,1]
[1,1,1,1,2,3,2,1]=>[5,2,1,2,2]
[1,1,1,1,5,1,2]=>[5,1,1,1,3,1]
[1,1,1,1,1,1,1,2,1,2]=>[8,3,1]
[1,1,1,1,1,1,3,1,2]=>[7,1,3,1]
[1,1,1,1,1,4,1,2]=>[6,1,1,3,1]
[1,1,1,6,1,2]=>[4,1,1,1,1,3,1]
[1,1,7,1,2]=>[3,1,1,1,1,1,3,1]
[1,2,2,2,2,1,3]=>[2,2,2,2,3,1,1]
[1,2,2,2,1,1,4]=>[2,2,2,4,1,1,1]
[1,2,2,1,2,1,4]=>[2,2,3,3,1,1,1]
[1,2,2,1,1,1,5]=>[2,2,5,1,1,1,1]
[1,2,1,3,1,1,4]=>[2,3,1,4,1,1,1]
[1,2,1,2,2,1,4]=>[2,3,2,3,1,1,1]
[1,2,1,2,1,1,5]=>[2,3,4,1,1,1,1]
[1,2,1,1,2,1,5]=>[2,4,3,1,1,1,1]
[1,2,1,1,1,1,6]=>[2,6,1,1,1,1,1]
[1,1,3,2,1,1,4]=>[3,1,2,4,1,1,1]
[1,1,3,1,2,1,4]=>[3,1,3,3,1,1,1]
[1,1,3,1,1,1,5]=>[3,1,5,1,1,1,1]
[1,1,2,3,1,1,4]=>[3,2,1,4,1,1,1]
[1,1,2,2,2,1,4]=>[3,2,2,3,1,1,1]
[1,1,2,2,1,1,5]=>[3,2,4,1,1,1,1]
[1,1,2,1,2,1,5]=>[3,3,3,1,1,1,1]
[1,1,2,1,1,1,6]=>[3,5,1,1,1,1,1]
[1,1,1,3,1,1,5]=>[4,1,4,1,1,1,1]
[1,1,1,2,3,3,2]=>[4,2,1,2,1,2,1]
[1,1,1,2,2,2,4]=>[4,2,2,2,1,1,1]
[1,1,1,2,2,1,5]=>[4,2,3,1,1,1,1]
[1,1,1,2,1,1,6]=>[4,4,1,1,1,1,1]
[1,1,1,1,2,3,4]=>[5,2,1,2,1,1,1]
[1,1,1,1,2,1,6]=>[5,3,1,1,1,1,1]
[1,1,1,1,1,1,7]=>[7,1,1,1,1,1,1]
[3,1,2,2,2,2,1]=>[1,1,3,2,2,2,2]
[4,1,1,2,2,2,1]=>[1,1,1,4,2,2,2]
[4,1,2,1,2,2,1]=>[1,1,1,3,3,2,2]
[5,1,1,1,2,2,1]=>[1,1,1,1,5,2,2]
[4,1,1,3,1,2,1]=>[1,1,1,4,1,3,2]
[4,1,2,2,1,2,1]=>[1,1,1,3,2,3,2]
[5,1,1,2,1,2,1]=>[1,1,1,1,4,3,2]
[5,1,2,1,1,2,1]=>[1,1,1,1,3,4,2]
[6,1,1,1,1,2,1]=>[1,1,1,1,1,6,2]
[4,1,1,2,3,1,1]=>[1,1,1,4,2,1,3]
[4,1,2,1,3,1,1]=>[1,1,1,3,3,1,3]
[5,1,1,1,3,1,1]=>[1,1,1,1,5,1,3]
[3,1,2,3,2,1,1]=>[1,1,3,2,1,2,3]
[4,1,1,3,2,1,1]=>[1,1,1,4,1,2,3]
[4,1,2,2,2,1,1]=>[1,1,1,3,2,2,3]
[5,1,1,2,2,1,1]=>[1,1,1,1,4,2,3]
[5,1,2,1,2,1,1]=>[1,1,1,1,3,3,3]
[6,1,1,1,2,1,1]=>[1,1,1,1,1,5,3]
[5,1,1,3,1,1,1]=>[1,1,1,1,4,1,4]
[5,1,2,2,1,1,1]=>[1,1,1,1,3,2,4]
[6,1,1,2,1,1,1]=>[1,1,1,1,1,4,4]
[6,1,2,1,1,1,1]=>[1,1,1,1,1,3,5]
[7,1,1,1,1,1,1]=>[1,1,1,1,1,1,7]
[4,3,3,2,1]=>[1,1,1,2,1,2,1,2,2]
[4,4,2,2,1]=>[1,1,1,2,1,1,2,2,2]
[5,3,2,2,1]=>[1,1,1,1,2,1,2,2,2]
[4,4,3,1,1]=>[1,1,1,2,1,1,2,1,3]
[5,3,3,1,1]=>[1,1,1,1,2,1,2,1,3]
[5,4,2,1,1]=>[1,1,1,1,2,1,1,2,3]
[4,4,3,2]=>[1,1,1,2,1,1,2,1,2,1]
[5,3,3,2]=>[1,1,1,1,2,1,2,1,2,1]
[5,4,2,2]=>[1,1,1,1,2,1,1,2,2,1]
[5,4,3,1]=>[1,1,1,1,2,1,1,2,1,2]
[2,2,1,2,3,2,1]=>[1,2,3,2,1,2,2]
[2,2,2,2,2,1,2]=>[1,2,2,2,2,3,1]
[2,2,2,2,1,1,3]=>[1,2,2,2,4,1,1]
[2,2,2,1,2,1,3]=>[1,2,2,3,3,1,1]
[2,2,2,1,1,1,4]=>[1,2,2,5,1,1,1]
[2,2,1,3,1,1,3]=>[1,2,3,1,4,1,1]
[2,2,1,2,2,1,3]=>[1,2,3,2,3,1,1]
[2,2,1,2,1,1,4]=>[1,2,3,4,1,1,1]
[2,2,1,1,2,1,4]=>[1,2,4,3,1,1,1]
[2,2,1,1,1,1,5]=>[1,2,6,1,1,1,1]
[2,1,3,2,1,1,3]=>[1,3,1,2,4,1,1]
[2,1,3,1,2,1,3]=>[1,3,1,3,3,1,1]
[2,1,3,1,1,1,4]=>[1,3,1,5,1,1,1]
[2,1,2,3,1,1,3]=>[1,3,2,1,4,1,1]
[2,1,2,2,2,2,2]=>[1,3,2,2,2,2,1]
[2,1,2,2,2,1,3]=>[1,3,2,2,3,1,1]
[2,1,2,2,1,3,2]=>[1,3,2,3,1,2,1]
[2,1,2,2,1,2,3]=>[1,3,2,3,2,1,1]
[2,1,2,2,1,1,4]=>[1,3,2,4,1,1,1]
[2,1,2,1,3,2,2]=>[1,3,3,1,2,2,1]
[2,1,2,1,3,1,3]=>[1,3,3,1,3,1,1]
[2,1,2,1,2,3,2]=>[1,3,3,2,1,2,1]
[2,1,2,1,2,2,3]=>[1,3,3,2,2,1,1]
[2,1,2,1,2,1,4]=>[1,3,3,3,1,1,1]
[2,1,2,1,1,4,2]=>[1,3,4,1,1,2,1]
[2,1,2,1,1,3,3]=>[1,3,4,1,2,1,1]
[2,1,2,1,1,2,4]=>[1,3,4,2,1,1,1]
[2,1,2,1,1,1,5]=>[1,3,5,1,1,1,1]
[2,1,1,3,2,2,2]=>[1,4,1,2,2,2,1]
[2,1,1,3,2,1,3]=>[1,4,1,2,3,1,1]
[2,1,1,3,1,3,2]=>[1,4,1,3,1,2,1]
[2,1,1,3,1,2,3]=>[1,4,1,3,2,1,1]
[2,1,1,3,1,1,4]=>[1,4,1,4,1,1,1]
[2,1,1,2,3,2,2]=>[1,4,2,1,2,2,1]
[2,1,1,2,3,1,3]=>[1,4,2,1,3,1,1]
[2,1,1,2,2,3,2]=>[1,4,2,2,1,2,1]
[2,1,1,2,2,2,3]=>[1,4,2,2,2,1,1]
[2,1,1,2,2,1,4]=>[1,4,2,3,1,1,1]
[2,1,1,2,1,4,2]=>[1,4,3,1,1,2,1]
[2,1,1,2,1,3,3]=>[1,4,3,1,2,1,1]
[2,1,1,2,1,2,4]=>[1,4,3,2,1,1,1]
[2,1,1,2,1,1,5]=>[1,4,4,1,1,1,1]
[2,1,1,1,4,2,2]=>[1,5,1,1,2,2,1]
[2,1,1,1,4,1,3]=>[1,5,1,1,3,1,1]
[2,1,1,1,3,3,2]=>[1,5,1,2,1,2,1]
[2,1,1,1,3,2,3]=>[1,5,1,2,2,1,1]
[2,1,1,1,3,1,4]=>[1,5,1,3,1,1,1]
[2,1,1,1,2,4,2]=>[1,5,2,1,1,2,1]
[2,1,1,1,2,3,3]=>[1,5,2,1,2,1,1]
[2,1,1,1,2,2,4]=>[1,5,2,2,1,1,1]
[2,1,1,1,2,1,5]=>[1,5,3,1,1,1,1]
[2,1,1,1,1,5,2]=>[1,6,1,1,1,2,1]
[2,1,1,1,1,4,3]=>[1,6,1,1,2,1,1]
[2,1,1,1,1,3,4]=>[1,6,1,2,1,1,1]
[2,1,1,1,1,2,5]=>[1,6,2,1,1,1,1]
[2,1,1,1,1,1,6]=>[1,7,1,1,1,1,1]
[3,1,1,1,4,1,2]=>[1,1,5,1,1,3,1]
[3,1,1,1,3,2,2]=>[1,1,5,1,2,2,1]
[3,1,1,1,3,1,3]=>[1,1,5,1,3,1,1]
[4,1,1,3,1,1,2]=>[1,1,1,4,1,4,1]
[3,2,1,2,2,1,2]=>[1,1,2,3,2,3,1]
[3,1,1,1,2,3,2]=>[1,1,5,2,1,2,1]
[3,1,1,1,2,2,3]=>[1,1,5,2,2,1,1]
[4,1,1,2,2,1,2]=>[1,1,1,4,2,3,1]
[1,3,1,1,2,1,4]=>[2,1,4,3,1,1,1]
[3,1,1,1,2,1,4]=>[1,1,5,3,1,1,1]
[4,1,1,2,1,2,2]=>[1,1,1,4,3,2,1]
[1,4,1,2,1,1,3]=>[2,1,1,3,4,1,1]
[2,3,1,2,1,1,3]=>[1,2,1,3,4,1,1]
[3,2,1,2,1,1,3]=>[1,1,2,3,4,1,1]
[4,1,1,2,1,1,3]=>[1,1,1,4,4,1,1]
[5,1,2,1,1,1,2]=>[1,1,1,1,3,5,1]
[3,1,2,1,3,1,2]=>[1,1,3,3,1,3,1]
[3,1,2,1,2,2,2]=>[1,1,3,3,2,2,1]
[1,3,2,1,2,1,3]=>[2,1,2,3,3,1,1]
[3,1,2,1,2,1,3]=>[1,1,3,3,3,1,1]
[4,2,1,2,1,1,2]=>[1,1,1,2,3,4,1]
[3,1,1,1,1,4,2]=>[1,1,6,1,1,2,1]
[3,1,1,1,1,3,3]=>[1,1,6,1,2,1,1]
[4,1,1,1,3,1,2]=>[1,1,1,5,1,3,1]
[3,1,1,1,1,2,4]=>[1,1,6,2,1,1,1]
[4,1,1,1,2,2,2]=>[1,1,1,5,2,2,1]
[1,4,1,1,2,1,3]=>[2,1,1,4,3,1,1]
[2,3,1,1,2,1,3]=>[1,2,1,4,3,1,1]
[3,2,1,1,2,1,3]=>[1,1,2,4,3,1,1]
[4,1,1,1,2,1,3]=>[1,1,1,5,3,1,1]
[5,1,1,2,1,1,2]=>[1,1,1,1,4,4,1]
[3,3,1,1,2,1,2]=>[1,1,2,1,4,3,1]
[3,1,2,1,1,3,2]=>[1,1,3,4,1,2,1]
[3,1,2,1,1,2,3]=>[1,1,3,4,2,1,1]
[4,2,1,1,2,1,2]=>[1,1,1,2,4,3,1]
[1,3,1,1,1,1,5]=>[2,1,6,1,1,1,1]
[3,1,1,1,1,1,5]=>[1,1,7,1,1,1,1]
[4,1,1,1,1,3,2]=>[1,1,1,6,1,2,1]
[4,1,1,1,1,2,3]=>[1,1,1,6,2,1,1]
[5,1,1,1,2,1,2]=>[1,1,1,1,5,3,1]
[1,1,4,1,1,1,4]=>[3,1,1,5,1,1,1]
[1,2,3,1,1,1,4]=>[2,2,1,5,1,1,1]
[1,3,2,1,1,1,4]=>[2,1,2,5,1,1,1]
[3,1,2,1,1,1,4]=>[1,1,3,5,1,1,1]
[1,4,1,1,1,1,4]=>[2,1,1,6,1,1,1]
[2,3,1,1,1,1,4]=>[1,2,1,6,1,1,1]
[3,2,1,1,1,1,4]=>[1,1,2,6,1,1,1]
[4,1,1,1,1,1,4]=>[1,1,1,7,1,1,1]
[5,1,1,1,1,2,2]=>[1,1,1,1,6,2,1]
[1,5,1,1,1,1,3]=>[2,1,1,1,6,1,1]
[2,4,1,1,1,1,3]=>[1,2,1,1,6,1,1]
[3,3,1,1,1,1,3]=>[1,1,2,1,6,1,1]
[4,2,1,1,1,1,3]=>[1,1,1,2,6,1,1]
[5,1,1,1,1,1,3]=>[1,1,1,1,7,1,1]
[6,1,1,1,1,1,2]=>[1,1,1,1,1,7,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1]=>[13]
[1,1,1,1,1,1,2,1,1,1,1,1]=>[7,6]
[1,1,1,1,1,1,3,1,1,1,1]=>[7,1,5]
[3,1,2,2,2,1,2]=>[1,1,3,2,2,3,1]
[3,1,2,2,1,3,1]=>[1,1,3,2,3,1,2]
[3,1,2,2,1,2,2]=>[1,1,3,2,3,2,1]
[3,1,2,2,1,1,3]=>[1,1,3,2,4,1,1]
[4,1,2,2,1,1,2]=>[1,1,1,3,2,4,1]
[3,1,2,1,3,2,1]=>[1,1,3,3,1,2,2]
[3,1,2,1,2,3,1]=>[1,1,3,3,2,1,2]
[4,1,2,1,2,1,2]=>[1,1,1,3,3,3,1]
[3,1,2,1,1,4,1]=>[1,1,3,4,1,1,2]
[4,1,2,1,1,3,1]=>[1,1,1,3,4,1,2]
[4,1,2,1,1,2,2]=>[1,1,1,3,4,2,1]
[4,1,2,1,1,1,3]=>[1,1,1,3,5,1,1]
[3,1,1,3,2,2,1]=>[1,1,4,1,2,2,2]
[3,1,1,3,2,1,2]=>[1,1,4,1,2,3,1]
[3,1,1,3,1,3,1]=>[1,1,4,1,3,1,2]
[3,1,1,3,1,2,2]=>[1,1,4,1,3,2,1]
[3,1,1,3,1,1,3]=>[1,1,4,1,4,1,1]
[3,1,1,2,3,2,1]=>[1,1,4,2,1,2,2]
[3,1,1,2,3,1,2]=>[1,1,4,2,1,3,1]
[3,1,1,2,2,3,1]=>[1,1,4,2,2,1,2]
[3,1,1,2,2,2,2]=>[1,1,4,2,2,2,1]
[3,1,1,2,2,1,3]=>[1,1,4,2,3,1,1]
[3,1,1,2,1,4,1]=>[1,1,4,3,1,1,2]
[3,1,1,2,1,3,2]=>[1,1,4,3,1,2,1]
[4,1,1,2,1,3,1]=>[1,1,1,4,3,1,2]
[3,1,1,2,1,2,3]=>[1,1,4,3,2,1,1]
[3,1,1,2,1,1,4]=>[1,1,4,4,1,1,1]
[3,1,1,1,4,2,1]=>[1,1,5,1,1,2,2]
[4,1,1,1,4,1,1]=>[1,1,1,5,1,1,3]
[3,1,1,1,3,3,1]=>[1,1,5,1,2,1,2]
[4,1,1,1,3,2,1]=>[1,1,1,5,1,2,2]
[3,1,1,1,2,4,1]=>[1,1,5,2,1,1,2]
[4,1,1,1,2,3,1]=>[1,1,1,5,2,1,2]
[3,1,1,1,1,5,1]=>[1,1,6,1,1,1,2]
[4,1,1,1,1,4,1]=>[1,1,1,6,1,1,2]
[5,1,1,1,1,3,1]=>[1,1,1,1,6,1,2]
[1,2,1,2,2,2,2,1]=>[2,3,2,2,2,2]
[1,2,1,2,3,2,1,1]=>[2,3,2,1,2,3]
[1,1,1,1,2,2,2,3]=>[5,2,2,2,1,1]
[1,1,1,2,2,2,3,1]=>[4,2,2,2,1,2]
[2,3,1,2,2,1,2]=>[1,2,1,3,2,3,1]
[2,2,3,1,2,1,2]=>[1,2,2,1,3,3,1]
[3,1,3,1,2,1,2]=>[1,1,3,1,3,3,1]
[2,3,2,1,2,1,2]=>[1,2,1,2,3,3,1]
[3,2,2,1,2,1,2]=>[1,1,2,2,3,3,1]
[2,4,1,1,2,1,2]=>[1,2,1,1,4,3,1]
[2,2,2,3,1,1,2]=>[1,2,2,2,1,4,1]
[3,1,2,3,1,1,2]=>[1,1,3,2,1,4,1]
[2,3,1,3,1,1,2]=>[1,2,1,3,1,4,1]
[3,2,1,3,1,1,2]=>[1,1,2,3,1,4,1]
[2,2,3,2,1,1,2]=>[1,2,2,1,2,4,1]
[3,1,3,2,1,1,2]=>[1,1,3,1,2,4,1]
[2,3,2,2,1,1,2]=>[1,2,1,2,2,4,1]
[3,2,2,2,1,1,2]=>[1,1,2,2,2,4,1]
[2,4,1,2,1,1,2]=>[1,2,1,1,3,4,1]
[3,3,1,2,1,1,2]=>[1,1,2,1,3,4,1]
[2,2,4,1,1,1,2]=>[1,2,2,1,1,5,1]
[3,1,4,1,1,1,2]=>[1,1,3,1,1,5,1]
[2,3,3,1,1,1,2]=>[1,2,1,2,1,5,1]
[3,2,3,1,1,1,2]=>[1,1,2,2,1,5,1]
[4,1,3,1,1,1,2]=>[1,1,1,3,1,5,1]
[2,4,2,1,1,1,2]=>[1,2,1,1,2,5,1]
[3,3,2,1,1,1,2]=>[1,1,2,1,2,5,1]
[4,2,2,1,1,1,2]=>[1,1,1,2,2,5,1]
[2,5,1,1,1,1,2]=>[1,2,1,1,1,6,1]
[3,4,1,1,1,1,2]=>[1,1,2,1,1,6,1]
[4,3,1,1,1,1,2]=>[1,1,1,2,1,6,1]
[5,2,1,1,1,1,2]=>[1,1,1,1,2,6,1]
[2,2,2,1,1,2,2,1]=>[1,2,2,4,2,2]
[2,2,2,1,2,2,1,1]=>[1,2,2,3,2,3]
[3,2,1,1,2,2,1,1]=>[1,1,2,4,2,3]
[1,2,2,1,1,2,2,1,1]=>[2,2,4,2,3]
[2,1,2,2,2,2,1,1]=>[1,3,2,2,2,3]
[1,2,2,3,1,1,3]=>[2,2,2,1,4,1,1]
[1,2,3,1,2,1,3]=>[2,2,1,3,3,1,1]
[1,2,3,2,1,1,3]=>[2,2,1,2,4,1,1]
[1,2,4,1,1,1,3]=>[2,2,1,1,5,1,1]
[1,3,1,2,2,1,3]=>[2,1,3,2,3,1,1]
[1,3,1,3,1,1,3]=>[2,1,3,1,4,1,1]
[1,3,2,2,1,1,3]=>[2,1,2,2,4,1,1]
[1,3,3,1,1,1,3]=>[2,1,2,1,5,1,1]
[1,4,2,1,1,1,3]=>[2,1,1,2,5,1,1]
[2,1,4,1,1,1,3]=>[1,3,1,1,5,1,1]
[2,2,3,1,1,1,3]=>[1,2,2,1,5,1,1]
[2,3,2,1,1,1,3]=>[1,2,1,2,5,1,1]
[3,1,3,1,1,1,3]=>[1,1,3,1,5,1,1]
[3,2,2,1,1,1,3]=>[1,1,2,2,5,1,1]
[1,3,1,2,1,1,4]=>[2,1,3,4,1,1,1]
[1,1,1,2,2,2,2,2]=>[4,2,2,2,2,1]
[1,1,1,1,2,3,2,2]=>[5,2,1,2,2,1]
[1,1,1,1,2,3,3,1]=>[5,2,1,2,1,2]
[1,1,1,1,2,2,2,2,1]=>[5,2,2,2,2]
[4,4,3,2,1]=>[1,1,1,2,1,1,2,1,2,2]
[5,3,3,2,1]=>[1,1,1,1,2,1,2,1,2,2]
[5,4,2,2,1]=>[1,1,1,1,2,1,1,2,2,2]
[5,4,3,1,1]=>[1,1,1,1,2,1,1,2,1,3]
[5,4,3,2]=>[1,1,1,1,2,1,1,2,1,2,1]
[2,3,4,5]=>[1,2,1,2,1,1,2,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[14]
[1,1,1,1,1,1,1,1,1,1,2,2]=>[11,2,1]
[1,1,1,1,1,1,1,1,2,1,1,2]=>[9,4,1]
[1,1,1,1,1,1,2,1,1,1,1,2]=>[7,6,1]
[1,1,1,1,2,1,1,1,1,1,1,2]=>[5,8,1]
[1,1,2,1,1,1,1,1,1,1,1,2]=>[3,10,1]
[2,1,1,1,1,1,1,1,1,1,1,2]=>[1,12,1]
[1,1,1,1,1,1,1,1,3,3]=>[9,1,2,1,1]
[1,1,1,1,1,1,3,2,1,2]=>[7,1,2,3,1]
[1,1,1,1,3,2,1,1,1,2]=>[5,1,2,5,1]
[1,1,3,2,1,1,1,1,1,2]=>[3,1,2,7,1]
[3,2,1,1,1,1,1,1,1,2]=>[1,1,2,9,1]
[1,1,1,1,1,1,3,1,1,3]=>[7,1,4,1,1]
[1,1,1,1,3,1,1,2,1,2]=>[5,1,4,3,1]
[1,1,1,1,1,1,4,4]=>[7,1,1,2,1,1,1]
[1,1,3,1,1,2,1,1,1,2]=>[3,1,4,5,1]
[1,1,1,1,4,3,1,2]=>[5,1,1,2,1,3,1]
[3,1,1,2,1,1,1,1,1,2]=>[1,1,4,7,1]
[1,1,4,3,1,1,1,2]=>[3,1,1,2,1,5,1]
[4,3,1,1,1,1,1,2]=>[1,1,1,2,1,7,1]
[1,1,1,1,3,1,1,1,1,3]=>[5,1,6,1,1]
[1,1,3,1,1,1,1,2,1,2]=>[3,1,6,3,1]
[1,1,1,1,3,1,2,4]=>[5,1,3,2,1,1,1]
[3,1,1,1,1,2,1,1,1,2]=>[1,1,6,5,1]
[1,1,3,1,2,3,1,2]=>[3,1,3,2,1,3,1]
[1,1,1,1,4,1,1,4]=>[5,1,1,4,1,1,1]
[3,1,2,3,1,1,1,2]=>[1,1,3,2,1,5,1]
[1,1,4,1,1,3,1,2]=>[3,1,1,4,1,3,1]
[4,1,1,3,1,1,1,2]=>[1,1,1,4,1,5,1]
[2,1,1,1,1,1,1,1,2,3]=>[1,9,2,1,1]
[2,1,1,1,1,1,2,2,1,2]=>[1,7,2,3,1]
[2,1,1,1,1,1,2,1,1,3]=>[1,7,4,1,1]
[2,1,1,1,1,1,3,4]=>[1,7,1,2,1,1,1]
[2,1,1,1,2,2,1,1,1,2]=>[1,5,2,5,1]
[2,1,1,1,2,2,2,3]=>[1,5,2,2,2,1,1]
[2,1,1,1,2,1,1,2,1,2]=>[1,5,4,3,1]
[2,1,1,1,2,1,1,1,1,3]=>[1,5,6,1,1]
[2,1,1,1,2,1,2,4]=>[1,5,3,2,1,1,1]
[2,1,1,1,3,3,1,2]=>[1,5,1,2,1,3,1]
[2,1,1,1,3,2,1,3]=>[1,5,1,2,3,1,1]
[2,1,1,1,3,1,1,4]=>[1,5,1,4,1,1,1]
[2,1,1,1,4,5]=>[1,5,1,1,2,1,1,1,1]
[2,1,2,2,1,1,1,1,1,2]=>[1,3,2,7,1]
[2,1,2,2,1,1,2,3]=>[1,3,2,4,2,1,1]
[2,1,2,2,2,2,1,2]=>[1,3,2,2,2,3,1]
[2,1,2,2,2,1,1,3]=>[1,3,2,2,4,1,1]
[2,1,2,2,3,4]=>[1,3,2,2,1,2,1,1,1]
[2,1,2,1,1,2,1,1,1,2]=>[1,3,4,5,1]
[2,1,2,1,1,2,2,3]=>[1,3,4,2,2,1,1]
[2,1,2,1,1,1,1,2,1,2]=>[1,3,6,3,1]
[2,1,2,1,1,1,1,1,1,3]=>[1,3,8,1,1]
[2,1,2,1,1,1,2,4]=>[1,3,5,2,1,1,1]
[2,1,2,1,2,3,1,2]=>[1,3,3,2,1,3,1]
[2,1,2,1,2,2,1,3]=>[1,3,3,2,3,1,1]
[2,1,2,1,2,1,1,4]=>[1,3,3,4,1,1,1]
[2,1,2,1,3,5]=>[1,3,3,1,2,1,1,1,1]
[2,1,3,3,1,1,1,2]=>[1,3,1,2,1,5,1]
[2,1,3,3,2,3]=>[1,3,1,2,1,2,2,1,1]
[2,1,3,2,1,2,1,2]=>[1,3,1,2,3,3,1]
[2,1,3,2,1,1,1,3]=>[1,3,1,2,5,1,1]
[2,1,3,2,2,4]=>[1,3,1,2,2,2,1,1,1]
[2,1,3,1,1,3,1,2]=>[1,3,1,4,1,3,1]
[2,1,3,1,1,2,1,3]=>[1,3,1,4,3,1,1]
[2,1,3,1,1,1,1,4]=>[1,3,1,6,1,1,1]
[2,1,3,1,2,5]=>[1,3,1,3,2,1,1,1,1]
[2,1,4,4,1,2]=>[1,3,1,1,2,1,1,3,1]
[2,1,4,3,1,3]=>[1,3,1,1,2,1,3,1,1]
[2,1,4,2,1,4]=>[1,3,1,1,2,3,1,1,1]
[2,1,4,1,1,5]=>[1,3,1,1,4,1,1,1,1]
[2,1,5,6]=>[1,3,1,1,1,2,1,1,1,1,1]
[3,2,1,1,1,1,2,3]=>[1,1,2,6,2,1,1]
[3,2,1,1,2,2,1,2]=>[1,1,2,4,2,3,1]
[3,2,1,1,2,1,1,3]=>[1,1,2,4,4,1,1]
[3,2,1,1,3,4]=>[1,1,2,4,1,2,1,1,1]
[3,2,2,2,1,1,1,2]=>[1,1,2,2,2,5,1]
[3,2,2,2,2,3]=>[1,1,2,2,2,2,2,1,1]
[3,2,2,1,1,2,1,2]=>[1,1,2,2,4,3,1]
[3,2,2,1,1,1,1,3]=>[1,1,2,2,6,1,1]
[3,2,2,1,2,4]=>[1,1,2,2,3,2,1,1,1]
[3,2,3,3,1,2]=>[1,1,2,2,1,2,1,3,1]
[3,2,3,2,1,3]=>[1,1,2,2,1,2,3,1,1]
[3,2,3,1,1,4]=>[1,1,2,2,1,4,1,1,1]
[3,2,4,5]=>[1,1,2,2,1,1,2,1,1,1,1]
[3,1,1,2,1,1,2,3]=>[1,1,4,4,2,1,1]
[3,1,1,2,2,2,1,2]=>[1,1,4,2,2,3,1]
[3,1,1,2,2,1,1,3]=>[1,1,4,2,4,1,1]
[3,1,1,2,3,4]=>[1,1,4,2,1,2,1,1,1]
[3,1,1,1,1,2,2,3]=>[1,1,6,2,2,1,1]
[3,1,1,1,1,1,1,2,1,2]=>[1,1,8,3,1]
[3,1,1,1,1,1,1,1,1,3]=>[1,1,10,1,1]
[3,1,1,1,1,1,2,4]=>[1,1,7,2,1,1,1]
[3,1,1,1,2,3,1,2]=>[1,1,5,2,1,3,1]
[3,1,1,1,2,2,1,3]=>[1,1,5,2,3,1,1]
[3,1,1,1,2,1,1,4]=>[1,1,5,4,1,1,1]
[3,1,1,1,3,5]=>[1,1,5,1,2,1,1,1,1]
[3,1,2,3,2,3]=>[1,1,3,2,1,2,2,1,1]
[3,1,2,2,1,2,1,2]=>[1,1,3,2,3,3,1]
[3,1,2,2,1,1,1,3]=>[1,1,3,2,5,1,1]
[3,1,2,2,2,4]=>[1,1,3,2,2,2,1,1,1]
[3,1,2,1,1,3,1,2]=>[1,1,3,4,1,3,1]
[3,1,2,1,1,2,1,3]=>[1,1,3,4,3,1,1]
[3,1,2,1,1,1,1,4]=>[1,1,3,6,1,1,1]
[3,1,2,1,2,5]=>[1,1,3,3,2,1,1,1,1]
[3,1,3,4,1,2]=>[1,1,3,1,2,1,1,3,1]
[3,1,3,3,1,3]=>[1,1,3,1,2,1,3,1,1]
[3,1,3,2,1,4]=>[1,1,3,1,2,3,1,1,1]
[3,1,3,1,1,5]=>[1,1,3,1,4,1,1,1,1]
[3,1,4,6]=>[1,1,3,1,1,2,1,1,1,1,1]
[4,3,1,1,2,3]=>[1,1,1,2,1,4,2,1,1]
[4,3,2,2,1,2]=>[1,1,1,2,1,2,2,3,1]
[4,3,2,1,1,3]=>[1,1,1,2,1,2,4,1,1]
[4,3,3,4]=>[1,1,1,2,1,2,1,2,1,1,1]
[4,2,1,2,1,1,1,2]=>[1,1,1,2,3,5,1]
[4,2,1,2,2,3]=>[1,1,1,2,3,2,2,1,1]
[4,2,1,1,1,2,1,2]=>[1,1,1,2,5,3,1]
[4,2,1,1,1,1,1,3]=>[1,1,1,2,7,1,1]
[4,2,1,1,2,4]=>[1,1,1,2,4,2,1,1,1]
[4,2,2,3,1,2]=>[1,1,1,2,2,2,1,3,1]
[4,2,2,2,1,3]=>[1,1,1,2,2,2,3,1,1]
[4,2,2,1,1,4]=>[1,1,1,2,2,4,1,1,1]
[4,2,3,5]=>[1,1,1,2,2,1,2,1,1,1,1]
[4,1,1,3,2,3]=>[1,1,1,4,1,2,2,1,1]
[4,1,1,2,1,2,1,2]=>[1,1,1,4,3,3,1]
[4,1,1,2,1,1,1,3]=>[1,1,1,4,5,1,1]
[4,1,1,2,2,4]=>[1,1,1,4,2,2,1,1,1]
[4,1,1,1,1,3,1,2]=>[1,1,1,6,1,3,1]
[4,1,1,1,1,2,1,3]=>[1,1,1,6,3,1,1]
[4,1,1,1,1,1,1,4]=>[1,1,1,8,1,1,1]
[4,1,1,1,2,5]=>[1,1,1,5,2,1,1,1,1]
[4,1,2,4,1,2]=>[1,1,1,3,2,1,1,3,1]
[4,1,2,3,1,3]=>[1,1,1,3,2,1,3,1,1]
[4,1,2,2,1,4]=>[1,1,1,3,2,3,1,1,1]
[4,1,2,1,1,5]=>[1,1,1,3,4,1,1,1,1]
[4,1,3,6]=>[1,1,1,3,1,2,1,1,1,1,1]
[5,4,1,1,1,2]=>[1,1,1,1,2,1,1,5,1]
[5,4,2,3]=>[1,1,1,1,2,1,1,2,2,1,1]
[5,3,1,2,1,2]=>[1,1,1,1,2,1,3,3,1]
[5,3,1,1,1,3]=>[1,1,1,1,2,1,5,1,1]
[5,3,2,4]=>[1,1,1,1,2,1,2,2,1,1,1]
[5,2,1,3,1,2]=>[1,1,1,1,2,3,1,3,1]
[5,2,1,2,1,3]=>[1,1,1,1,2,3,3,1,1]
[5,2,1,1,1,4]=>[1,1,1,1,2,5,1,1,1]
[5,2,2,5]=>[1,1,1,1,2,2,2,1,1,1,1]
[5,1,1,4,1,2]=>[1,1,1,1,4,1,1,3,1]
[5,1,1,3,1,3]=>[1,1,1,1,4,1,3,1,1]
[5,1,1,2,1,4]=>[1,1,1,1,4,3,1,1,1]
[5,1,1,1,1,5]=>[1,1,1,1,6,1,1,1,1]
[5,1,2,6]=>[1,1,1,1,3,2,1,1,1,1,1]
[6,5,1,2]=>[1,1,1,1,1,2,1,1,1,3,1]
[6,4,1,3]=>[1,1,1,1,1,2,1,1,3,1,1]
[6,3,1,4]=>[1,1,1,1,1,2,1,3,1,1,1]
[6,2,1,5]=>[1,1,1,1,1,2,3,1,1,1,1]
[6,1,1,6]=>[1,1,1,1,1,4,1,1,1,1,1]
[7,7]=>[1,1,1,1,1,1,2,1,1,1,1,1,1]
[6,7,1]=>[1,1,1,1,1,2,1,1,1,1,1,2]
[1,7,6]=>[2,1,1,1,1,1,2,1,1,1,1,1]
[5,2,6,1]=>[1,1,1,1,2,2,1,1,1,1,2]
[1,6,2,5]=>[2,1,1,1,1,2,2,1,1,1,1]
[5,3,5,1]=>[1,1,1,1,2,1,2,1,1,1,2]
[4,3,6,1]=>[1,1,1,2,1,2,1,1,1,1,2]
[1,6,3,4]=>[2,1,1,1,1,2,1,2,1,1,1]
[1,5,3,5]=>[2,1,1,1,2,1,2,1,1,1,1]
[5,4,4,1]=>[1,1,1,1,2,1,1,2,1,1,2]
[4,2,2,5,1]=>[1,1,1,2,2,2,1,1,1,2]
[3,4,6,1]=>[1,1,2,1,1,2,1,1,1,1,2]
[1,6,4,3]=>[2,1,1,1,1,2,1,1,2,1,1]
[1,5,2,2,4]=>[2,1,1,1,2,2,2,1,1,1]
[1,4,4,5]=>[2,1,1,2,1,1,2,1,1,1,1]
[5,5,3,1]=>[1,1,1,1,2,1,1,1,2,1,2]
[4,2,3,4,1]=>[1,1,1,2,2,1,2,1,1,2]
[4,4,5,1]=>[1,1,1,2,1,1,2,1,1,1,2]
[3,3,2,5,1]=>[1,1,2,1,2,2,1,1,1,2]
[2,5,6,1]=>[1,2,1,1,1,2,1,1,1,1,2]
[5,7,2]=>[1,1,1,1,2,1,1,1,1,1,2,1]
[1,6,5,2]=>[2,1,1,1,1,2,1,1,1,2,1]
[1,5,2,3,3]=>[2,1,1,1,2,2,1,2,1,1]
[1,5,4,4]=>[2,1,1,1,2,1,1,2,1,1,1]
[1,4,3,2,4]=>[2,1,1,2,1,2,2,1,1,1]
[2,7,5]=>[1,2,1,1,1,1,1,2,1,1,1,1]
[1,3,5,5]=>[2,1,2,1,1,1,2,1,1,1,1]
[6,6,1,1]=>[1,1,1,1,1,2,1,1,1,1,3]
[1,1,6,6]=>[3,1,1,1,1,2,1,1,1,1,1]
[5,1,1,5,1,1]=>[1,1,1,1,4,1,1,1,3]
[1,1,5,1,1,5]=>[3,1,1,1,4,1,1,1,1]
[5,2,1,4,1,1]=>[1,1,1,1,2,3,1,1,3]
[4,1,2,5,1,1]=>[1,1,1,3,2,1,1,1,3]
[1,1,5,2,1,4]=>[3,1,1,1,2,3,1,1,1]
[1,1,4,1,2,5]=>[3,1,1,3,2,1,1,1,1]
[5,3,1,3,1,1]=>[1,1,1,1,2,1,3,1,3]
[4,1,1,1,1,4,1,1]=>[1,1,1,6,1,1,3]
[3,1,3,5,1,1]=>[1,1,3,1,2,1,1,1,3]
[1,1,5,3,1,3]=>[3,1,1,1,2,1,3,1,1]
[1,1,4,1,1,1,1,4]=>[3,1,1,6,1,1,1]
[1,1,3,1,3,5]=>[3,1,3,1,2,1,1,1,1]
[5,4,1,2,1,1]=>[1,1,1,1,2,1,1,3,3]
[4,1,1,2,1,3,1,1]=>[1,1,1,4,3,1,3]
[4,2,2,4,1,1]=>[1,1,1,2,2,2,1,1,3]
[3,1,2,1,1,4,1,1]=>[1,1,3,4,1,1,3]
[2,1,4,5,1,1]=>[1,3,1,1,2,1,1,1,3]
[5,5,2,2]=>[1,1,1,1,2,1,1,1,2,2,1]
[1,1,5,4,1,2]=>[3,1,1,1,2,1,1,3,1]
[1,1,4,1,1,2,1,3]=>[3,1,1,4,3,1,1]
[1,1,4,2,2,4]=>[3,1,1,2,2,2,1,1,1]
[1,1,3,1,2,1,1,4]=>[3,1,3,4,1,1,1]
[2,2,5,5]=>[1,2,2,1,1,1,2,1,1,1,1]
[1,1,2,1,4,5]=>[3,3,1,1,2,1,1,1,1]
[1,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,2]
[1,2,2,2,2,3,2]=>[2,2,2,2,2,1,2,1]
[1,2,2,2,3,2,2]=>[2,2,2,2,1,2,2,1]
[1,2,2,3,2,2,2]=>[2,2,2,1,2,2,2,1]
[1,2,3,2,2,2,2]=>[2,2,1,2,2,2,2,1]
[1,3,2,2,2,2,2]=>[2,1,2,2,2,2,2,1]
[2,2,2,2,2,2,2]=>[1,2,2,2,2,2,2,1]
[1,2,2,2,4,3]=>[2,2,2,2,1,1,2,1,1]
[1,2,2,4,3,2]=>[2,2,2,1,1,2,1,2,1]
[1,2,4,3,2,2]=>[2,2,1,1,2,1,2,2,1]
[1,4,3,2,2,2]=>[2,1,1,2,1,2,2,2,1]
[3,3,2,2,2,2]=>[1,1,2,1,2,2,2,2,1]
[1,2,2,4,2,3]=>[2,2,2,1,1,2,2,1,1]
[1,2,4,2,3,2]=>[2,2,1,1,2,2,1,2,1]
[1,2,2,5,4]=>[2,2,2,1,1,1,2,1,1,1]
[1,4,2,3,2,2]=>[2,1,1,2,2,1,2,2,1]
[1,2,5,4,2]=>[2,2,1,1,1,2,1,1,2,1]
[3,2,3,2,2,2]=>[1,1,2,2,1,2,2,2,1]
[1,5,4,2,2]=>[2,1,1,1,2,1,1,2,2,1]
[4,4,2,2,2]=>[1,1,1,2,1,1,2,2,2,1]
[1,2,4,2,2,3]=>[2,2,1,1,2,2,2,1,1]
[1,4,2,2,3,2]=>[2,1,1,2,2,2,1,2,1]
[1,2,4,3,4]=>[2,2,1,1,2,1,2,1,1,1]
[3,2,2,3,2,2]=>[1,1,2,2,2,1,2,2,1]
[1,4,3,4,2]=>[2,1,1,2,1,2,1,1,2,1]
[1,2,5,2,4]=>[2,2,1,1,1,2,2,1,1,1]
[3,3,4,2,2]=>[1,1,2,1,2,1,1,2,2,1]
[1,5,2,4,2]=>[2,1,1,1,2,2,1,1,2,1]
[4,2,4,2,2]=>[1,1,1,2,2,1,1,2,2,1]
[2,2,2,2,3,3]=>[1,2,2,2,2,1,2,1,1]
[2,2,2,3,3,2]=>[1,2,2,2,1,2,1,2,1]
[2,2,2,3,2,3]=>[1,2,2,2,1,2,2,1,1]
[2,2,2,4,4]=>[1,2,2,2,1,1,2,1,1,1]
[2,2,3,3,2,2]=>[1,2,2,1,2,1,2,2,1]
[2,2,3,4,3]=>[1,2,2,1,2,1,1,2,1,1]
[2,2,3,2,3,2]=>[1,2,2,1,2,2,1,2,1]
[2,2,3,2,2,3]=>[1,2,2,1,2,2,2,1,1]
[2,2,3,3,4]=>[1,2,2,1,2,1,2,1,1,1]
[2,2,4,4,2]=>[1,2,2,1,1,2,1,1,2,1]
[2,2,4,3,3]=>[1,2,2,1,1,2,1,2,1,1]
[2,2,4,2,4]=>[1,2,2,1,1,2,2,1,1,1]
[2,3,3,2,2,2]=>[1,2,1,2,1,2,2,2,1]
[2,3,3,3,3]=>[1,2,1,2,1,2,1,2,1,1]
[2,3,4,3,2]=>[1,2,1,2,1,1,2,1,2,1]
[2,3,4,2,3]=>[1,2,1,2,1,1,2,2,1,1]
[2,3,5,4]=>[1,2,1,2,1,1,1,2,1,1,1]
[2,3,2,3,2,2]=>[1,2,1,2,2,1,2,2,1]
[2,3,2,4,3]=>[1,2,1,2,2,1,1,2,1,1]
[2,3,2,2,3,2]=>[1,2,1,2,2,2,1,2,1]
[2,3,2,2,2,3]=>[1,2,1,2,2,2,2,1,1]
[2,3,2,3,4]=>[1,2,1,2,2,1,2,1,1,1]
[2,3,3,4,2]=>[1,2,1,2,1,2,1,1,2,1]
[2,3,3,2,4]=>[1,2,1,2,1,2,2,1,1,1]
[2,4,4,2,2]=>[1,2,1,1,2,1,1,2,2,1]
[2,4,5,3]=>[1,2,1,1,2,1,1,1,2,1,1]
[2,4,3,3,2]=>[1,2,1,1,2,1,2,1,2,1]
[2,4,3,2,3]=>[1,2,1,1,2,1,2,2,1,1]
[2,4,4,4]=>[1,2,1,1,2,1,1,2,1,1,1]
[2,4,2,4,2]=>[1,2,1,1,2,2,1,1,2,1]
[2,4,2,3,3]=>[1,2,1,1,2,2,1,2,1,1]
[2,4,2,2,4]=>[1,2,1,1,2,2,2,1,1,1]
[2,4,3,5]=>[1,2,1,1,2,1,2,1,1,1,1]
[2,5,5,2]=>[1,2,1,1,1,2,1,1,1,2,1]
[2,5,4,3]=>[1,2,1,1,1,2,1,1,2,1,1]
[2,5,3,4]=>[1,2,1,1,1,2,1,2,1,1,1]
[2,5,2,5]=>[1,2,1,1,1,2,2,1,1,1,1]
[2,6,6]=>[1,2,1,1,1,1,2,1,1,1,1,1]
[3,3,2,3,3]=>[1,1,2,1,2,2,1,2,1,1]
[3,3,3,3,2]=>[1,1,2,1,2,1,2,1,2,1]
[3,3,3,2,3]=>[1,1,2,1,2,1,2,2,1,1]
[3,3,4,4]=>[1,1,2,1,2,1,1,2,1,1,1]
[3,4,3,2,2]=>[1,1,2,1,1,2,1,2,2,1]
[3,4,4,3]=>[1,1,2,1,1,2,1,1,2,1,1]
[3,4,2,3,2]=>[1,1,2,1,1,2,2,1,2,1]
[3,4,2,2,3]=>[1,1,2,1,1,2,2,2,1,1]
[3,4,3,4]=>[1,1,2,1,1,2,1,2,1,1,1]
[3,5,4,2]=>[1,1,2,1,1,1,2,1,1,2,1]
[3,5,3,3]=>[1,1,2,1,1,1,2,1,2,1,1]
[3,5,2,4]=>[1,1,2,1,1,1,2,2,1,1,1]
[3,6,5]=>[1,1,2,1,1,1,1,2,1,1,1,1]
[3,2,3,3,3]=>[1,1,2,2,1,2,1,2,1,1]
[3,2,4,3,2]=>[1,1,2,2,1,1,2,1,2,1]
[3,2,4,2,3]=>[1,1,2,2,1,1,2,2,1,1]
[3,2,5,4]=>[1,1,2,2,1,1,1,2,1,1,1]
[3,2,2,4,3]=>[1,1,2,2,2,1,1,2,1,1]
[3,2,2,2,3,2]=>[1,1,2,2,2,2,1,2,1]
[3,2,2,3,4]=>[1,1,2,2,2,1,2,1,1,1]
[3,2,3,4,2]=>[1,1,2,2,1,2,1,1,2,1]
[3,2,3,2,4]=>[1,1,2,2,1,2,2,1,1,1]
[3,3,5,3]=>[1,1,2,1,2,1,1,1,2,1,1]
[3,3,2,4,2]=>[1,1,2,1,2,2,1,1,2,1]
[3,3,2,2,4]=>[1,1,2,1,2,2,2,1,1,1]
[3,3,3,5]=>[1,1,2,1,2,1,2,1,1,1,1]
[3,4,5,2]=>[1,1,2,1,1,2,1,1,1,2,1]
[3,4,2,5]=>[1,1,2,1,1,2,2,1,1,1,1]
[3,5,6]=>[1,1,2,1,1,1,2,1,1,1,1,1]
[4,4,3,3]=>[1,1,1,2,1,1,2,1,2,1,1]
[4,5,3,2]=>[1,1,1,2,1,1,1,2,1,2,1]
[4,5,2,3]=>[1,1,1,2,1,1,1,2,2,1,1]
[4,6,4]=>[1,1,1,2,1,1,1,1,2,1,1,1]
[4,3,3,2,2]=>[1,1,1,2,1,2,1,2,2,1]
[4,3,4,3]=>[1,1,1,2,1,2,1,1,2,1,1]
[4,3,2,3,2]=>[1,1,1,2,1,2,2,1,2,1]
[4,3,2,2,3]=>[1,1,1,2,1,2,2,2,1,1]
[4,4,4,2]=>[1,1,1,2,1,1,2,1,1,2,1]
[4,4,2,4]=>[1,1,1,2,1,1,2,2,1,1,1]
[4,5,5]=>[1,1,1,2,1,1,1,2,1,1,1,1]
[4,2,5,3]=>[1,1,1,2,2,1,1,1,2,1,1]
[4,2,3,3,2]=>[1,1,1,2,2,1,2,1,2,1]
[4,2,3,2,3]=>[1,1,1,2,2,1,2,2,1,1]
[4,2,4,4]=>[1,1,1,2,2,1,1,2,1,1,1]
[4,2,2,4,2]=>[1,1,1,2,2,2,1,1,2,1]
[4,2,2,3,3]=>[1,1,1,2,2,2,1,2,1,1]
[4,2,2,2,4]=>[1,1,1,2,2,2,2,1,1,1]
[4,3,5,2]=>[1,1,1,2,1,2,1,1,1,2,1]
[4,3,2,5]=>[1,1,1,2,1,2,2,1,1,1,1]
[4,4,6]=>[1,1,1,2,1,1,2,1,1,1,1,1]
[5,6,3]=>[1,1,1,1,2,1,1,1,1,2,1,1]
[5,5,4]=>[1,1,1,1,2,1,1,1,2,1,1,1]
[5,3,4,2]=>[1,1,1,1,2,1,2,1,1,2,1]
[5,3,3,3]=>[1,1,1,1,2,1,2,1,2,1,1]
[5,4,5]=>[1,1,1,1,2,1,1,2,1,1,1,1]
[5,2,5,2]=>[1,1,1,1,2,2,1,1,1,2,1]
[5,2,4,3]=>[1,1,1,1,2,2,1,1,2,1,1]
[5,2,3,4]=>[1,1,1,1,2,2,1,2,1,1,1]
[5,3,6]=>[1,1,1,1,2,1,2,1,1,1,1,1]
[6,6,2]=>[1,1,1,1,1,2,1,1,1,1,2,1]
[6,5,3]=>[1,1,1,1,1,2,1,1,1,2,1,1]
[6,4,4]=>[1,1,1,1,1,2,1,1,2,1,1,1]
[6,3,5]=>[1,1,1,1,1,2,1,2,1,1,1,1]
[6,2,6]=>[1,1,1,1,1,2,2,1,1,1,1,1]
[1,1,1,1,2,2,2,3,1]=>[5,2,2,2,1,2]
[1,1,1,2,2,2,3,2]=>[4,2,2,2,1,2,1]
[1,1,1,2,1,1,2,1,2,2]=>[4,4,3,2,1]
[1,1,1,1,2,1,2,1,2,2]=>[5,3,3,2,1]
[1,1,1,1,2,1,1,2,2,2]=>[5,4,2,2,1]
[1,2,2,2,1,2,1,2,1]=>[2,2,2,3,3,2]
[1,2,2,1,2,1,2,2,1]=>[2,2,3,3,2,2]
[1,2,2,1,2,2,1,2,1]=>[2,2,3,2,3,2]
[1,2,1,2,1,2,2,2,1]=>[2,3,3,2,2,2]
[1,2,1,2,1,1,2,1,2,1]=>[2,3,4,3,2]
[1,2,1,2,2,1,2,2,1]=>[2,3,2,3,2,2]
[1,2,1,2,2,2,1,2,1]=>[2,3,2,2,3,2]
[1,2,1,2,2,2,2,1,1]=>[2,3,2,2,2,3]
[1,2,1,1,2,1,1,2,2,1]=>[2,4,4,2,2]
[1,2,1,1,2,1,2,1,2,1]=>[2,4,3,3,2]
[1,1,2,1,2,2,2,2,1]=>[3,3,2,2,2,2]
[1,1,2,1,2,1,2,1,2,1]=>[3,3,3,3,2]
[1,1,2,1,1,2,1,2,2,1]=>[3,4,3,2,2]
[1,1,2,1,1,2,2,1,2,1]=>[3,4,2,3,2]
[1,1,2,2,1,2,2,2,1]=>[3,2,3,2,2,2]
[1,1,2,2,1,1,2,1,2,1]=>[3,2,4,3,2]
[1,1,2,2,2,1,2,2,1]=>[3,2,2,3,2,2]
[1,1,2,2,2,2,1,2,1]=>[3,2,2,2,3,2]
[1,1,2,1,2,1,1,2,2,1]=>[3,3,4,2,2]
[1,1,1,2,1,1,2,2,2,1]=>[4,4,2,2,2]
[1,1,1,2,1,2,1,2,2,1]=>[4,3,3,2,2]
[1,1,1,2,1,2,2,1,2,1]=>[4,3,2,3,2]
[1,1,1,2,2,1,1,2,2,1]=>[4,2,4,2,2]
[1,1,1,2,2,1,2,1,2,1]=>[4,2,3,3,2]
[2,2,1,2,2,2,2,1]=>[1,2,3,2,2,2,2]
[2,2,1,2,3,2,1,1]=>[1,2,3,2,1,2,3]
[2,2,2,1,1,2,2,1,1]=>[1,2,2,4,2,3]
[3,1,2,2,2,2,1,1]=>[1,1,3,2,2,2,3]
[2,2,2,2,2,1,2,1]=>[1,2,2,2,2,3,2]
[2,2,2,2,1,2,2,1]=>[1,2,2,2,3,2,2]
[2,2,2,1,2,2,2,1]=>[1,2,2,3,2,2,2]
[2,1,2,2,2,2,2,1]=>[1,3,2,2,2,2,2]
[2,2,2,2,1,1,2,2]=>[1,2,2,2,4,2,1]
[2,2,2,1,1,2,1,2,1]=>[1,2,2,4,3,2]
[2,2,1,1,2,1,2,2,1]=>[1,2,4,3,2,2]
[2,1,1,2,1,2,2,2,1]=>[1,4,3,2,2,2]
[2,2,2,1,1,2,2,2]=>[1,2,2,4,2,2,1]
[2,2,1,1,2,2,1,2,1]=>[1,2,4,2,3,2]
[2,2,2,1,1,1,2,2,1]=>[1,2,2,5,2,2]
[2,1,1,2,2,1,2,2,1]=>[1,4,2,3,2,2]
[2,2,1,1,1,2,2,2,1]=>[1,2,5,2,2,2]
[2,1,1,1,2,2,2,2,1]=>[1,5,2,2,2,2]
[1,1,1,2,2,2,2,2,1]=>[4,2,2,2,2,2]
[2,2,1,1,2,2,2,2]=>[1,2,4,2,2,2,1]
[2,1,1,2,2,2,1,2,1]=>[1,4,2,2,3,2]
[1,2,1,2,2,2,2,2]=>[2,3,2,2,2,2,1]
[1,2,2,1,2,2,2,2]=>[2,2,3,2,2,2,1]
[1,2,2,2,1,2,2,2]=>[2,2,2,3,2,2,1]
[1,2,2,2,2,1,2,2]=>[2,2,2,2,3,2,1]
[1,1,2,1,1,2,2,2,2]=>[3,4,2,2,2,1]
[1,2,1,2,1,1,2,2,2]=>[2,3,4,2,2,1]
[1,2,2,1,2,1,1,2,2]=>[2,2,3,4,2,1]
[1,1,2,2,1,1,2,2,2]=>[3,2,4,2,2,1]
[1,2,1,2,2,1,1,2,2]=>[2,3,2,4,2,1]
[1,1,1,2,1,1,1,2,2,2]=>[4,5,2,2,1]
[1,1,2,2,2,1,1,2,2]=>[3,2,2,4,2,1]
[1,1,1,2,1,2,1,1,2,2]=>[4,3,4,2,1]
[1,1,1,1,2,3,3,2]=>[5,2,1,2,1,2,1]
[1,1,1,1,2,2,2,2,2]=>[5,2,2,2,2,1]
[1,1,1,1,2,2,2,4]=>[5,2,2,2,1,1,1]
[1,2,2,2,1,1,2,2,1]=>[2,2,2,4,2,2]
[1,2,2,1,1,2,2,2,1]=>[2,2,4,2,2,2]
[1,2,2,1,1,2,1,2,2]=>[2,2,4,3,2,1]
[1,2,2,1,1,1,2,2,2]=>[2,2,5,2,2,1]
[1,2,1,2,1,2,1,2,2]=>[2,3,3,3,2,1]
[1,2,1,2,1,1,1,2,2,1]=>[2,3,5,2,2]
[1,2,1,1,2,2,2,2,1]=>[2,4,2,2,2,2]
[1,2,1,1,2,2,1,2,2]=>[2,4,2,3,2,1]
[1,2,1,1,2,1,2,2,2]=>[2,4,3,2,2,1]
[1,2,1,1,1,2,2,1,2,1]=>[2,5,2,3,2]
[1,2,1,1,1,2,2,2,2]=>[2,5,2,2,2,1]
[1,2,1,1,1,2,1,2,2,1]=>[2,5,3,2,2]
[1,2,1,1,1,1,2,2,2,1]=>[2,6,2,2,2]
[1,1,2,1,2,2,1,2,2]=>[3,3,2,3,2,1]
[1,1,2,1,2,1,2,2,2]=>[3,3,3,2,2,1]
[1,1,2,1,1,2,1,1,2,2]=>[3,4,4,2,1]
[1,1,2,1,1,1,2,2,2,1]=>[3,5,2,2,2]
[1,1,2,1,1,1,2,1,2,2]=>[3,5,3,2,1]
[1,1,2,1,1,1,1,2,2,2]=>[3,6,2,2,1]
[1,1,2,2,1,2,1,2,2]=>[3,2,3,3,2,1]
[1,1,2,2,1,1,1,2,2,1]=>[3,2,5,2,2]
[1,1,2,2,2,2,2,2]=>[3,2,2,2,2,2,1]
[1,1,1,2,2,2,1,2,2]=>[4,2,2,3,2,1]
[1,1,1,2,2,1,2,2,2]=>[4,2,3,2,2,1]
[1,1,1,2,1,2,2,2,2]=>[4,3,2,2,2,1]
[1,1,1,1,2,2,1,2,2,1]=>[5,2,3,2,2]
[1,1,1,1,2,2,1,1,2,2]=>[5,2,4,2,1]
[1,1,1,1,2,2,2,1,2,1]=>[5,2,2,3,2]
[1,1,1,1,2,1,2,2,2,1]=>[5,3,2,2,2]
[1,1,1,1,1,2,2,2,2,1]=>[6,2,2,2,2]
[1,1,1,1,1,2,2,1,2,2]=>[6,2,3,2,1]
[1,1,1,1,1,2,1,2,2,2]=>[6,3,2,2,1]
[1,1,1,1,1,1,2,2,2,2]=>[7,2,2,2,1]
[1,1,1,1,1,2,2,2,1,2]=>[6,2,2,3,1]
[2,1,1,1,1,1,2,2,2,1]=>[1,7,2,2,2]
[2,1,1,1,1,2,2,2,2]=>[1,6,2,2,2,1]
[1,1,1,1,2,1,2,2,1,2]=>[5,3,2,3,1]
[2,1,1,1,1,2,1,2,2,1]=>[1,6,3,2,2]
[2,1,1,1,2,1,2,2,2]=>[1,5,3,2,2,1]
[1,1,1,2,2,2,2,1,2]=>[4,2,2,2,3,1]
[2,1,1,2,1,1,2,2,2]=>[1,4,4,2,2,1]
[1,1,1,1,2,2,1,2,1,2]=>[5,2,3,3,1]
[1,1,1,2,1,1,2,2,1,2]=>[4,4,2,3,1]
[1,1,2,1,2,2,2,1,2]=>[3,3,2,2,3,1]
[2,1,1,1,1,2,2,1,2,1]=>[1,6,2,3,2]
[2,1,1,1,2,2,1,2,2]=>[1,5,2,3,2,1]
[2,1,1,1,2,1,1,2,2,1]=>[1,5,4,2,2]
[1,2,1,1,1,1,1,2,2,2]=>[2,7,2,2,1]
[2,1,2,1,1,1,2,2,2]=>[1,3,5,2,2,1]
[5,4,3,2,1]=>[1,1,1,1,2,1,1,2,1,2,2]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[15]
[1,1,1,1,1,1,2,1,1,1,1,1,2]=>[7,7,1]
[1,1,1,1,2,2,2,3,2]=>[5,2,2,2,1,2,1]
[2,2,1,2,2,2,2,1,1]=>[1,2,3,2,2,2,3]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[16]
[1,1,1,1,1,1,1,1,1,1,1,1,2,2]=>[13,2,1]
[1,1,1,1,1,1,1,1,1,1,2,1,1,2]=>[11,4,1]
[1,1,1,1,1,1,1,1,2,1,1,1,1,2]=>[9,6,1]
[1,1,1,1,1,1,2,1,1,1,1,1,1,2]=>[7,8,1]
[1,1,1,1,2,1,1,1,1,1,1,1,1,2]=>[5,10,1]
[1,1,2,1,1,1,1,1,1,1,1,1,1,2]=>[3,12,1]
[2,1,1,1,1,1,1,1,1,1,1,1,1,2]=>[1,14,1]
[1,1,1,1,1,1,1,1,1,1,3,3]=>[11,1,2,1,1]
[1,1,1,1,1,1,1,1,3,2,1,2]=>[9,1,2,3,1]
[1,1,1,1,1,1,3,2,1,1,1,2]=>[7,1,2,5,1]
[1,1,1,1,3,2,1,1,1,1,1,2]=>[5,1,2,7,1]
[1,1,3,2,1,1,1,1,1,1,1,2]=>[3,1,2,9,1]
[3,2,1,1,1,1,1,1,1,1,1,2]=>[1,1,2,11,1]
[1,1,1,1,1,1,1,1,3,1,1,3]=>[9,1,4,1,1]
[1,1,1,1,1,1,3,1,1,2,1,2]=>[7,1,4,3,1]
[1,1,1,1,1,1,1,1,4,4]=>[9,1,1,2,1,1,1]
[1,1,1,1,3,1,1,2,1,1,1,2]=>[5,1,4,5,1]
[1,1,1,1,1,1,4,3,1,2]=>[7,1,1,2,1,3,1]
[1,1,3,1,1,2,1,1,1,1,1,2]=>[3,1,4,7,1]
[1,1,1,1,4,3,1,1,1,2]=>[5,1,1,2,1,5,1]
[3,1,1,2,1,1,1,1,1,1,1,2]=>[1,1,4,9,1]
[1,1,4,3,1,1,1,1,1,2]=>[3,1,1,2,1,7,1]
[4,3,1,1,1,1,1,1,1,2]=>[1,1,1,2,1,9,1]
[1,1,1,1,1,1,2,1,1,1,1,1,3]=>[7,7,1,1]
[7,8,1]=>[1,1,1,1,1,1,2,1,1,1,1,1,1,2]
[1,8,7]=>[2,1,1,1,1,1,1,2,1,1,1,1,1,1]
[6,2,7,1]=>[1,1,1,1,1,2,2,1,1,1,1,1,2]
[1,7,2,6]=>[2,1,1,1,1,1,2,2,1,1,1,1,1]
[6,3,6,1]=>[1,1,1,1,1,2,1,2,1,1,1,1,2]
[5,3,7,1]=>[1,1,1,1,2,1,2,1,1,1,1,1,2]
[1,7,3,5]=>[2,1,1,1,1,1,2,1,2,1,1,1,1]
[1,6,3,6]=>[2,1,1,1,1,2,1,2,1,1,1,1,1]
[6,4,5,1]=>[1,1,1,1,1,2,1,1,2,1,1,1,2]
[5,2,2,6,1]=>[1,1,1,1,2,2,2,1,1,1,1,2]
[4,4,7,1]=>[1,1,1,2,1,1,2,1,1,1,1,1,2]
[1,7,4,4]=>[2,1,1,1,1,1,2,1,1,2,1,1,1]
[1,6,2,2,5]=>[2,1,1,1,1,2,2,2,1,1,1,1]
[1,5,4,6]=>[2,1,1,1,2,1,1,2,1,1,1,1,1]
[7,7,1,1]=>[1,1,1,1,1,1,2,1,1,1,1,1,3]
[1,1,7,7]=>[3,1,1,1,1,1,2,1,1,1,1,1,1]
[6,1,1,6,1,1]=>[1,1,1,1,1,4,1,1,1,1,3]
[1,1,6,1,1,6]=>[3,1,1,1,1,4,1,1,1,1,1]
[6,2,1,5,1,1]=>[1,1,1,1,1,2,3,1,1,1,3]
[5,1,2,6,1,1]=>[1,1,1,1,3,2,1,1,1,1,3]
[1,1,6,2,1,5]=>[3,1,1,1,1,2,3,1,1,1,1]
[1,1,5,1,2,6]=>[3,1,1,1,3,2,1,1,1,1,1]
[6,3,1,4,1,1]=>[1,1,1,1,1,2,1,3,1,1,3]
[5,1,1,1,1,5,1,1]=>[1,1,1,1,6,1,1,1,3]
[4,1,3,6,1,1]=>[1,1,1,3,1,2,1,1,1,1,3]
[1,1,6,3,1,4]=>[3,1,1,1,1,2,1,3,1,1,1]
[1,1,5,1,1,1,1,5]=>[3,1,1,1,6,1,1,1,1]
[1,1,4,1,3,6]=>[3,1,1,3,1,2,1,1,1,1,1]
[1,2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,2,2]
[1,2,2,2,2,2,3,2]=>[2,2,2,2,2,2,1,2,1]
[1,2,2,2,2,3,2,2]=>[2,2,2,2,2,1,2,2,1]
[1,2,2,2,3,2,2,2]=>[2,2,2,2,1,2,2,2,1]
[1,2,2,3,2,2,2,2]=>[2,2,2,1,2,2,2,2,1]
[1,2,3,2,2,2,2,2]=>[2,2,1,2,2,2,2,2,1]
[1,3,2,2,2,2,2,2]=>[2,1,2,2,2,2,2,2,1]
[2,2,2,2,2,2,2,2]=>[1,2,2,2,2,2,2,2,1]
[1,2,2,2,2,4,3]=>[2,2,2,2,2,1,1,2,1,1]
[1,2,2,2,4,3,2]=>[2,2,2,2,1,1,2,1,2,1]
[1,2,2,4,3,2,2]=>[2,2,2,1,1,2,1,2,2,1]
[1,2,4,3,2,2,2]=>[2,2,1,1,2,1,2,2,2,1]
[1,4,3,2,2,2,2]=>[2,1,1,2,1,2,2,2,2,1]
[3,3,2,2,2,2,2]=>[1,1,2,1,2,2,2,2,2,1]
[1,2,2,2,4,2,3]=>[2,2,2,2,1,1,2,2,1,1]
[1,2,2,4,2,3,2]=>[2,2,2,1,1,2,2,1,2,1]
[1,2,2,2,5,4]=>[2,2,2,2,1,1,1,2,1,1,1]
[1,2,4,2,3,2,2]=>[2,2,1,1,2,2,1,2,2,1]
[1,2,2,5,4,2]=>[2,2,2,1,1,1,2,1,1,2,1]
[1,4,2,3,2,2,2]=>[2,1,1,2,2,1,2,2,2,1]
[1,2,5,4,2,2]=>[2,2,1,1,1,2,1,1,2,2,1]
[3,2,3,2,2,2,2]=>[1,1,2,2,1,2,2,2,2,1]
[1,5,4,2,2,2]=>[2,1,1,1,2,1,1,2,2,2,1]
[4,4,2,2,2,2]=>[1,1,1,2,1,1,2,2,2,2,1]
[2,2,2,2,2,2,1,2,1]=>[1,2,2,2,2,2,3,2]
[2,2,2,2,2,1,2,2,1]=>[1,2,2,2,2,3,2,2]
[2,2,2,2,1,2,2,2,1]=>[1,2,2,2,3,2,2,2]
[2,2,2,1,2,2,2,2,1]=>[1,2,2,3,2,2,2,2]
[2,2,1,2,2,2,2,2,1]=>[1,2,3,2,2,2,2,2]
[2,1,2,2,2,2,2,2,1]=>[1,3,2,2,2,2,2,2]
[2,2,2,2,2,1,1,2,2]=>[1,2,2,2,2,4,2,1]
[2,2,2,2,1,1,2,1,2,1]=>[1,2,2,2,4,3,2]
[2,2,2,1,1,2,1,2,2,1]=>[1,2,2,4,3,2,2]
[2,2,1,1,2,1,2,2,2,1]=>[1,2,4,3,2,2,2]
[2,1,1,2,1,2,2,2,2,1]=>[1,4,3,2,2,2,2]
[1,1,2,1,2,2,2,2,2,1]=>[3,3,2,2,2,2,2]
[2,2,2,2,1,1,2,2,2]=>[1,2,2,2,4,2,2,1]
[2,2,2,1,1,2,2,1,2,1]=>[1,2,2,4,2,3,2]
[2,2,2,2,1,1,1,2,2,1]=>[1,2,2,2,5,2,2]
[2,2,1,1,2,2,1,2,2,1]=>[1,2,4,2,3,2,2]
[2,2,2,1,1,1,2,2,2,1]=>[1,2,2,5,2,2,2]
[2,1,1,2,2,1,2,2,2,1]=>[1,4,2,3,2,2,2]
[2,2,1,1,1,2,2,2,2,1]=>[1,2,5,2,2,2,2]
[1,1,2,2,1,2,2,2,2,1]=>[3,2,3,2,2,2,2]
[2,1,1,1,2,2,2,2,2,1]=>[1,5,2,2,2,2,2]
[1,1,1,2,2,2,2,2,2,1]=>[4,2,2,2,2,2,2]
[1,1,1,1,1,1,2,2,2,2,2]=>[7,2,2,2,2,1]
[2,1,1,1,1,1,1,2,2,2,2]=>[1,8,2,2,2,1]
[1,1,1,1,1,2,2,2,2,1,2]=>[6,2,2,2,3,1]
[2,1,1,1,1,1,2,2,2,2,1]=>[1,7,2,2,2,2]
[1,1,1,1,1,2,1,2,2,2,2]=>[6,3,2,2,2,1]
[1,1,1,1,2,1,2,2,2,1,2]=>[5,3,2,2,3,1]
[2,1,1,1,1,1,2,1,2,2,2]=>[1,7,3,2,2,1]
[2,1,1,1,1,2,1,2,2,2,1]=>[1,6,3,2,2,2]
[1,1,1,1,2,2,2,2,2,2]=>[5,2,2,2,2,2,1]
[1,1,1,2,1,1,2,2,2,1,2]=>[4,4,2,2,3,1]
[2,1,1,1,1,2,2,2,2,2]=>[1,6,2,2,2,2,1]
[2,1,1,1,2,1,1,2,2,2,1]=>[1,5,4,2,2,2]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[18]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2]=>[15,2,1]
[1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,2]=>[13,4,1]
[1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2]=>[11,6,1]
[1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2]=>[9,8,1]
[1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2]=>[7,10,1]
[1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,2]=>[5,12,1]
[1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,2]=>[3,14,1]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2]=>[1,16,1]
[1,1,1,1,1,1,1,1,1,1,1,1,3,3]=>[13,1,2,1,1]
[1,1,1,1,1,1,1,1,1,1,3,2,1,2]=>[11,1,2,3,1]
[1,1,1,1,1,1,1,1,3,2,1,1,1,2]=>[9,1,2,5,1]
[1,1,1,1,1,1,3,2,1,1,1,1,1,2]=>[7,1,2,7,1]
[1,1,1,1,3,2,1,1,1,1,1,1,1,2]=>[5,1,2,9,1]
[1,1,3,2,1,1,1,1,1,1,1,1,1,2]=>[3,1,2,11,1]
[3,2,1,1,1,1,1,1,1,1,1,1,1,2]=>[1,1,2,13,1]
[8,9,1]=>[1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2]
[1,9,8]=>[2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1]
[7,2,8,1]=>[1,1,1,1,1,1,2,2,1,1,1,1,1,1,2]
[1,8,2,7]=>[2,1,1,1,1,1,1,2,2,1,1,1,1,1,1]
[7,3,7,1]=>[1,1,1,1,1,1,2,1,2,1,1,1,1,1,2]
[6,3,8,1]=>[1,1,1,1,1,2,1,2,1,1,1,1,1,1,2]
[1,8,3,6]=>[2,1,1,1,1,1,1,2,1,2,1,1,1,1,1]
[1,7,3,7]=>[2,1,1,1,1,1,2,1,2,1,1,1,1,1,1]
[8,8,1,1]=>[1,1,1,1,1,1,1,2,1,1,1,1,1,1,3]
[1,1,8,8]=>[3,1,1,1,1,1,1,2,1,1,1,1,1,1,1]
[7,1,1,7,1,1]=>[1,1,1,1,1,1,4,1,1,1,1,1,3]
[1,1,7,1,1,7]=>[3,1,1,1,1,1,4,1,1,1,1,1,1]
[7,2,1,6,1,1]=>[1,1,1,1,1,1,2,3,1,1,1,1,3]
[6,1,2,7,1,1]=>[1,1,1,1,1,3,2,1,1,1,1,1,3]
[1,1,7,2,1,6]=>[3,1,1,1,1,1,2,3,1,1,1,1,1]
[1,1,6,1,2,7]=>[3,1,1,1,1,3,2,1,1,1,1,1,1]
[1,2,2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,2,2,2]
[1,2,2,2,2,2,2,3,2]=>[2,2,2,2,2,2,2,1,2,1]
[1,2,2,2,2,2,3,2,2]=>[2,2,2,2,2,2,1,2,2,1]
[1,2,2,2,2,3,2,2,2]=>[2,2,2,2,2,1,2,2,2,1]
[1,2,2,2,3,2,2,2,2]=>[2,2,2,2,1,2,2,2,2,1]
[1,2,2,3,2,2,2,2,2]=>[2,2,2,1,2,2,2,2,2,1]
[1,2,3,2,2,2,2,2,2]=>[2,2,1,2,2,2,2,2,2,1]
[1,3,2,2,2,2,2,2,2]=>[2,1,2,2,2,2,2,2,2,1]
[2,2,2,2,2,2,2,2,2]=>[1,2,2,2,2,2,2,2,2,1]
[1,2,2,2,2,2,4,3]=>[2,2,2,2,2,2,1,1,2,1,1]
[1,2,2,2,2,4,3,2]=>[2,2,2,2,2,1,1,2,1,2,1]
[1,2,2,2,4,3,2,2]=>[2,2,2,2,1,1,2,1,2,2,1]
[1,2,2,4,3,2,2,2]=>[2,2,2,1,1,2,1,2,2,2,1]
[1,2,4,3,2,2,2,2]=>[2,2,1,1,2,1,2,2,2,2,1]
[1,4,3,2,2,2,2,2]=>[2,1,1,2,1,2,2,2,2,2,1]
[3,3,2,2,2,2,2,2]=>[1,1,2,1,2,2,2,2,2,2,1]
[2,2,2,2,2,2,2,1,2,1]=>[1,2,2,2,2,2,2,3,2]
[2,2,2,2,2,2,1,2,2,1]=>[1,2,2,2,2,2,3,2,2]
[2,2,2,2,2,1,2,2,2,1]=>[1,2,2,2,2,3,2,2,2]
[2,2,2,2,1,2,2,2,2,1]=>[1,2,2,2,3,2,2,2,2]
[2,2,2,1,2,2,2,2,2,1]=>[1,2,2,3,2,2,2,2,2]
[2,2,1,2,2,2,2,2,2,1]=>[1,2,3,2,2,2,2,2,2]
[2,1,2,2,2,2,2,2,2,1]=>[1,3,2,2,2,2,2,2,2]
[2,2,2,2,2,2,1,1,2,2]=>[1,2,2,2,2,2,4,2,1]
[2,2,2,2,2,1,1,2,1,2,1]=>[1,2,2,2,2,4,3,2]
[2,2,2,2,1,1,2,1,2,2,1]=>[1,2,2,2,4,3,2,2]
[2,2,2,1,1,2,1,2,2,2,1]=>[1,2,2,4,3,2,2,2]
[2,2,1,1,2,1,2,2,2,2,1]=>[1,2,4,3,2,2,2,2]
[2,1,1,2,1,2,2,2,2,2,1]=>[1,4,3,2,2,2,2,2]
[1,1,2,1,2,2,2,2,2,2,1]=>[3,3,2,2,2,2,2,2]
[1,1,1,1,1,1,1,2,2,2,2,1,2]=>[8,2,2,2,3,1]
[2,1,1,1,1,1,1,1,2,2,2,2,1]=>[1,9,2,2,2,2]
[1,1,1,1,1,1,2,2,2,2,2,2]=>[7,2,2,2,2,2,1]
[2,1,1,1,1,1,1,2,2,2,2,2]=>[1,8,2,2,2,2,1]
[1,1,1,1,1,1,2,1,2,2,2,1,2]=>[7,3,2,2,3,1]
[1,1,1,1,1,2,1,2,2,2,2,2]=>[6,3,2,2,2,2,1]
[2,1,1,1,1,1,1,2,1,2,2,2,1]=>[1,8,3,2,2,2]
[2,1,1,1,1,1,2,1,2,2,2,2]=>[1,7,3,2,2,2,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[20]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2]=>[17,2,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,2]=>[15,4,1]
[1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2]=>[13,6,1]
[1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2]=>[11,8,1]
[1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2]=>[9,10,1]
[1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,2]=>[7,12,1]
[1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,2]=>[5,14,1]
[1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2]=>[3,16,1]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2]=>[1,18,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3]=>[18,1,1]
[9,10,1]=>[1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2]
[1,10,9]=>[2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1]
[8,2,9,1]=>[1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,2]
[1,9,2,8]=>[2,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1]
[9,9,1,1]=>[1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,3]
[1,1,9,9]=>[3,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1]
[8,1,1,8,1,1]=>[1,1,1,1,1,1,1,4,1,1,1,1,1,1,3]
[1,1,8,1,1,8]=>[3,1,1,1,1,1,1,4,1,1,1,1,1,1,1]
[1,2,2,2,2,2,2,2,2,2,1]=>[2,2,2,2,2,2,2,2,2,2]
[1,2,2,2,2,2,2,2,3,2]=>[2,2,2,2,2,2,2,2,1,2,1]
[1,2,2,2,2,2,2,3,2,2]=>[2,2,2,2,2,2,2,1,2,2,1]
[1,2,2,2,2,2,3,2,2,2]=>[2,2,2,2,2,2,1,2,2,2,1]
[1,2,2,2,2,3,2,2,2,2]=>[2,2,2,2,2,1,2,2,2,2,1]
[1,2,2,2,3,2,2,2,2,2]=>[2,2,2,2,1,2,2,2,2,2,1]
[1,2,2,3,2,2,2,2,2,2]=>[2,2,2,1,2,2,2,2,2,2,1]
[1,2,3,2,2,2,2,2,2,2]=>[2,2,1,2,2,2,2,2,2,2,1]
[1,3,2,2,2,2,2,2,2,2]=>[2,1,2,2,2,2,2,2,2,2,1]
[2,2,2,2,2,2,2,2,2,2]=>[1,2,2,2,2,2,2,2,2,2,1]
[2,2,2,2,2,2,2,2,1,2,1]=>[1,2,2,2,2,2,2,2,3,2]
[2,2,2,2,2,2,2,1,2,2,1]=>[1,2,2,2,2,2,2,3,2,2]
[2,2,2,2,2,2,1,2,2,2,1]=>[1,2,2,2,2,2,3,2,2,2]
[2,2,2,2,2,1,2,2,2,2,1]=>[1,2,2,2,2,3,2,2,2,2]
[2,2,2,2,1,2,2,2,2,2,1]=>[1,2,2,2,3,2,2,2,2,2]
[2,2,2,1,2,2,2,2,2,2,1]=>[1,2,2,3,2,2,2,2,2,2]
[2,2,1,2,2,2,2,2,2,2,1]=>[1,2,3,2,2,2,2,2,2,2]
[2,1,2,2,2,2,2,2,2,2,1]=>[1,3,2,2,2,2,2,2,2,2]
[1,1,1,1,1,1,1,1,2,2,2,2,2,2]=>[9,2,2,2,2,2,1]
[2,1,1,1,1,1,1,1,1,2,2,2,2,2]=>[1,10,2,2,2,2,1]
[1,1,1,1,1,1,1,2,2,2,2,2,1,2]=>[8,2,2,2,2,3,1]
[2,1,1,1,1,1,1,1,2,2,2,2,2,1]=>[1,9,2,2,2,2,2]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[21]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2]=>[20,1]
[10,11,1]=>[1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2]
[1,11,10]=>[2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1]
[10,10,1,1]=>[1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,3]
[1,1,10,10]=>[3,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,2,2,2,2,2,1,2]=>[10,2,2,2,2,3,1]
[2,1,1,1,1,1,1,1,1,1,2,2,2,2,2,1]=>[1,11,2,2,2,2,2]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[24]
[1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,5]=>[9,11,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[25]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3]=>[23,1,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[30]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3]=>[28,1,1]
click to show experimental identities
(only identities of compositions of up to three maps are shown)
Description
The complement of a composition.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
Properties
bijective, graded, involutive
Sage code
def mapping(elt): return elt.conjugate().reversed()
Weight
11
Created
Jan 19, 2020 at 07:28 by FindStatCrew
Updated
Jan 19, 2020 at 07:28 by Martin Rubey
searching the database
Sorry, this map was not found in the database.