Identifier
Images
=>
[1]=>[1]
[1,1]=>[2]
[2]=>[1,1]
[1,1,1]=>[3]
[1,2]=>[1,2]
[2,1]=>[2,1]
[3]=>[1,1,1]
[1,1,1,1]=>[4]
[1,1,2]=>[1,3]
[1,2,1]=>[2,2]
[1,3]=>[1,1,2]
[2,1,1]=>[3,1]
[2,2]=>[1,2,1]
[3,1]=>[2,1,1]
[4]=>[1,1,1,1]
[1,1,1,1,1]=>[5]
[1,1,1,2]=>[1,4]
[1,1,2,1]=>[2,3]
[1,1,3]=>[1,1,3]
[1,2,1,1]=>[3,2]
[1,2,2]=>[1,2,2]
[1,3,1]=>[2,1,2]
[1,4]=>[1,1,1,2]
[2,1,1,1]=>[4,1]
[2,1,2]=>[1,3,1]
[2,2,1]=>[2,2,1]
[2,3]=>[1,1,2,1]
[3,1,1]=>[3,1,1]
[3,2]=>[1,2,1,1]
[4,1]=>[2,1,1,1]
[5]=>[1,1,1,1,1]
[1,1,1,1,1,1]=>[6]
[1,1,1,1,2]=>[1,5]
[1,1,1,2,1]=>[2,4]
[1,1,1,3]=>[1,1,4]
[1,1,2,1,1]=>[3,3]
[1,1,2,2]=>[1,2,3]
[1,1,3,1]=>[2,1,3]
[1,1,4]=>[1,1,1,3]
[1,2,1,1,1]=>[4,2]
[1,2,1,2]=>[1,3,2]
[1,2,2,1]=>[2,2,2]
[1,2,3]=>[1,1,2,2]
[1,3,1,1]=>[3,1,2]
[1,3,2]=>[1,2,1,2]
[1,4,1]=>[2,1,1,2]
[1,5]=>[1,1,1,1,2]
[2,1,1,1,1]=>[5,1]
[2,1,1,2]=>[1,4,1]
[2,1,2,1]=>[2,3,1]
[2,1,3]=>[1,1,3,1]
[2,2,1,1]=>[3,2,1]
[2,2,2]=>[1,2,2,1]
[2,3,1]=>[2,1,2,1]
[2,4]=>[1,1,1,2,1]
[3,1,1,1]=>[4,1,1]
[3,1,2]=>[1,3,1,1]
[3,2,1]=>[2,2,1,1]
[3,3]=>[1,1,2,1,1]
[4,1,1]=>[3,1,1,1]
[4,2]=>[1,2,1,1,1]
[5,1]=>[2,1,1,1,1]
[6]=>[1,1,1,1,1,1]
[1,1,1,1,1,1,1]=>[7]
[1,1,1,1,1,2]=>[1,6]
[1,1,1,1,2,1]=>[2,5]
[1,1,1,1,3]=>[1,1,5]
[1,1,1,2,1,1]=>[3,4]
[1,1,1,2,2]=>[1,2,4]
[1,1,1,3,1]=>[2,1,4]
[1,1,1,4]=>[1,1,1,4]
[1,1,2,1,1,1]=>[4,3]
[1,1,2,1,2]=>[1,3,3]
[1,1,2,2,1]=>[2,2,3]
[1,1,2,3]=>[1,1,2,3]
[1,1,3,1,1]=>[3,1,3]
[1,1,3,2]=>[1,2,1,3]
[1,1,4,1]=>[2,1,1,3]
[1,1,5]=>[1,1,1,1,3]
[1,2,1,1,1,1]=>[5,2]
[1,2,1,1,2]=>[1,4,2]
[1,2,1,2,1]=>[2,3,2]
[1,2,1,3]=>[1,1,3,2]
[1,2,2,1,1]=>[3,2,2]
[1,2,2,2]=>[1,2,2,2]
[1,2,3,1]=>[2,1,2,2]
[1,2,4]=>[1,1,1,2,2]
[1,3,1,1,1]=>[4,1,2]
[1,3,1,2]=>[1,3,1,2]
[1,3,2,1]=>[2,2,1,2]
[1,3,3]=>[1,1,2,1,2]
[1,4,1,1]=>[3,1,1,2]
[1,4,2]=>[1,2,1,1,2]
[1,5,1]=>[2,1,1,1,2]
[1,6]=>[1,1,1,1,1,2]
[2,1,1,1,1,1]=>[6,1]
[2,1,1,1,2]=>[1,5,1]
[2,1,1,2,1]=>[2,4,1]
[2,1,1,3]=>[1,1,4,1]
[2,1,2,1,1]=>[3,3,1]
[2,1,2,2]=>[1,2,3,1]
[2,1,3,1]=>[2,1,3,1]
[2,1,4]=>[1,1,1,3,1]
[2,2,1,1,1]=>[4,2,1]
[2,2,1,2]=>[1,3,2,1]
[2,2,2,1]=>[2,2,2,1]
[2,2,3]=>[1,1,2,2,1]
[2,3,1,1]=>[3,1,2,1]
[2,3,2]=>[1,2,1,2,1]
[2,4,1]=>[2,1,1,2,1]
[2,5]=>[1,1,1,1,2,1]
[3,1,1,1,1]=>[5,1,1]
[3,1,1,2]=>[1,4,1,1]
[3,1,2,1]=>[2,3,1,1]
[3,1,3]=>[1,1,3,1,1]
[3,2,1,1]=>[3,2,1,1]
[3,2,2]=>[1,2,2,1,1]
[3,3,1]=>[2,1,2,1,1]
[3,4]=>[1,1,1,2,1,1]
[4,1,1,1]=>[4,1,1,1]
[4,1,2]=>[1,3,1,1,1]
[4,2,1]=>[2,2,1,1,1]
[4,3]=>[1,1,2,1,1,1]
[5,1,1]=>[3,1,1,1,1]
[5,2]=>[1,2,1,1,1,1]
[6,1]=>[2,1,1,1,1,1]
[7]=>[1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1]=>[8]
[1,1,1,1,1,1,2]=>[1,7]
[1,1,1,1,1,2,1]=>[2,6]
[1,1,1,1,1,3]=>[1,1,6]
[1,1,1,1,2,1,1]=>[3,5]
[1,1,1,1,2,2]=>[1,2,5]
[1,1,1,1,3,1]=>[2,1,5]
[1,1,1,1,4]=>[1,1,1,5]
[1,1,1,2,1,1,1]=>[4,4]
[1,1,1,2,1,2]=>[1,3,4]
[1,1,1,2,2,1]=>[2,2,4]
[1,1,1,2,3]=>[1,1,2,4]
[1,1,1,3,1,1]=>[3,1,4]
[1,1,1,3,2]=>[1,2,1,4]
[1,1,1,4,1]=>[2,1,1,4]
[1,1,1,5]=>[1,1,1,1,4]
[1,1,2,1,1,1,1]=>[5,3]
[1,1,2,1,1,2]=>[1,4,3]
[1,1,2,1,2,1]=>[2,3,3]
[1,1,2,1,3]=>[1,1,3,3]
[1,1,2,2,1,1]=>[3,2,3]
[1,1,2,2,2]=>[1,2,2,3]
[1,1,2,3,1]=>[2,1,2,3]
[1,1,2,4]=>[1,1,1,2,3]
[1,1,3,1,1,1]=>[4,1,3]
[1,1,3,1,2]=>[1,3,1,3]
[1,1,3,2,1]=>[2,2,1,3]
[1,1,3,3]=>[1,1,2,1,3]
[1,1,4,1,1]=>[3,1,1,3]
[1,1,4,2]=>[1,2,1,1,3]
[1,1,5,1]=>[2,1,1,1,3]
[1,1,6]=>[1,1,1,1,1,3]
[1,2,1,1,1,1,1]=>[6,2]
[1,2,1,1,1,2]=>[1,5,2]
[1,2,1,1,2,1]=>[2,4,2]
[1,2,1,1,3]=>[1,1,4,2]
[1,2,1,2,1,1]=>[3,3,2]
[1,2,1,2,2]=>[1,2,3,2]
[1,2,1,3,1]=>[2,1,3,2]
[1,2,1,4]=>[1,1,1,3,2]
[1,2,2,1,1,1]=>[4,2,2]
[1,2,2,1,2]=>[1,3,2,2]
[1,2,2,2,1]=>[2,2,2,2]
[1,2,2,3]=>[1,1,2,2,2]
[1,2,3,1,1]=>[3,1,2,2]
[1,2,3,2]=>[1,2,1,2,2]
[1,2,4,1]=>[2,1,1,2,2]
[1,2,5]=>[1,1,1,1,2,2]
[1,3,1,1,1,1]=>[5,1,2]
[1,3,1,1,2]=>[1,4,1,2]
[1,3,1,2,1]=>[2,3,1,2]
[1,3,1,3]=>[1,1,3,1,2]
[1,3,2,1,1]=>[3,2,1,2]
[1,3,2,2]=>[1,2,2,1,2]
[1,3,3,1]=>[2,1,2,1,2]
[1,3,4]=>[1,1,1,2,1,2]
[1,4,1,1,1]=>[4,1,1,2]
[1,4,1,2]=>[1,3,1,1,2]
[1,4,2,1]=>[2,2,1,1,2]
[1,4,3]=>[1,1,2,1,1,2]
[1,5,1,1]=>[3,1,1,1,2]
[1,5,2]=>[1,2,1,1,1,2]
[1,6,1]=>[2,1,1,1,1,2]
[1,7]=>[1,1,1,1,1,1,2]
[2,1,1,1,1,1,1]=>[7,1]
[2,1,1,1,1,2]=>[1,6,1]
[2,1,1,1,2,1]=>[2,5,1]
[2,1,1,1,3]=>[1,1,5,1]
[2,1,1,2,1,1]=>[3,4,1]
[2,1,1,2,2]=>[1,2,4,1]
[2,1,1,3,1]=>[2,1,4,1]
[2,1,1,4]=>[1,1,1,4,1]
[2,1,2,1,1,1]=>[4,3,1]
[2,1,2,1,2]=>[1,3,3,1]
[2,1,2,2,1]=>[2,2,3,1]
[2,1,2,3]=>[1,1,2,3,1]
[2,1,3,1,1]=>[3,1,3,1]
[2,1,3,2]=>[1,2,1,3,1]
[2,1,4,1]=>[2,1,1,3,1]
[2,1,5]=>[1,1,1,1,3,1]
[2,2,1,1,1,1]=>[5,2,1]
[2,2,1,1,2]=>[1,4,2,1]
[2,2,1,2,1]=>[2,3,2,1]
[2,2,1,3]=>[1,1,3,2,1]
[2,2,2,1,1]=>[3,2,2,1]
[2,2,2,2]=>[1,2,2,2,1]
[2,2,3,1]=>[2,1,2,2,1]
[2,2,4]=>[1,1,1,2,2,1]
[2,3,1,1,1]=>[4,1,2,1]
[2,3,1,2]=>[1,3,1,2,1]
[2,3,2,1]=>[2,2,1,2,1]
[2,3,3]=>[1,1,2,1,2,1]
[2,4,1,1]=>[3,1,1,2,1]
[2,4,2]=>[1,2,1,1,2,1]
[2,5,1]=>[2,1,1,1,2,1]
[2,6]=>[1,1,1,1,1,2,1]
[3,1,1,1,1,1]=>[6,1,1]
[3,1,1,1,2]=>[1,5,1,1]
[3,1,1,2,1]=>[2,4,1,1]
[3,1,1,3]=>[1,1,4,1,1]
[3,1,2,1,1]=>[3,3,1,1]
[3,1,2,2]=>[1,2,3,1,1]
[3,1,3,1]=>[2,1,3,1,1]
[3,1,4]=>[1,1,1,3,1,1]
[3,2,1,1,1]=>[4,2,1,1]
[3,2,1,2]=>[1,3,2,1,1]
[3,2,2,1]=>[2,2,2,1,1]
[3,2,3]=>[1,1,2,2,1,1]
[3,3,1,1]=>[3,1,2,1,1]
[3,3,2]=>[1,2,1,2,1,1]
[3,4,1]=>[2,1,1,2,1,1]
[3,5]=>[1,1,1,1,2,1,1]
[4,1,1,1,1]=>[5,1,1,1]
[4,1,1,2]=>[1,4,1,1,1]
[4,1,2,1]=>[2,3,1,1,1]
[4,1,3]=>[1,1,3,1,1,1]
[4,2,1,1]=>[3,2,1,1,1]
[4,2,2]=>[1,2,2,1,1,1]
[4,3,1]=>[2,1,2,1,1,1]
[4,4]=>[1,1,1,2,1,1,1]
[5,1,1,1]=>[4,1,1,1,1]
[5,1,2]=>[1,3,1,1,1,1]
[5,2,1]=>[2,2,1,1,1,1]
[5,3]=>[1,1,2,1,1,1,1]
[6,1,1]=>[3,1,1,1,1,1]
[6,2]=>[1,2,1,1,1,1,1]
[7,1]=>[2,1,1,1,1,1,1]
[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]=>[1,8]
[1,1,1,1,1,1,2,1]=>[2,7]
[1,1,1,1,1,1,3]=>[1,1,7]
[1,1,1,1,1,2,1,1]=>[3,6]
[1,1,1,1,1,2,2]=>[1,2,6]
[1,1,1,1,1,3,1]=>[2,1,6]
[1,1,1,1,1,4]=>[1,1,1,6]
[1,1,1,1,2,1,1,1]=>[4,5]
[1,1,1,1,2,1,2]=>[1,3,5]
[1,1,1,1,2,2,1]=>[2,2,5]
[1,1,1,1,2,3]=>[1,1,2,5]
[1,1,1,1,3,1,1]=>[3,1,5]
[1,1,1,1,3,2]=>[1,2,1,5]
[1,1,1,1,4,1]=>[2,1,1,5]
[1,1,1,1,5]=>[1,1,1,1,5]
[1,1,1,2,1,1,1,1]=>[5,4]
[1,1,1,2,1,1,2]=>[1,4,4]
[1,1,1,2,1,2,1]=>[2,3,4]
[1,1,1,2,1,3]=>[1,1,3,4]
[1,1,1,2,2,1,1]=>[3,2,4]
[1,1,1,2,2,2]=>[1,2,2,4]
[1,1,1,2,3,1]=>[2,1,2,4]
[1,1,1,2,4]=>[1,1,1,2,4]
[1,1,1,3,1,1,1]=>[4,1,4]
[1,1,1,3,1,2]=>[1,3,1,4]
[1,1,1,3,2,1]=>[2,2,1,4]
[1,1,1,3,3]=>[1,1,2,1,4]
[1,1,1,4,1,1]=>[3,1,1,4]
[1,1,1,4,2]=>[1,2,1,1,4]
[1,1,1,5,1]=>[2,1,1,1,4]
[1,1,1,6]=>[1,1,1,1,1,4]
[1,1,2,1,1,1,1,1]=>[6,3]
[1,1,2,1,1,1,2]=>[1,5,3]
[1,1,2,1,1,2,1]=>[2,4,3]
[1,1,2,1,1,3]=>[1,1,4,3]
[1,1,2,1,2,1,1]=>[3,3,3]
[1,1,2,1,2,2]=>[1,2,3,3]
[1,1,2,1,3,1]=>[2,1,3,3]
[1,1,2,1,4]=>[1,1,1,3,3]
[1,1,2,2,1,1,1]=>[4,2,3]
[1,1,2,2,1,2]=>[1,3,2,3]
[1,1,2,2,2,1]=>[2,2,2,3]
[1,1,2,2,3]=>[1,1,2,2,3]
[1,1,2,3,1,1]=>[3,1,2,3]
[1,1,2,3,2]=>[1,2,1,2,3]
[1,1,2,4,1]=>[2,1,1,2,3]
[1,1,2,5]=>[1,1,1,1,2,3]
[1,1,3,1,1,1,1]=>[5,1,3]
[1,1,3,1,1,2]=>[1,4,1,3]
[1,1,3,1,2,1]=>[2,3,1,3]
[1,1,3,1,3]=>[1,1,3,1,3]
[1,1,3,2,1,1]=>[3,2,1,3]
[1,1,3,2,2]=>[1,2,2,1,3]
[1,1,3,3,1]=>[2,1,2,1,3]
[1,1,3,4]=>[1,1,1,2,1,3]
[1,1,4,1,1,1]=>[4,1,1,3]
[1,1,4,1,2]=>[1,3,1,1,3]
[1,1,4,2,1]=>[2,2,1,1,3]
[1,1,4,3]=>[1,1,2,1,1,3]
[1,1,5,1,1]=>[3,1,1,1,3]
[1,1,5,2]=>[1,2,1,1,1,3]
[1,1,6,1]=>[2,1,1,1,1,3]
[1,1,7]=>[1,1,1,1,1,1,3]
[1,2,1,1,1,1,1,1]=>[7,2]
[1,2,1,1,1,1,2]=>[1,6,2]
[1,2,1,1,1,2,1]=>[2,5,2]
[1,2,1,1,1,3]=>[1,1,5,2]
[1,2,1,1,2,1,1]=>[3,4,2]
[1,2,1,1,2,2]=>[1,2,4,2]
[1,2,1,1,3,1]=>[2,1,4,2]
[1,2,1,1,4]=>[1,1,1,4,2]
[1,2,1,2,1,1,1]=>[4,3,2]
[1,2,1,2,1,2]=>[1,3,3,2]
[1,2,1,2,2,1]=>[2,2,3,2]
[1,2,1,2,3]=>[1,1,2,3,2]
[1,2,1,3,1,1]=>[3,1,3,2]
[1,2,1,3,2]=>[1,2,1,3,2]
[1,2,1,4,1]=>[2,1,1,3,2]
[1,2,1,5]=>[1,1,1,1,3,2]
[1,2,2,1,1,1,1]=>[5,2,2]
[1,2,2,1,1,2]=>[1,4,2,2]
[1,2,2,1,2,1]=>[2,3,2,2]
[1,2,2,1,3]=>[1,1,3,2,2]
[1,2,2,2,1,1]=>[3,2,2,2]
[1,2,2,2,2]=>[1,2,2,2,2]
[1,2,2,3,1]=>[2,1,2,2,2]
[1,2,2,4]=>[1,1,1,2,2,2]
[1,2,3,1,1,1]=>[4,1,2,2]
[1,2,3,1,2]=>[1,3,1,2,2]
[1,2,3,2,1]=>[2,2,1,2,2]
[1,2,3,3]=>[1,1,2,1,2,2]
[1,2,4,1,1]=>[3,1,1,2,2]
[1,2,4,2]=>[1,2,1,1,2,2]
[1,2,5,1]=>[2,1,1,1,2,2]
[1,2,6]=>[1,1,1,1,1,2,2]
[1,3,1,1,1,1,1]=>[6,1,2]
[1,3,1,1,1,2]=>[1,5,1,2]
[1,3,1,1,2,1]=>[2,4,1,2]
[1,3,1,1,3]=>[1,1,4,1,2]
[1,3,1,2,1,1]=>[3,3,1,2]
[1,3,1,2,2]=>[1,2,3,1,2]
[1,3,1,3,1]=>[2,1,3,1,2]
[1,3,1,4]=>[1,1,1,3,1,2]
[1,3,2,1,1,1]=>[4,2,1,2]
[1,3,2,1,2]=>[1,3,2,1,2]
[1,3,2,2,1]=>[2,2,2,1,2]
[1,3,2,3]=>[1,1,2,2,1,2]
[1,3,3,1,1]=>[3,1,2,1,2]
[1,3,3,2]=>[1,2,1,2,1,2]
[1,3,4,1]=>[2,1,1,2,1,2]
[1,3,5]=>[1,1,1,1,2,1,2]
[1,4,1,1,1,1]=>[5,1,1,2]
[1,4,1,1,2]=>[1,4,1,1,2]
[1,4,1,2,1]=>[2,3,1,1,2]
[1,4,1,3]=>[1,1,3,1,1,2]
[1,4,2,1,1]=>[3,2,1,1,2]
[1,4,2,2]=>[1,2,2,1,1,2]
[1,4,3,1]=>[2,1,2,1,1,2]
[1,4,4]=>[1,1,1,2,1,1,2]
[1,5,1,1,1]=>[4,1,1,1,2]
[1,5,1,2]=>[1,3,1,1,1,2]
[1,5,2,1]=>[2,2,1,1,1,2]
[1,5,3]=>[1,1,2,1,1,1,2]
[1,6,1,1]=>[3,1,1,1,1,2]
[1,6,2]=>[1,2,1,1,1,1,2]
[1,7,1]=>[2,1,1,1,1,1,2]
[1,8]=>[1,1,1,1,1,1,1,2]
[2,1,1,1,1,1,1,1]=>[8,1]
[2,1,1,1,1,1,2]=>[1,7,1]
[2,1,1,1,1,2,1]=>[2,6,1]
[2,1,1,1,1,3]=>[1,1,6,1]
[2,1,1,1,2,1,1]=>[3,5,1]
[2,1,1,1,2,2]=>[1,2,5,1]
[2,1,1,1,3,1]=>[2,1,5,1]
[2,1,1,1,4]=>[1,1,1,5,1]
[2,1,1,2,1,1,1]=>[4,4,1]
[2,1,1,2,1,2]=>[1,3,4,1]
[2,1,1,2,2,1]=>[2,2,4,1]
[2,1,1,2,3]=>[1,1,2,4,1]
[2,1,1,3,1,1]=>[3,1,4,1]
[2,1,1,3,2]=>[1,2,1,4,1]
[2,1,1,4,1]=>[2,1,1,4,1]
[2,1,1,5]=>[1,1,1,1,4,1]
[2,1,2,1,1,1,1]=>[5,3,1]
[2,1,2,1,1,2]=>[1,4,3,1]
[2,1,2,1,2,1]=>[2,3,3,1]
[2,1,2,1,3]=>[1,1,3,3,1]
[2,1,2,2,1,1]=>[3,2,3,1]
[2,1,2,2,2]=>[1,2,2,3,1]
[2,1,2,3,1]=>[2,1,2,3,1]
[2,1,2,4]=>[1,1,1,2,3,1]
[2,1,3,1,1,1]=>[4,1,3,1]
[2,1,3,1,2]=>[1,3,1,3,1]
[2,1,3,2,1]=>[2,2,1,3,1]
[2,1,3,3]=>[1,1,2,1,3,1]
[2,1,4,1,1]=>[3,1,1,3,1]
[2,1,4,2]=>[1,2,1,1,3,1]
[2,1,5,1]=>[2,1,1,1,3,1]
[2,1,6]=>[1,1,1,1,1,3,1]
[2,2,1,1,1,1,1]=>[6,2,1]
[2,2,1,1,1,2]=>[1,5,2,1]
[2,2,1,1,2,1]=>[2,4,2,1]
[2,2,1,1,3]=>[1,1,4,2,1]
[2,2,1,2,1,1]=>[3,3,2,1]
[2,2,1,2,2]=>[1,2,3,2,1]
[2,2,1,3,1]=>[2,1,3,2,1]
[2,2,1,4]=>[1,1,1,3,2,1]
[2,2,2,1,1,1]=>[4,2,2,1]
[2,2,2,1,2]=>[1,3,2,2,1]
[2,2,2,2,1]=>[2,2,2,2,1]
[2,2,2,3]=>[1,1,2,2,2,1]
[2,2,3,1,1]=>[3,1,2,2,1]
[2,2,3,2]=>[1,2,1,2,2,1]
[2,2,4,1]=>[2,1,1,2,2,1]
[2,2,5]=>[1,1,1,1,2,2,1]
[2,3,1,1,1,1]=>[5,1,2,1]
[2,3,1,1,2]=>[1,4,1,2,1]
[2,3,1,2,1]=>[2,3,1,2,1]
[2,3,1,3]=>[1,1,3,1,2,1]
[2,3,2,1,1]=>[3,2,1,2,1]
[2,3,2,2]=>[1,2,2,1,2,1]
[2,3,3,1]=>[2,1,2,1,2,1]
[2,3,4]=>[1,1,1,2,1,2,1]
[2,4,1,1,1]=>[4,1,1,2,1]
[2,4,1,2]=>[1,3,1,1,2,1]
[2,4,2,1]=>[2,2,1,1,2,1]
[2,4,3]=>[1,1,2,1,1,2,1]
[2,5,1,1]=>[3,1,1,1,2,1]
[2,5,2]=>[1,2,1,1,1,2,1]
[2,6,1]=>[2,1,1,1,1,2,1]
[2,7]=>[1,1,1,1,1,1,2,1]
[3,1,1,1,1,1,1]=>[7,1,1]
[3,1,1,1,1,2]=>[1,6,1,1]
[3,1,1,1,2,1]=>[2,5,1,1]
[3,1,1,1,3]=>[1,1,5,1,1]
[3,1,1,2,1,1]=>[3,4,1,1]
[3,1,1,2,2]=>[1,2,4,1,1]
[3,1,1,3,1]=>[2,1,4,1,1]
[3,1,1,4]=>[1,1,1,4,1,1]
[3,1,2,1,1,1]=>[4,3,1,1]
[3,1,2,1,2]=>[1,3,3,1,1]
[3,1,2,2,1]=>[2,2,3,1,1]
[3,1,2,3]=>[1,1,2,3,1,1]
[3,1,3,1,1]=>[3,1,3,1,1]
[3,1,3,2]=>[1,2,1,3,1,1]
[3,1,4,1]=>[2,1,1,3,1,1]
[3,1,5]=>[1,1,1,1,3,1,1]
[3,2,1,1,1,1]=>[5,2,1,1]
[3,2,1,1,2]=>[1,4,2,1,1]
[3,2,1,2,1]=>[2,3,2,1,1]
[3,2,1,3]=>[1,1,3,2,1,1]
[3,2,2,1,1]=>[3,2,2,1,1]
[3,2,2,2]=>[1,2,2,2,1,1]
[3,2,3,1]=>[2,1,2,2,1,1]
[3,2,4]=>[1,1,1,2,2,1,1]
[3,3,1,1,1]=>[4,1,2,1,1]
[3,3,1,2]=>[1,3,1,2,1,1]
[3,3,2,1]=>[2,2,1,2,1,1]
[3,3,3]=>[1,1,2,1,2,1,1]
[3,4,1,1]=>[3,1,1,2,1,1]
[3,4,2]=>[1,2,1,1,2,1,1]
[3,5,1]=>[2,1,1,1,2,1,1]
[3,6]=>[1,1,1,1,1,2,1,1]
[4,1,1,1,1,1]=>[6,1,1,1]
[4,1,1,1,2]=>[1,5,1,1,1]
[4,1,1,2,1]=>[2,4,1,1,1]
[4,1,1,3]=>[1,1,4,1,1,1]
[4,1,2,1,1]=>[3,3,1,1,1]
[4,1,2,2]=>[1,2,3,1,1,1]
[4,1,3,1]=>[2,1,3,1,1,1]
[4,1,4]=>[1,1,1,3,1,1,1]
[4,2,1,1,1]=>[4,2,1,1,1]
[4,2,1,2]=>[1,3,2,1,1,1]
[4,2,2,1]=>[2,2,2,1,1,1]
[4,2,3]=>[1,1,2,2,1,1,1]
[4,3,1,1]=>[3,1,2,1,1,1]
[4,3,2]=>[1,2,1,2,1,1,1]
[4,4,1]=>[2,1,1,2,1,1,1]
[4,5]=>[1,1,1,1,2,1,1,1]
[5,1,1,1,1]=>[5,1,1,1,1]
[5,1,1,2]=>[1,4,1,1,1,1]
[5,1,2,1]=>[2,3,1,1,1,1]
[5,1,3]=>[1,1,3,1,1,1,1]
[5,2,1,1]=>[3,2,1,1,1,1]
[5,2,2]=>[1,2,2,1,1,1,1]
[5,3,1]=>[2,1,2,1,1,1,1]
[5,4]=>[1,1,1,2,1,1,1,1]
[6,1,1,1]=>[4,1,1,1,1,1]
[6,1,2]=>[1,3,1,1,1,1,1]
[6,2,1]=>[2,2,1,1,1,1,1]
[6,3]=>[1,1,2,1,1,1,1,1]
[7,1,1]=>[3,1,1,1,1,1,1]
[7,2]=>[1,2,1,1,1,1,1,1]
[8,1]=>[2,1,1,1,1,1,1,1]
[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]=>[1,9]
[1,1,1,1,1,1,1,2,1]=>[2,8]
[1,1,1,1,1,1,1,3]=>[1,1,8]
[1,1,1,1,1,1,2,1,1]=>[3,7]
[1,1,1,1,1,1,2,2]=>[1,2,7]
[1,1,1,1,1,1,3,1]=>[2,1,7]
[1,1,1,1,1,1,4]=>[1,1,1,7]
[1,1,1,1,1,2,1,1,1]=>[4,6]
[1,1,1,1,1,2,1,2]=>[1,3,6]
[1,1,1,1,1,2,2,1]=>[2,2,6]
[1,1,1,1,1,2,3]=>[1,1,2,6]
[1,1,1,1,1,3,1,1]=>[3,1,6]
[1,1,1,1,1,3,2]=>[1,2,1,6]
[1,1,1,1,1,4,1]=>[2,1,1,6]
[1,1,1,1,1,5]=>[1,1,1,1,6]
[1,1,1,1,2,1,1,1,1]=>[5,5]
[1,1,1,1,2,1,1,2]=>[1,4,5]
[1,1,1,1,2,1,2,1]=>[2,3,5]
[1,1,1,1,2,1,3]=>[1,1,3,5]
[1,1,1,1,2,2,1,1]=>[3,2,5]
[1,1,1,1,2,2,2]=>[1,2,2,5]
[1,1,1,1,2,3,1]=>[2,1,2,5]
[1,1,1,1,2,4]=>[1,1,1,2,5]
[1,1,1,1,3,1,1,1]=>[4,1,5]
[1,1,1,1,3,1,2]=>[1,3,1,5]
[1,1,1,1,3,2,1]=>[2,2,1,5]
[1,1,1,1,3,3]=>[1,1,2,1,5]
[1,1,1,1,4,1,1]=>[3,1,1,5]
[1,1,1,1,4,2]=>[1,2,1,1,5]
[1,1,1,1,5,1]=>[2,1,1,1,5]
[1,1,1,1,6]=>[1,1,1,1,1,5]
[1,1,1,2,1,1,1,1,1]=>[6,4]
[1,1,1,2,1,1,1,2]=>[1,5,4]
[1,1,1,2,1,1,2,1]=>[2,4,4]
[1,1,1,2,1,1,3]=>[1,1,4,4]
[1,1,1,2,1,2,1,1]=>[3,3,4]
[1,1,1,2,1,2,2]=>[1,2,3,4]
[1,1,1,2,1,3,1]=>[2,1,3,4]
[1,1,1,2,1,4]=>[1,1,1,3,4]
[1,1,1,2,2,1,1,1]=>[4,2,4]
[1,1,1,2,2,1,2]=>[1,3,2,4]
[1,1,1,2,2,2,1]=>[2,2,2,4]
[1,1,1,2,2,3]=>[1,1,2,2,4]
[1,1,1,2,3,1,1]=>[3,1,2,4]
[1,1,1,2,3,2]=>[1,2,1,2,4]
[1,1,1,2,4,1]=>[2,1,1,2,4]
[1,1,1,2,5]=>[1,1,1,1,2,4]
[1,1,1,3,1,1,1,1]=>[5,1,4]
[1,1,1,3,1,1,2]=>[1,4,1,4]
[1,1,1,3,1,2,1]=>[2,3,1,4]
[1,1,1,3,1,3]=>[1,1,3,1,4]
[1,1,1,3,2,1,1]=>[3,2,1,4]
[1,1,1,3,2,2]=>[1,2,2,1,4]
[1,1,1,3,3,1]=>[2,1,2,1,4]
[1,1,1,3,4]=>[1,1,1,2,1,4]
[1,1,1,4,1,1,1]=>[4,1,1,4]
[1,1,1,4,1,2]=>[1,3,1,1,4]
[1,1,1,4,2,1]=>[2,2,1,1,4]
[1,1,1,4,3]=>[1,1,2,1,1,4]
[1,1,1,5,1,1]=>[3,1,1,1,4]
[1,1,1,5,2]=>[1,2,1,1,1,4]
[1,1,1,6,1]=>[2,1,1,1,1,4]
[1,1,1,7]=>[1,1,1,1,1,1,4]
[1,1,2,1,1,1,1,1,1]=>[7,3]
[1,1,2,1,1,1,1,2]=>[1,6,3]
[1,1,2,1,1,1,2,1]=>[2,5,3]
[1,1,2,1,1,1,3]=>[1,1,5,3]
[1,1,2,1,1,2,1,1]=>[3,4,3]
[1,1,2,1,1,2,2]=>[1,2,4,3]
[1,1,2,1,1,3,1]=>[2,1,4,3]
[1,1,2,1,1,4]=>[1,1,1,4,3]
[1,1,2,1,2,1,1,1]=>[4,3,3]
[1,1,2,1,2,1,2]=>[1,3,3,3]
[1,1,2,1,2,2,1]=>[2,2,3,3]
[1,1,2,1,2,3]=>[1,1,2,3,3]
[1,1,2,1,3,1,1]=>[3,1,3,3]
[1,1,2,1,3,2]=>[1,2,1,3,3]
[1,1,2,1,4,1]=>[2,1,1,3,3]
[1,1,2,1,5]=>[1,1,1,1,3,3]
[1,1,2,2,1,1,1,1]=>[5,2,3]
[1,1,2,2,1,1,2]=>[1,4,2,3]
[1,1,2,2,1,2,1]=>[2,3,2,3]
[1,1,2,2,1,3]=>[1,1,3,2,3]
[1,1,2,2,2,1,1]=>[3,2,2,3]
[1,1,2,2,2,2]=>[1,2,2,2,3]
[1,1,2,2,3,1]=>[2,1,2,2,3]
[1,1,2,2,4]=>[1,1,1,2,2,3]
[1,1,2,3,1,1,1]=>[4,1,2,3]
[1,1,2,3,1,2]=>[1,3,1,2,3]
[1,1,2,3,2,1]=>[2,2,1,2,3]
[1,1,2,3,3]=>[1,1,2,1,2,3]
[1,1,2,4,1,1]=>[3,1,1,2,3]
[1,1,2,4,2]=>[1,2,1,1,2,3]
[1,1,2,5,1]=>[2,1,1,1,2,3]
[1,1,2,6]=>[1,1,1,1,1,2,3]
[1,1,3,1,1,1,1,1]=>[6,1,3]
[1,1,3,1,1,1,2]=>[1,5,1,3]
[1,1,3,1,1,2,1]=>[2,4,1,3]
[1,1,3,1,1,3]=>[1,1,4,1,3]
[1,1,3,1,2,1,1]=>[3,3,1,3]
[1,1,3,1,2,2]=>[1,2,3,1,3]
[1,1,3,1,3,1]=>[2,1,3,1,3]
[1,1,3,1,4]=>[1,1,1,3,1,3]
[1,1,3,2,1,1,1]=>[4,2,1,3]
[1,1,3,2,1,2]=>[1,3,2,1,3]
[1,1,3,2,2,1]=>[2,2,2,1,3]
[1,1,3,2,3]=>[1,1,2,2,1,3]
[1,1,3,3,1,1]=>[3,1,2,1,3]
[1,1,3,3,2]=>[1,2,1,2,1,3]
[1,1,3,4,1]=>[2,1,1,2,1,3]
[1,1,3,5]=>[1,1,1,1,2,1,3]
[1,1,4,1,1,1,1]=>[5,1,1,3]
[1,1,4,1,1,2]=>[1,4,1,1,3]
[1,1,4,1,2,1]=>[2,3,1,1,3]
[1,1,4,1,3]=>[1,1,3,1,1,3]
[1,1,4,2,1,1]=>[3,2,1,1,3]
[1,1,4,2,2]=>[1,2,2,1,1,3]
[1,1,4,3,1]=>[2,1,2,1,1,3]
[1,1,4,4]=>[1,1,1,2,1,1,3]
[1,1,5,1,1,1]=>[4,1,1,1,3]
[1,1,5,1,2]=>[1,3,1,1,1,3]
[1,1,5,2,1]=>[2,2,1,1,1,3]
[1,1,5,3]=>[1,1,2,1,1,1,3]
[1,1,6,1,1]=>[3,1,1,1,1,3]
[1,1,6,2]=>[1,2,1,1,1,1,3]
[1,1,7,1]=>[2,1,1,1,1,1,3]
[1,1,8]=>[1,1,1,1,1,1,1,3]
[1,2,1,1,1,1,1,1,1]=>[8,2]
[1,2,1,1,1,1,1,2]=>[1,7,2]
[1,2,1,1,1,1,2,1]=>[2,6,2]
[1,2,1,1,1,1,3]=>[1,1,6,2]
[1,2,1,1,1,2,1,1]=>[3,5,2]
[1,2,1,1,1,2,2]=>[1,2,5,2]
[1,2,1,1,1,3,1]=>[2,1,5,2]
[1,2,1,1,1,4]=>[1,1,1,5,2]
[1,2,1,1,2,1,1,1]=>[4,4,2]
[1,2,1,1,2,1,2]=>[1,3,4,2]
[1,2,1,1,2,2,1]=>[2,2,4,2]
[1,2,1,1,2,3]=>[1,1,2,4,2]
[1,2,1,1,3,1,1]=>[3,1,4,2]
[1,2,1,1,3,2]=>[1,2,1,4,2]
[1,2,1,1,4,1]=>[2,1,1,4,2]
[1,2,1,1,5]=>[1,1,1,1,4,2]
[1,2,1,2,1,1,1,1]=>[5,3,2]
[1,2,1,2,1,1,2]=>[1,4,3,2]
[1,2,1,2,1,2,1]=>[2,3,3,2]
[1,2,1,2,1,3]=>[1,1,3,3,2]
[1,2,1,2,2,1,1]=>[3,2,3,2]
[1,2,1,2,2,2]=>[1,2,2,3,2]
[1,2,1,2,3,1]=>[2,1,2,3,2]
[1,2,1,2,4]=>[1,1,1,2,3,2]
[1,2,1,3,1,1,1]=>[4,1,3,2]
[1,2,1,3,1,2]=>[1,3,1,3,2]
[1,2,1,3,2,1]=>[2,2,1,3,2]
[1,2,1,3,3]=>[1,1,2,1,3,2]
[1,2,1,4,1,1]=>[3,1,1,3,2]
[1,2,1,4,2]=>[1,2,1,1,3,2]
[1,2,1,5,1]=>[2,1,1,1,3,2]
[1,2,1,6]=>[1,1,1,1,1,3,2]
[1,2,2,1,1,1,1,1]=>[6,2,2]
[1,2,2,1,1,1,2]=>[1,5,2,2]
[1,2,2,1,1,2,1]=>[2,4,2,2]
[1,2,2,1,1,3]=>[1,1,4,2,2]
[1,2,2,1,2,1,1]=>[3,3,2,2]
[1,2,2,1,2,2]=>[1,2,3,2,2]
[1,2,2,1,3,1]=>[2,1,3,2,2]
[1,2,2,1,4]=>[1,1,1,3,2,2]
[1,2,2,2,1,1,1]=>[4,2,2,2]
[1,2,2,2,1,2]=>[1,3,2,2,2]
[1,2,2,2,2,1]=>[2,2,2,2,2]
[1,2,2,2,3]=>[1,1,2,2,2,2]
[1,2,2,3,1,1]=>[3,1,2,2,2]
[1,2,2,3,2]=>[1,2,1,2,2,2]
[1,2,2,4,1]=>[2,1,1,2,2,2]
[1,2,2,5]=>[1,1,1,1,2,2,2]
[1,2,3,1,1,1,1]=>[5,1,2,2]
[1,2,3,1,1,2]=>[1,4,1,2,2]
[1,2,3,1,2,1]=>[2,3,1,2,2]
[1,2,3,1,3]=>[1,1,3,1,2,2]
[1,2,3,2,1,1]=>[3,2,1,2,2]
[1,2,3,2,2]=>[1,2,2,1,2,2]
[1,2,3,3,1]=>[2,1,2,1,2,2]
[1,2,3,4]=>[1,1,1,2,1,2,2]
[1,2,4,1,1,1]=>[4,1,1,2,2]
[1,2,4,1,2]=>[1,3,1,1,2,2]
[1,2,4,2,1]=>[2,2,1,1,2,2]
[1,2,4,3]=>[1,1,2,1,1,2,2]
[1,2,5,1,1]=>[3,1,1,1,2,2]
[1,2,5,2]=>[1,2,1,1,1,2,2]
[1,2,6,1]=>[2,1,1,1,1,2,2]
[1,2,7]=>[1,1,1,1,1,1,2,2]
[1,3,1,1,1,1,1,1]=>[7,1,2]
[1,3,1,1,1,1,2]=>[1,6,1,2]
[1,3,1,1,1,2,1]=>[2,5,1,2]
[1,3,1,1,1,3]=>[1,1,5,1,2]
[1,3,1,1,2,1,1]=>[3,4,1,2]
[1,3,1,1,2,2]=>[1,2,4,1,2]
[1,3,1,1,3,1]=>[2,1,4,1,2]
[1,3,1,1,4]=>[1,1,1,4,1,2]
[1,3,1,2,1,1,1]=>[4,3,1,2]
[1,3,1,2,1,2]=>[1,3,3,1,2]
[1,3,1,2,2,1]=>[2,2,3,1,2]
[1,3,1,2,3]=>[1,1,2,3,1,2]
[1,3,1,3,1,1]=>[3,1,3,1,2]
[1,3,1,3,2]=>[1,2,1,3,1,2]
[1,3,1,4,1]=>[2,1,1,3,1,2]
[1,3,1,5]=>[1,1,1,1,3,1,2]
[1,3,2,1,1,1,1]=>[5,2,1,2]
[1,3,2,1,1,2]=>[1,4,2,1,2]
[1,3,2,1,2,1]=>[2,3,2,1,2]
[1,3,2,1,3]=>[1,1,3,2,1,2]
[1,3,2,2,1,1]=>[3,2,2,1,2]
[1,3,2,2,2]=>[1,2,2,2,1,2]
[1,3,2,3,1]=>[2,1,2,2,1,2]
[1,3,2,4]=>[1,1,1,2,2,1,2]
[1,3,3,1,1,1]=>[4,1,2,1,2]
[1,3,3,1,2]=>[1,3,1,2,1,2]
[1,3,3,2,1]=>[2,2,1,2,1,2]
[1,3,3,3]=>[1,1,2,1,2,1,2]
[1,3,4,1,1]=>[3,1,1,2,1,2]
[1,3,4,2]=>[1,2,1,1,2,1,2]
[1,3,5,1]=>[2,1,1,1,2,1,2]
[1,3,6]=>[1,1,1,1,1,2,1,2]
[1,4,1,1,1,1,1]=>[6,1,1,2]
[1,4,1,1,1,2]=>[1,5,1,1,2]
[1,4,1,1,2,1]=>[2,4,1,1,2]
[1,4,1,1,3]=>[1,1,4,1,1,2]
[1,4,1,2,1,1]=>[3,3,1,1,2]
[1,4,1,2,2]=>[1,2,3,1,1,2]
[1,4,1,3,1]=>[2,1,3,1,1,2]
[1,4,1,4]=>[1,1,1,3,1,1,2]
[1,4,2,1,1,1]=>[4,2,1,1,2]
[1,4,2,1,2]=>[1,3,2,1,1,2]
[1,4,2,2,1]=>[2,2,2,1,1,2]
[1,4,2,3]=>[1,1,2,2,1,1,2]
[1,4,3,1,1]=>[3,1,2,1,1,2]
[1,4,3,2]=>[1,2,1,2,1,1,2]
[1,4,4,1]=>[2,1,1,2,1,1,2]
[1,4,5]=>[1,1,1,1,2,1,1,2]
[1,5,1,1,1,1]=>[5,1,1,1,2]
[1,5,1,1,2]=>[1,4,1,1,1,2]
[1,5,1,2,1]=>[2,3,1,1,1,2]
[1,5,1,3]=>[1,1,3,1,1,1,2]
[1,5,2,1,1]=>[3,2,1,1,1,2]
[1,5,2,2]=>[1,2,2,1,1,1,2]
[1,5,3,1]=>[2,1,2,1,1,1,2]
[1,5,4]=>[1,1,1,2,1,1,1,2]
[1,6,1,1,1]=>[4,1,1,1,1,2]
[1,6,1,2]=>[1,3,1,1,1,1,2]
[1,6,2,1]=>[2,2,1,1,1,1,2]
[1,6,3]=>[1,1,2,1,1,1,1,2]
[1,7,1,1]=>[3,1,1,1,1,1,2]
[1,7,2]=>[1,2,1,1,1,1,1,2]
[1,8,1]=>[2,1,1,1,1,1,1,2]
[1,9]=>[1,1,1,1,1,1,1,1,2]
[2,1,1,1,1,1,1,1,1]=>[9,1]
[2,1,1,1,1,1,1,2]=>[1,8,1]
[2,1,1,1,1,1,2,1]=>[2,7,1]
[2,1,1,1,1,1,3]=>[1,1,7,1]
[2,1,1,1,1,2,1,1]=>[3,6,1]
[2,1,1,1,1,2,2]=>[1,2,6,1]
[2,1,1,1,1,3,1]=>[2,1,6,1]
[2,1,1,1,1,4]=>[1,1,1,6,1]
[2,1,1,1,2,1,1,1]=>[4,5,1]
[2,1,1,1,2,1,2]=>[1,3,5,1]
[2,1,1,1,2,2,1]=>[2,2,5,1]
[2,1,1,1,2,3]=>[1,1,2,5,1]
[2,1,1,1,3,1,1]=>[3,1,5,1]
[2,1,1,1,3,2]=>[1,2,1,5,1]
[2,1,1,1,4,1]=>[2,1,1,5,1]
[2,1,1,1,5]=>[1,1,1,1,5,1]
[2,1,1,2,1,1,1,1]=>[5,4,1]
[2,1,1,2,1,1,2]=>[1,4,4,1]
[2,1,1,2,1,2,1]=>[2,3,4,1]
[2,1,1,2,1,3]=>[1,1,3,4,1]
[2,1,1,2,2,1,1]=>[3,2,4,1]
[2,1,1,2,2,2]=>[1,2,2,4,1]
[2,1,1,2,3,1]=>[2,1,2,4,1]
[2,1,1,2,4]=>[1,1,1,2,4,1]
[2,1,1,3,1,1,1]=>[4,1,4,1]
[2,1,1,3,1,2]=>[1,3,1,4,1]
[2,1,1,3,2,1]=>[2,2,1,4,1]
[2,1,1,3,3]=>[1,1,2,1,4,1]
[2,1,1,4,1,1]=>[3,1,1,4,1]
[2,1,1,4,2]=>[1,2,1,1,4,1]
[2,1,1,5,1]=>[2,1,1,1,4,1]
[2,1,1,6]=>[1,1,1,1,1,4,1]
[2,1,2,1,1,1,1,1]=>[6,3,1]
[2,1,2,1,1,1,2]=>[1,5,3,1]
[2,1,2,1,1,2,1]=>[2,4,3,1]
[2,1,2,1,1,3]=>[1,1,4,3,1]
[2,1,2,1,2,1,1]=>[3,3,3,1]
[2,1,2,1,2,2]=>[1,2,3,3,1]
[2,1,2,1,3,1]=>[2,1,3,3,1]
[2,1,2,1,4]=>[1,1,1,3,3,1]
[2,1,2,2,1,1,1]=>[4,2,3,1]
[2,1,2,2,1,2]=>[1,3,2,3,1]
[2,1,2,2,2,1]=>[2,2,2,3,1]
[2,1,2,2,3]=>[1,1,2,2,3,1]
[2,1,2,3,1,1]=>[3,1,2,3,1]
[2,1,2,3,2]=>[1,2,1,2,3,1]
[2,1,2,4,1]=>[2,1,1,2,3,1]
[2,1,2,5]=>[1,1,1,1,2,3,1]
[2,1,3,1,1,1,1]=>[5,1,3,1]
[2,1,3,1,1,2]=>[1,4,1,3,1]
[2,1,3,1,2,1]=>[2,3,1,3,1]
[2,1,3,1,3]=>[1,1,3,1,3,1]
[2,1,3,2,1,1]=>[3,2,1,3,1]
[2,1,3,2,2]=>[1,2,2,1,3,1]
[2,1,3,3,1]=>[2,1,2,1,3,1]
[2,1,3,4]=>[1,1,1,2,1,3,1]
[2,1,4,1,1,1]=>[4,1,1,3,1]
[2,1,4,1,2]=>[1,3,1,1,3,1]
[2,1,4,2,1]=>[2,2,1,1,3,1]
[2,1,4,3]=>[1,1,2,1,1,3,1]
[2,1,5,1,1]=>[3,1,1,1,3,1]
[2,1,5,2]=>[1,2,1,1,1,3,1]
[2,1,6,1]=>[2,1,1,1,1,3,1]
[2,1,7]=>[1,1,1,1,1,1,3,1]
[2,2,1,1,1,1,1,1]=>[7,2,1]
[2,2,1,1,1,1,2]=>[1,6,2,1]
[2,2,1,1,1,2,1]=>[2,5,2,1]
[2,2,1,1,1,3]=>[1,1,5,2,1]
[2,2,1,1,2,1,1]=>[3,4,2,1]
[2,2,1,1,2,2]=>[1,2,4,2,1]
[2,2,1,1,3,1]=>[2,1,4,2,1]
[2,2,1,1,4]=>[1,1,1,4,2,1]
[2,2,1,2,1,1,1]=>[4,3,2,1]
[2,2,1,2,1,2]=>[1,3,3,2,1]
[2,2,1,2,2,1]=>[2,2,3,2,1]
[2,2,1,2,3]=>[1,1,2,3,2,1]
[2,2,1,3,1,1]=>[3,1,3,2,1]
[2,2,1,3,2]=>[1,2,1,3,2,1]
[2,2,1,4,1]=>[2,1,1,3,2,1]
[2,2,1,5]=>[1,1,1,1,3,2,1]
[2,2,2,1,1,1,1]=>[5,2,2,1]
[2,2,2,1,1,2]=>[1,4,2,2,1]
[2,2,2,1,2,1]=>[2,3,2,2,1]
[2,2,2,1,3]=>[1,1,3,2,2,1]
[2,2,2,2,1,1]=>[3,2,2,2,1]
[2,2,2,2,2]=>[1,2,2,2,2,1]
[2,2,2,3,1]=>[2,1,2,2,2,1]
[2,2,2,4]=>[1,1,1,2,2,2,1]
[2,2,3,1,1,1]=>[4,1,2,2,1]
[2,2,3,1,2]=>[1,3,1,2,2,1]
[2,2,3,2,1]=>[2,2,1,2,2,1]
[2,2,3,3]=>[1,1,2,1,2,2,1]
[2,2,4,1,1]=>[3,1,1,2,2,1]
[2,2,4,2]=>[1,2,1,1,2,2,1]
[2,2,5,1]=>[2,1,1,1,2,2,1]
[2,2,6]=>[1,1,1,1,1,2,2,1]
[2,3,1,1,1,1,1]=>[6,1,2,1]
[2,3,1,1,1,2]=>[1,5,1,2,1]
[2,3,1,1,2,1]=>[2,4,1,2,1]
[2,3,1,1,3]=>[1,1,4,1,2,1]
[2,3,1,2,1,1]=>[3,3,1,2,1]
[2,3,1,2,2]=>[1,2,3,1,2,1]
[2,3,1,3,1]=>[2,1,3,1,2,1]
[2,3,1,4]=>[1,1,1,3,1,2,1]
[2,3,2,1,1,1]=>[4,2,1,2,1]
[2,3,2,1,2]=>[1,3,2,1,2,1]
[2,3,2,2,1]=>[2,2,2,1,2,1]
[2,3,2,3]=>[1,1,2,2,1,2,1]
[2,3,3,1,1]=>[3,1,2,1,2,1]
[2,3,3,2]=>[1,2,1,2,1,2,1]
[2,3,4,1]=>[2,1,1,2,1,2,1]
[2,3,5]=>[1,1,1,1,2,1,2,1]
[2,4,1,1,1,1]=>[5,1,1,2,1]
[2,4,1,1,2]=>[1,4,1,1,2,1]
[2,4,1,2,1]=>[2,3,1,1,2,1]
[2,4,1,3]=>[1,1,3,1,1,2,1]
[2,4,2,1,1]=>[3,2,1,1,2,1]
[2,4,2,2]=>[1,2,2,1,1,2,1]
[2,4,3,1]=>[2,1,2,1,1,2,1]
[2,4,4]=>[1,1,1,2,1,1,2,1]
[2,5,1,1,1]=>[4,1,1,1,2,1]
[2,5,1,2]=>[1,3,1,1,1,2,1]
[2,5,2,1]=>[2,2,1,1,1,2,1]
[2,5,3]=>[1,1,2,1,1,1,2,1]
[2,6,1,1]=>[3,1,1,1,1,2,1]
[2,6,2]=>[1,2,1,1,1,1,2,1]
[2,7,1]=>[2,1,1,1,1,1,2,1]
[2,8]=>[1,1,1,1,1,1,1,2,1]
[3,1,1,1,1,1,1,1]=>[8,1,1]
[3,1,1,1,1,1,2]=>[1,7,1,1]
[3,1,1,1,1,2,1]=>[2,6,1,1]
[3,1,1,1,1,3]=>[1,1,6,1,1]
[3,1,1,1,2,1,1]=>[3,5,1,1]
[3,1,1,1,2,2]=>[1,2,5,1,1]
[3,1,1,1,3,1]=>[2,1,5,1,1]
[3,1,1,1,4]=>[1,1,1,5,1,1]
[3,1,1,2,1,1,1]=>[4,4,1,1]
[3,1,1,2,1,2]=>[1,3,4,1,1]
[3,1,1,2,2,1]=>[2,2,4,1,1]
[3,1,1,2,3]=>[1,1,2,4,1,1]
[3,1,1,3,1,1]=>[3,1,4,1,1]
[3,1,1,3,2]=>[1,2,1,4,1,1]
[3,1,1,4,1]=>[2,1,1,4,1,1]
[3,1,1,5]=>[1,1,1,1,4,1,1]
[3,1,2,1,1,1,1]=>[5,3,1,1]
[3,1,2,1,1,2]=>[1,4,3,1,1]
[3,1,2,1,2,1]=>[2,3,3,1,1]
[3,1,2,1,3]=>[1,1,3,3,1,1]
[3,1,2,2,1,1]=>[3,2,3,1,1]
[3,1,2,2,2]=>[1,2,2,3,1,1]
[3,1,2,3,1]=>[2,1,2,3,1,1]
[3,1,2,4]=>[1,1,1,2,3,1,1]
[3,1,3,1,1,1]=>[4,1,3,1,1]
[3,1,3,1,2]=>[1,3,1,3,1,1]
[3,1,3,2,1]=>[2,2,1,3,1,1]
[3,1,3,3]=>[1,1,2,1,3,1,1]
[3,1,4,1,1]=>[3,1,1,3,1,1]
[3,1,4,2]=>[1,2,1,1,3,1,1]
[3,1,5,1]=>[2,1,1,1,3,1,1]
[3,1,6]=>[1,1,1,1,1,3,1,1]
[3,2,1,1,1,1,1]=>[6,2,1,1]
[3,2,1,1,1,2]=>[1,5,2,1,1]
[3,2,1,1,2,1]=>[2,4,2,1,1]
[3,2,1,1,3]=>[1,1,4,2,1,1]
[3,2,1,2,1,1]=>[3,3,2,1,1]
[3,2,1,2,2]=>[1,2,3,2,1,1]
[3,2,1,3,1]=>[2,1,3,2,1,1]
[3,2,1,4]=>[1,1,1,3,2,1,1]
[3,2,2,1,1,1]=>[4,2,2,1,1]
[3,2,2,1,2]=>[1,3,2,2,1,1]
[3,2,2,2,1]=>[2,2,2,2,1,1]
[3,2,2,3]=>[1,1,2,2,2,1,1]
[3,2,3,1,1]=>[3,1,2,2,1,1]
[3,2,3,2]=>[1,2,1,2,2,1,1]
[3,2,4,1]=>[2,1,1,2,2,1,1]
[3,2,5]=>[1,1,1,1,2,2,1,1]
[3,3,1,1,1,1]=>[5,1,2,1,1]
[3,3,1,1,2]=>[1,4,1,2,1,1]
[3,3,1,2,1]=>[2,3,1,2,1,1]
[3,3,1,3]=>[1,1,3,1,2,1,1]
[3,3,2,1,1]=>[3,2,1,2,1,1]
[3,3,2,2]=>[1,2,2,1,2,1,1]
[3,3,3,1]=>[2,1,2,1,2,1,1]
[3,3,4]=>[1,1,1,2,1,2,1,1]
[3,4,1,1,1]=>[4,1,1,2,1,1]
[3,4,1,2]=>[1,3,1,1,2,1,1]
[3,4,2,1]=>[2,2,1,1,2,1,1]
[3,4,3]=>[1,1,2,1,1,2,1,1]
[3,5,1,1]=>[3,1,1,1,2,1,1]
[3,5,2]=>[1,2,1,1,1,2,1,1]
[3,6,1]=>[2,1,1,1,1,2,1,1]
[3,7]=>[1,1,1,1,1,1,2,1,1]
[4,1,1,1,1,1,1]=>[7,1,1,1]
[4,1,1,1,1,2]=>[1,6,1,1,1]
[4,1,1,1,2,1]=>[2,5,1,1,1]
[4,1,1,1,3]=>[1,1,5,1,1,1]
[4,1,1,2,1,1]=>[3,4,1,1,1]
[4,1,1,2,2]=>[1,2,4,1,1,1]
[4,1,1,3,1]=>[2,1,4,1,1,1]
[4,1,1,4]=>[1,1,1,4,1,1,1]
[4,1,2,1,1,1]=>[4,3,1,1,1]
[4,1,2,1,2]=>[1,3,3,1,1,1]
[4,1,2,2,1]=>[2,2,3,1,1,1]
[4,1,2,3]=>[1,1,2,3,1,1,1]
[4,1,3,1,1]=>[3,1,3,1,1,1]
[4,1,3,2]=>[1,2,1,3,1,1,1]
[4,1,4,1]=>[2,1,1,3,1,1,1]
[4,1,5]=>[1,1,1,1,3,1,1,1]
[4,2,1,1,1,1]=>[5,2,1,1,1]
[4,2,1,1,2]=>[1,4,2,1,1,1]
[4,2,1,2,1]=>[2,3,2,1,1,1]
[4,2,1,3]=>[1,1,3,2,1,1,1]
[4,2,2,1,1]=>[3,2,2,1,1,1]
[4,2,2,2]=>[1,2,2,2,1,1,1]
[4,2,3,1]=>[2,1,2,2,1,1,1]
[4,2,4]=>[1,1,1,2,2,1,1,1]
[4,3,1,1,1]=>[4,1,2,1,1,1]
[4,3,1,2]=>[1,3,1,2,1,1,1]
[4,3,2,1]=>[2,2,1,2,1,1,1]
[4,3,3]=>[1,1,2,1,2,1,1,1]
[4,4,1,1]=>[3,1,1,2,1,1,1]
[4,4,2]=>[1,2,1,1,2,1,1,1]
[4,5,1]=>[2,1,1,1,2,1,1,1]
[4,6]=>[1,1,1,1,1,2,1,1,1]
[5,1,1,1,1,1]=>[6,1,1,1,1]
[5,1,1,1,2]=>[1,5,1,1,1,1]
[5,1,1,2,1]=>[2,4,1,1,1,1]
[5,1,1,3]=>[1,1,4,1,1,1,1]
[5,1,2,1,1]=>[3,3,1,1,1,1]
[5,1,2,2]=>[1,2,3,1,1,1,1]
[5,1,3,1]=>[2,1,3,1,1,1,1]
[5,1,4]=>[1,1,1,3,1,1,1,1]
[5,2,1,1,1]=>[4,2,1,1,1,1]
[5,2,1,2]=>[1,3,2,1,1,1,1]
[5,2,2,1]=>[2,2,2,1,1,1,1]
[5,2,3]=>[1,1,2,2,1,1,1,1]
[5,3,1,1]=>[3,1,2,1,1,1,1]
[5,3,2]=>[1,2,1,2,1,1,1,1]
[5,4,1]=>[2,1,1,2,1,1,1,1]
[5,5]=>[1,1,1,1,2,1,1,1,1]
[6,1,1,1,1]=>[5,1,1,1,1,1]
[6,1,1,2]=>[1,4,1,1,1,1,1]
[6,1,2,1]=>[2,3,1,1,1,1,1]
[6,1,3]=>[1,1,3,1,1,1,1,1]
[6,2,1,1]=>[3,2,1,1,1,1,1]
[6,2,2]=>[1,2,2,1,1,1,1,1]
[6,3,1]=>[2,1,2,1,1,1,1,1]
[6,4]=>[1,1,1,2,1,1,1,1,1]
[7,1,1,1]=>[4,1,1,1,1,1,1]
[7,1,2]=>[1,3,1,1,1,1,1,1]
[7,2,1]=>[2,2,1,1,1,1,1,1]
[7,3]=>[1,1,2,1,1,1,1,1,1]
[8,1,1]=>[3,1,1,1,1,1,1,1]
[8,2]=>[1,2,1,1,1,1,1,1,1]
[9,1]=>[2,1,1,1,1,1,1,1,1]
[10]=>[1,1,1,1,1,1,1,1,1,1]
[1,10]=>[1,1,1,1,1,1,1,1,1,2]
[1,8,1,1]=>[3,1,1,1,1,1,1,2]
[1,7,2,1]=>[2,2,1,1,1,1,1,2]
[1,6,3,1]=>[2,1,2,1,1,1,1,2]
[1,5,4,1]=>[2,1,1,2,1,1,1,2]
[1,4,5,1]=>[2,1,1,1,2,1,1,2]
[1,3,6,1]=>[2,1,1,1,1,2,1,2]
[1,2,7,1]=>[2,1,1,1,1,1,2,2]
[1,1,8,1]=>[2,1,1,1,1,1,1,3]
[10,1]=>[2,1,1,1,1,1,1,1,1,1]
[1,8,2]=>[1,2,1,1,1,1,1,1,2]
[1,7,1,2]=>[1,3,1,1,1,1,1,2]
[1,6,1,1,2]=>[1,4,1,1,1,1,2]
[1,5,1,1,1,2]=>[1,5,1,1,1,2]
[1,4,1,1,1,1,2]=>[1,6,1,1,2]
[1,3,1,1,1,1,1,2]=>[1,7,1,2]
[1,2,1,1,1,1,1,1,2]=>[1,8,2]
[1,1,1,1,1,1,1,1,1,2]=>[1,10]
[1,7,3]=>[1,1,2,1,1,1,1,1,2]
[1,6,2,2]=>[1,2,2,1,1,1,1,2]
[1,5,2,1,2]=>[1,3,2,1,1,1,2]
[1,4,2,1,1,2]=>[1,4,2,1,1,2]
[1,3,2,1,1,1,2]=>[1,5,2,1,2]
[1,2,2,1,1,1,1,2]=>[1,6,2,2]
[1,1,2,1,1,1,1,1,2]=>[1,7,3]
[1,2,2,2,2,2]=>[1,2,2,2,2,2]
[1,2,2,2,1,3]=>[1,1,3,2,2,2]
[1,2,2,1,3,2]=>[1,2,1,3,2,2]
[1,2,2,1,2,3]=>[1,1,2,3,2,2]
[1,2,2,1,1,4]=>[1,1,1,4,2,2]
[1,2,1,3,2,2]=>[1,2,2,1,3,2]
[1,2,1,3,1,3]=>[1,1,3,1,3,2]
[1,2,1,2,3,2]=>[1,2,1,2,3,2]
[1,2,1,2,2,3]=>[1,1,2,2,3,2]
[1,2,1,2,1,4]=>[1,1,1,3,3,2]
[1,2,1,1,4,2]=>[1,2,1,1,4,2]
[1,2,1,1,3,3]=>[1,1,2,1,4,2]
[1,2,1,1,2,4]=>[1,1,1,2,4,2]
[1,2,1,1,1,5]=>[1,1,1,1,5,2]
[1,1,3,2,2,2]=>[1,2,2,2,1,3]
[1,1,3,2,1,3]=>[1,1,3,2,1,3]
[1,1,3,1,3,2]=>[1,2,1,3,1,3]
[1,1,3,1,2,3]=>[1,1,2,3,1,3]
[1,1,3,1,1,4]=>[1,1,1,4,1,3]
[1,1,2,3,2,2]=>[1,2,2,1,2,3]
[1,1,2,3,1,3]=>[1,1,3,1,2,3]
[1,1,2,2,3,2]=>[1,2,1,2,2,3]
[1,1,2,2,2,3]=>[1,1,2,2,2,3]
[1,1,2,2,1,4]=>[1,1,1,3,2,3]
[1,1,2,1,4,2]=>[1,2,1,1,3,3]
[1,1,2,1,3,3]=>[1,1,2,1,3,3]
[1,1,2,1,2,4]=>[1,1,1,2,3,3]
[1,1,2,1,1,5]=>[1,1,1,1,4,3]
[1,1,1,4,2,2]=>[1,2,2,1,1,4]
[1,1,1,4,1,3]=>[1,1,3,1,1,4]
[1,1,1,3,3,2]=>[1,2,1,2,1,4]
[1,1,1,3,2,3]=>[1,1,2,2,1,4]
[1,1,1,3,1,4]=>[1,1,1,3,1,4]
[1,1,1,2,4,2]=>[1,2,1,1,2,4]
[1,1,1,2,3,3]=>[1,1,2,1,2,4]
[1,1,1,2,2,4]=>[1,1,1,2,2,4]
[1,1,1,2,1,5]=>[1,1,1,1,3,4]
[1,1,1,1,5,2]=>[1,2,1,1,1,5]
[1,1,1,1,4,3]=>[1,1,2,1,1,5]
[1,1,1,1,3,4]=>[1,1,1,2,1,5]
[1,1,1,1,2,5]=>[1,1,1,1,2,5]
[1,1,1,1,1,6]=>[1,1,1,1,1,6]
[11]=>[1,1,1,1,1,1,1,1,1,1,1]
[2,9]=>[1,1,1,1,1,1,1,1,2,1]
[1,1,1,1,1,1,1,1,1,1,1,1]=>[12]
[1,1,1,1,1,1,1,1,2,2]=>[1,2,9]
[1,1,1,1,1,1,2,2,1,1]=>[3,2,7]
[1,1,1,1,1,1,2,1,1,2]=>[1,4,7]
[1,1,1,1,1,1,3,3]=>[1,1,2,1,7]
[1,1,1,1,2,2,1,1,1,1]=>[5,2,5]
[1,1,1,1,2,2,2,2]=>[1,2,2,2,5]
[1,1,1,1,2,1,1,2,1,1]=>[3,4,5]
[1,1,1,1,2,1,1,1,1,2]=>[1,6,5]
[1,1,1,1,2,1,2,3]=>[1,1,2,3,5]
[1,1,1,1,3,3,1,1]=>[3,1,2,1,5]
[1,1,1,1,3,2,1,2]=>[1,3,2,1,5]
[1,1,1,1,3,1,1,3]=>[1,1,4,1,5]
[1,1,1,1,4,4]=>[1,1,1,2,1,1,5]
[1,1,2,2,1,1,1,1,1,1]=>[7,2,3]
[1,1,2,2,1,1,2,2]=>[1,2,4,2,3]
[1,1,2,2,2,2,1,1]=>[3,2,2,2,3]
[1,1,2,2,2,1,1,2]=>[1,4,2,2,3]
[1,1,2,2,3,3]=>[1,1,2,1,2,2,3]
[1,1,2,1,1,2,1,1,1,1]=>[5,4,3]
[1,1,2,1,1,2,2,2]=>[1,2,2,4,3]
[1,1,2,1,1,1,1,2,1,1]=>[3,6,3]
[1,1,2,1,1,1,1,1,1,2]=>[1,8,3]
[1,1,2,1,1,1,2,3]=>[1,1,2,5,3]
[1,1,2,1,2,3,1,1]=>[3,1,2,3,3]
[1,1,2,1,2,2,1,2]=>[1,3,2,3,3]
[1,1,2,1,2,1,1,3]=>[1,1,4,3,3]
[1,1,2,1,3,4]=>[1,1,1,2,1,3,3]
[1,1,3,3,1,1,1,1]=>[5,1,2,1,3]
[1,1,3,3,2,2]=>[1,2,2,1,2,1,3]
[1,1,3,2,1,2,1,1]=>[3,3,2,1,3]
[1,1,3,2,1,1,1,2]=>[1,5,2,1,3]
[1,1,3,2,2,3]=>[1,1,2,2,2,1,3]
[1,1,3,1,1,3,1,1]=>[3,1,4,1,3]
[1,1,3,1,1,2,1,2]=>[1,3,4,1,3]
[1,1,3,1,1,1,1,3]=>[1,1,6,1,3]
[1,1,3,1,2,4]=>[1,1,1,2,3,1,3]
[1,1,4,4,1,1]=>[3,1,1,2,1,1,3]
[1,1,4,3,1,2]=>[1,3,1,2,1,1,3]
[1,1,4,2,1,3]=>[1,1,3,2,1,1,3]
[1,1,4,1,1,4]=>[1,1,1,4,1,1,3]
[1,1,5,5]=>[1,1,1,1,2,1,1,1,3]
[2,2,1,1,1,1,1,1,1,1]=>[9,2,1]
[2,2,1,1,1,1,2,2]=>[1,2,6,2,1]
[2,2,1,1,2,2,1,1]=>[3,2,4,2,1]
[2,2,1,1,2,1,1,2]=>[1,4,4,2,1]
[2,2,1,1,3,3]=>[1,1,2,1,4,2,1]
[2,2,2,2,1,1,1,1]=>[5,2,2,2,1]
[2,2,2,2,2,2]=>[1,2,2,2,2,2,1]
[2,2,2,1,1,2,1,1]=>[3,4,2,2,1]
[2,2,2,1,1,1,1,2]=>[1,6,2,2,1]
[2,2,2,1,2,3]=>[1,1,2,3,2,2,1]
[2,2,3,3,1,1]=>[3,1,2,1,2,2,1]
[2,2,3,2,1,2]=>[1,3,2,1,2,2,1]
[2,2,3,1,1,3]=>[1,1,4,1,2,2,1]
[2,2,4,4]=>[1,1,1,2,1,1,2,2,1]
[2,1,1,2,1,1,1,1,1,1]=>[7,4,1]
[2,1,1,2,1,1,2,2]=>[1,2,4,4,1]
[2,1,1,2,2,2,1,1]=>[3,2,2,4,1]
[2,1,1,2,2,1,1,2]=>[1,4,2,4,1]
[2,1,1,2,3,3]=>[1,1,2,1,2,4,1]
[2,1,1,1,1,2,1,1,1,1]=>[5,6,1]
[2,1,1,1,1,2,2,2]=>[1,2,2,6,1]
[2,1,1,1,1,1,1,2,1,1]=>[3,8,1]
[2,1,1,1,1,1,1,1,1,2]=>[1,10,1]
[2,1,1,1,1,1,2,3]=>[1,1,2,7,1]
[2,1,1,1,2,3,1,1]=>[3,1,2,5,1]
[2,1,1,1,2,2,1,2]=>[1,3,2,5,1]
[2,1,1,1,2,1,1,3]=>[1,1,4,5,1]
[2,1,1,1,3,4]=>[1,1,1,2,1,5,1]
[2,1,2,3,1,1,1,1]=>[5,1,2,3,1]
[2,1,2,3,2,2]=>[1,2,2,1,2,3,1]
[2,1,2,2,1,2,1,1]=>[3,3,2,3,1]
[2,1,2,2,1,1,1,2]=>[1,5,2,3,1]
[2,1,2,2,2,3]=>[1,1,2,2,2,3,1]
[2,1,2,1,1,3,1,1]=>[3,1,4,3,1]
[2,1,2,1,1,2,1,2]=>[1,3,4,3,1]
[2,1,2,1,1,1,1,3]=>[1,1,6,3,1]
[2,1,2,1,2,4]=>[1,1,1,2,3,3,1]
[2,1,3,4,1,1]=>[3,1,1,2,1,3,1]
[2,1,3,3,1,2]=>[1,3,1,2,1,3,1]
[2,1,3,2,1,3]=>[1,1,3,2,1,3,1]
[2,1,3,1,1,4]=>[1,1,1,4,1,3,1]
[2,1,4,5]=>[1,1,1,1,2,1,1,3,1]
[3,3,1,1,1,1,1,1]=>[7,1,2,1,1]
[3,3,1,1,2,2]=>[1,2,4,1,2,1,1]
[3,3,2,2,1,1]=>[3,2,2,1,2,1,1]
[3,3,2,1,1,2]=>[1,4,2,1,2,1,1]
[3,3,3,3]=>[1,1,2,1,2,1,2,1,1]
[3,2,1,2,1,1,1,1]=>[5,3,2,1,1]
[3,2,1,2,2,2]=>[1,2,2,3,2,1,1]
[3,2,1,1,1,2,1,1]=>[3,5,2,1,1]
[3,2,1,1,1,1,1,2]=>[1,7,2,1,1]
[3,2,1,1,2,3]=>[1,1,2,4,2,1,1]
[3,2,2,3,1,1]=>[3,1,2,2,2,1,1]
[3,2,2,2,1,2]=>[1,3,2,2,2,1,1]
[3,2,2,1,1,3]=>[1,1,4,2,2,1,1]
[3,2,3,4]=>[1,1,1,2,1,2,2,1,1]
[3,1,1,3,1,1,1,1]=>[5,1,4,1,1]
[3,1,1,3,2,2]=>[1,2,2,1,4,1,1]
[3,1,1,2,1,2,1,1]=>[3,3,4,1,1]
[3,1,1,2,1,1,1,2]=>[1,5,4,1,1]
[3,1,1,2,2,3]=>[1,1,2,2,4,1,1]
[3,1,1,1,1,3,1,1]=>[3,1,6,1,1]
[3,1,1,1,1,2,1,2]=>[1,3,6,1,1]
[3,1,1,1,1,1,1,3]=>[1,1,8,1,1]
[3,1,1,1,2,4]=>[1,1,1,2,5,1,1]
[3,1,2,4,1,1]=>[3,1,1,2,3,1,1]
[3,1,2,3,1,2]=>[1,3,1,2,3,1,1]
[3,1,2,2,1,3]=>[1,1,3,2,3,1,1]
[3,1,2,1,1,4]=>[1,1,1,4,3,1,1]
[3,1,3,5]=>[1,1,1,1,2,1,3,1,1]
[4,4,1,1,1,1]=>[5,1,1,2,1,1,1]
[4,4,2,2]=>[1,2,2,1,1,2,1,1,1]
[4,3,1,2,1,1]=>[3,3,1,2,1,1,1]
[4,3,1,1,1,2]=>[1,5,1,2,1,1,1]
[4,3,2,3]=>[1,1,2,2,1,2,1,1,1]
[4,2,1,3,1,1]=>[3,1,3,2,1,1,1]
[4,2,1,2,1,2]=>[1,3,3,2,1,1,1]
[4,2,1,1,1,3]=>[1,1,5,2,1,1,1]
[4,2,2,4]=>[1,1,1,2,2,2,1,1,1]
[4,1,1,4,1,1]=>[3,1,1,4,1,1,1]
[4,1,1,3,1,2]=>[1,3,1,4,1,1,1]
[4,1,1,2,1,3]=>[1,1,3,4,1,1,1]
[4,1,1,1,1,4]=>[1,1,1,6,1,1,1]
[4,1,2,5]=>[1,1,1,1,2,3,1,1,1]
[5,5,1,1]=>[3,1,1,1,2,1,1,1,1]
[5,4,1,2]=>[1,3,1,1,2,1,1,1,1]
[5,3,1,3]=>[1,1,3,1,2,1,1,1,1]
[5,2,1,4]=>[1,1,1,3,2,1,1,1,1]
[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]=>[1,2,1,2,2,2,2]
[1,2,2,3,3,1]=>[2,1,2,1,2,2,2]
[1,2,2,3,2,2]=>[1,2,2,1,2,2,2]
[1,2,2,4,3]=>[1,1,2,1,1,2,2,2]
[1,2,3,3,2,1]=>[2,2,1,2,1,2,2]
[1,2,3,4,2]=>[1,2,1,1,2,1,2,2]
[1,2,3,2,3,1]=>[2,1,2,2,1,2,2]
[1,2,3,2,2,2]=>[1,2,2,2,1,2,2]
[1,2,3,3,3]=>[1,1,2,1,2,1,2,2]
[1,2,4,4,1]=>[2,1,1,2,1,1,2,2]
[1,2,4,3,2]=>[1,2,1,2,1,1,2,2]
[1,2,4,2,3]=>[1,1,2,2,1,1,2,2]
[1,2,5,4]=>[1,1,1,2,1,1,1,2,2]
[1,3,3,2,2,1]=>[2,2,2,1,2,1,2]
[1,3,3,3,2]=>[1,2,1,2,1,2,1,2]
[1,3,4,3,1]=>[2,1,2,1,1,2,1,2]
[1,3,4,2,2]=>[1,2,2,1,1,2,1,2]
[1,3,5,3]=>[1,1,2,1,1,1,2,1,2]
[1,3,2,3,2,1]=>[2,2,1,2,2,1,2]
[1,3,2,4,2]=>[1,2,1,1,2,2,1,2]
[1,3,2,2,3,1]=>[2,1,2,2,2,1,2]
[1,3,2,2,2,2]=>[1,2,2,2,2,1,2]
[1,3,2,3,3]=>[1,1,2,1,2,2,1,2]
[1,3,3,4,1]=>[2,1,1,2,1,2,1,2]
[1,3,3,2,3]=>[1,1,2,2,1,2,1,2]
[1,3,4,4]=>[1,1,1,2,1,1,2,1,2]
[1,4,4,2,1]=>[2,2,1,1,2,1,1,2]
[1,4,5,2]=>[1,2,1,1,1,2,1,1,2]
[1,4,3,3,1]=>[2,1,2,1,2,1,1,2]
[1,4,3,2,2]=>[1,2,2,1,2,1,1,2]
[1,4,4,3]=>[1,1,2,1,1,2,1,1,2]
[1,4,2,4,1]=>[2,1,1,2,2,1,1,2]
[1,4,2,3,2]=>[1,2,1,2,2,1,1,2]
[1,4,2,2,3]=>[1,1,2,2,2,1,1,2]
[1,4,3,4]=>[1,1,1,2,1,2,1,1,2]
[1,5,5,1]=>[2,1,1,1,2,1,1,1,2]
[1,5,4,2]=>[1,2,1,1,2,1,1,1,2]
[1,5,3,3]=>[1,1,2,1,2,1,1,1,2]
[1,5,2,4]=>[1,1,1,2,2,1,1,1,2]
[1,6,5]=>[1,1,1,1,2,1,1,1,1,2]
[2,3,2,2,2,1]=>[2,2,2,2,1,2,1]
[2,3,2,3,2]=>[1,2,1,2,2,1,2,1]
[2,3,3,3,1]=>[2,1,2,1,2,1,2,1]
[2,3,3,2,2]=>[1,2,2,1,2,1,2,1]
[2,3,4,3]=>[1,1,2,1,1,2,1,2,1]
[2,4,3,2,1]=>[2,2,1,2,1,1,2,1]
[2,4,4,2]=>[1,2,1,1,2,1,1,2,1]
[2,4,2,3,1]=>[2,1,2,2,1,1,2,1]
[2,4,2,2,2]=>[1,2,2,2,1,1,2,1]
[2,4,3,3]=>[1,1,2,1,2,1,1,2,1]
[2,5,4,1]=>[2,1,1,2,1,1,1,2,1]
[2,5,3,2]=>[1,2,1,2,1,1,1,2,1]
[2,5,2,3]=>[1,1,2,2,1,1,1,2,1]
[2,6,4]=>[1,1,1,2,1,1,1,1,2,1]
[2,2,3,2,2,1]=>[2,2,2,1,2,2,1]
[2,2,3,3,2]=>[1,2,1,2,1,2,2,1]
[2,2,4,3,1]=>[2,1,2,1,1,2,2,1]
[2,2,4,2,2]=>[1,2,2,1,1,2,2,1]
[2,2,5,3]=>[1,1,2,1,1,1,2,2,1]
[2,2,2,3,2,1]=>[2,2,1,2,2,2,1]
[2,2,2,4,2]=>[1,2,1,1,2,2,2,1]
[2,2,2,2,3,1]=>[2,1,2,2,2,2,1]
[2,2,2,3,3]=>[1,1,2,1,2,2,2,1]
[2,2,3,4,1]=>[2,1,1,2,1,2,2,1]
[2,2,3,2,3]=>[1,1,2,2,1,2,2,1]
[2,3,4,2,1]=>[2,2,1,1,2,1,2,1]
[2,3,5,2]=>[1,2,1,1,1,2,1,2,1]
[2,3,2,4,1]=>[2,1,1,2,2,1,2,1]
[2,3,2,2,3]=>[1,1,2,2,2,1,2,1]
[2,3,3,4]=>[1,1,1,2,1,2,1,2,1]
[2,4,5,1]=>[2,1,1,1,2,1,1,2,1]
[2,4,2,4]=>[1,1,1,2,2,1,1,2,1]
[2,5,5]=>[1,1,1,1,2,1,1,1,2,1]
[3,4,2,2,1]=>[2,2,2,1,1,2,1,1]
[3,4,3,2]=>[1,2,1,2,1,1,2,1,1]
[3,5,3,1]=>[2,1,2,1,1,1,2,1,1]
[3,5,2,2]=>[1,2,2,1,1,1,2,1,1]
[3,6,3]=>[1,1,2,1,1,1,1,2,1,1]
[3,3,3,2,1]=>[2,2,1,2,1,2,1,1]
[3,3,4,2]=>[1,2,1,1,2,1,2,1,1]
[3,3,2,3,1]=>[2,1,2,2,1,2,1,1]
[3,3,2,2,2]=>[1,2,2,2,1,2,1,1]
[3,4,4,1]=>[2,1,1,2,1,1,2,1,1]
[3,4,2,3]=>[1,1,2,2,1,1,2,1,1]
[3,5,4]=>[1,1,1,2,1,1,1,2,1,1]
[3,2,4,2,1]=>[2,2,1,1,2,2,1,1]
[3,2,5,2]=>[1,2,1,1,1,2,2,1,1]
[3,2,3,3,1]=>[2,1,2,1,2,2,1,1]
[3,2,3,2,2]=>[1,2,2,1,2,2,1,1]
[3,2,4,3]=>[1,1,2,1,1,2,2,1,1]
[3,2,2,4,1]=>[2,1,1,2,2,2,1,1]
[3,2,2,3,2]=>[1,2,1,2,2,2,1,1]
[3,2,2,2,3]=>[1,1,2,2,2,2,1,1]
[3,3,5,1]=>[2,1,1,1,2,1,2,1,1]
[3,3,2,4]=>[1,1,1,2,2,1,2,1,1]
[3,4,5]=>[1,1,1,1,2,1,1,2,1,1]
[4,5,2,1]=>[2,2,1,1,1,2,1,1,1]
[4,6,2]=>[1,2,1,1,1,1,2,1,1,1]
[4,4,3,1]=>[2,1,2,1,1,2,1,1,1]
[4,5,3]=>[1,1,2,1,1,1,2,1,1,1]
[4,3,4,1]=>[2,1,1,2,1,2,1,1,1]
[4,3,3,2]=>[1,2,1,2,1,2,1,1,1]
[4,4,4]=>[1,1,1,2,1,1,2,1,1,1]
[4,2,5,1]=>[2,1,1,1,2,2,1,1,1]
[4,2,4,2]=>[1,2,1,1,2,2,1,1,1]
[4,2,3,3]=>[1,1,2,1,2,2,1,1,1]
[4,3,5]=>[1,1,1,1,2,1,2,1,1,1]
[5,6,1]=>[2,1,1,1,1,2,1,1,1,1]
[5,5,2]=>[1,2,1,1,1,2,1,1,1,1]
[5,4,3]=>[1,1,2,1,1,2,1,1,1,1]
[5,3,4]=>[1,1,1,2,1,2,1,1,1,1]
[5,2,5]=>[1,1,1,1,2,2,1,1,1,1]
[1,11]=>[1,1,1,1,1,1,1,1,1,1,2]
[1,9,2]=>[1,2,1,1,1,1,1,1,1,2]
[1,8,1,2]=>[1,3,1,1,1,1,1,1,2]
[1,7,1,1,2]=>[1,4,1,1,1,1,1,2]
[1,6,1,1,1,2]=>[1,5,1,1,1,1,2]
[1,5,1,1,1,1,2]=>[1,6,1,1,1,2]
[1,4,1,1,1,1,1,2]=>[1,7,1,1,2]
[1,3,1,1,1,1,1,1,2]=>[1,8,1,2]
[1,2,1,1,1,1,1,1,1,2]=>[1,9,2]
[1,1,1,1,1,1,1,1,1,1,2]=>[1,11]
[1,2,2,2,2,2,2]=>[1,2,2,2,2,2,2]
[1,2,2,2,2,1,3]=>[1,1,3,2,2,2,2]
[1,2,2,2,1,3,2]=>[1,2,1,3,2,2,2]
[1,2,2,2,1,2,3]=>[1,1,2,3,2,2,2]
[1,2,2,2,1,1,4]=>[1,1,1,4,2,2,2]
[1,2,2,1,3,2,2]=>[1,2,2,1,3,2,2]
[1,2,2,1,3,1,3]=>[1,1,3,1,3,2,2]
[1,2,2,1,2,3,2]=>[1,2,1,2,3,2,2]
[1,2,2,1,2,2,3]=>[1,1,2,2,3,2,2]
[1,2,2,1,2,1,4]=>[1,1,1,3,3,2,2]
[1,2,2,1,1,4,2]=>[1,2,1,1,4,2,2]
[1,2,2,1,1,3,3]=>[1,1,2,1,4,2,2]
[1,2,2,1,1,2,4]=>[1,1,1,2,4,2,2]
[1,2,2,1,1,1,5]=>[1,1,1,1,5,2,2]
[1,2,1,3,2,2,2]=>[1,2,2,2,1,3,2]
[1,2,1,3,2,1,3]=>[1,1,3,2,1,3,2]
[1,2,1,3,1,3,2]=>[1,2,1,3,1,3,2]
[1,2,1,3,1,2,3]=>[1,1,2,3,1,3,2]
[1,2,1,3,1,1,4]=>[1,1,1,4,1,3,2]
[1,2,1,2,3,2,2]=>[1,2,2,1,2,3,2]
[1,2,1,2,3,1,3]=>[1,1,3,1,2,3,2]
[1,2,1,2,2,3,2]=>[1,2,1,2,2,3,2]
[1,2,1,2,2,2,3]=>[1,1,2,2,2,3,2]
[1,2,1,2,2,1,4]=>[1,1,1,3,2,3,2]
[1,2,1,2,1,4,2]=>[1,2,1,1,3,3,2]
[1,2,1,2,1,3,3]=>[1,1,2,1,3,3,2]
[1,2,1,2,1,2,4]=>[1,1,1,2,3,3,2]
[1,2,1,2,1,1,5]=>[1,1,1,1,4,3,2]
[1,2,1,1,4,2,2]=>[1,2,2,1,1,4,2]
[1,2,1,1,4,1,3]=>[1,1,3,1,1,4,2]
[1,2,1,1,3,3,2]=>[1,2,1,2,1,4,2]
[1,2,1,1,3,2,3]=>[1,1,2,2,1,4,2]
[1,2,1,1,3,1,4]=>[1,1,1,3,1,4,2]
[1,2,1,1,2,4,2]=>[1,2,1,1,2,4,2]
[1,2,1,1,2,3,3]=>[1,1,2,1,2,4,2]
[1,2,1,1,2,2,4]=>[1,1,1,2,2,4,2]
[1,2,1,1,2,1,5]=>[1,1,1,1,3,4,2]
[1,2,1,1,1,5,2]=>[1,2,1,1,1,5,2]
[1,2,1,1,1,4,3]=>[1,1,2,1,1,5,2]
[1,2,1,1,1,3,4]=>[1,1,1,2,1,5,2]
[1,2,1,1,1,2,5]=>[1,1,1,1,2,5,2]
[1,2,1,1,1,1,6]=>[1,1,1,1,1,6,2]
[1,1,3,2,2,2,2]=>[1,2,2,2,2,1,3]
[1,1,3,2,2,1,3]=>[1,1,3,2,2,1,3]
[1,1,3,2,1,3,2]=>[1,2,1,3,2,1,3]
[1,1,3,2,1,2,3]=>[1,1,2,3,2,1,3]
[1,1,3,2,1,1,4]=>[1,1,1,4,2,1,3]
[1,1,3,1,3,2,2]=>[1,2,2,1,3,1,3]
[1,1,3,1,3,1,3]=>[1,1,3,1,3,1,3]
[1,1,3,1,2,3,2]=>[1,2,1,2,3,1,3]
[1,1,3,1,2,2,3]=>[1,1,2,2,3,1,3]
[1,1,3,1,2,1,4]=>[1,1,1,3,3,1,3]
[1,1,3,1,1,4,2]=>[1,2,1,1,4,1,3]
[1,1,3,1,1,3,3]=>[1,1,2,1,4,1,3]
[1,1,3,1,1,2,4]=>[1,1,1,2,4,1,3]
[1,1,3,1,1,1,5]=>[1,1,1,1,5,1,3]
[1,1,2,3,2,2,2]=>[1,2,2,2,1,2,3]
[1,1,2,3,2,1,3]=>[1,1,3,2,1,2,3]
[1,1,2,3,1,3,2]=>[1,2,1,3,1,2,3]
[1,1,2,3,1,2,3]=>[1,1,2,3,1,2,3]
[1,1,2,3,1,1,4]=>[1,1,1,4,1,2,3]
[1,1,2,2,3,2,2]=>[1,2,2,1,2,2,3]
[1,1,2,2,3,1,3]=>[1,1,3,1,2,2,3]
[1,1,2,2,2,3,2]=>[1,2,1,2,2,2,3]
[1,1,2,2,2,2,3]=>[1,1,2,2,2,2,3]
[1,1,2,2,2,1,4]=>[1,1,1,3,2,2,3]
[1,1,2,2,1,4,2]=>[1,2,1,1,3,2,3]
[1,1,2,2,1,3,3]=>[1,1,2,1,3,2,3]
[1,1,2,2,1,2,4]=>[1,1,1,2,3,2,3]
[1,1,2,2,1,1,5]=>[1,1,1,1,4,2,3]
[1,1,2,1,4,2,2]=>[1,2,2,1,1,3,3]
[1,1,2,1,4,1,3]=>[1,1,3,1,1,3,3]
[1,1,2,1,3,3,2]=>[1,2,1,2,1,3,3]
[1,1,2,1,3,2,3]=>[1,1,2,2,1,3,3]
[1,1,2,1,3,1,4]=>[1,1,1,3,1,3,3]
[1,1,2,1,2,4,2]=>[1,2,1,1,2,3,3]
[1,1,2,1,2,3,3]=>[1,1,2,1,2,3,3]
[1,1,2,1,2,2,4]=>[1,1,1,2,2,3,3]
[1,1,2,1,2,1,5]=>[1,1,1,1,3,3,3]
[1,1,2,1,1,5,2]=>[1,2,1,1,1,4,3]
[1,1,2,1,1,4,3]=>[1,1,2,1,1,4,3]
[1,1,2,1,1,3,4]=>[1,1,1,2,1,4,3]
[1,1,2,1,1,2,5]=>[1,1,1,1,2,4,3]
[1,1,2,1,1,1,6]=>[1,1,1,1,1,5,3]
[1,1,1,4,2,2,2]=>[1,2,2,2,1,1,4]
[1,1,1,4,2,1,3]=>[1,1,3,2,1,1,4]
[1,1,1,4,1,3,2]=>[1,2,1,3,1,1,4]
[1,1,1,4,1,2,3]=>[1,1,2,3,1,1,4]
[1,1,1,4,1,1,4]=>[1,1,1,4,1,1,4]
[1,1,1,3,3,2,2]=>[1,2,2,1,2,1,4]
[1,1,1,3,3,1,3]=>[1,1,3,1,2,1,4]
[1,1,1,3,2,3,2]=>[1,2,1,2,2,1,4]
[1,1,1,3,2,2,3]=>[1,1,2,2,2,1,4]
[1,1,1,3,2,1,4]=>[1,1,1,3,2,1,4]
[1,1,1,3,1,4,2]=>[1,2,1,1,3,1,4]
[1,1,1,3,1,3,3]=>[1,1,2,1,3,1,4]
[1,1,1,3,1,2,4]=>[1,1,1,2,3,1,4]
[1,1,1,3,1,1,5]=>[1,1,1,1,4,1,4]
[1,1,1,2,4,2,2]=>[1,2,2,1,1,2,4]
[1,1,1,2,4,1,3]=>[1,1,3,1,1,2,4]
[1,1,1,2,3,3,2]=>[1,2,1,2,1,2,4]
[1,1,1,2,3,2,3]=>[1,1,2,2,1,2,4]
[1,1,1,2,3,1,4]=>[1,1,1,3,1,2,4]
[1,1,1,2,2,4,2]=>[1,2,1,1,2,2,4]
[1,1,1,2,2,3,3]=>[1,1,2,1,2,2,4]
[1,1,1,2,2,2,4]=>[1,1,1,2,2,2,4]
[1,1,1,2,2,1,5]=>[1,1,1,1,3,2,4]
[1,1,1,2,1,5,2]=>[1,2,1,1,1,3,4]
[1,1,1,2,1,4,3]=>[1,1,2,1,1,3,4]
[1,1,1,2,1,3,4]=>[1,1,1,2,1,3,4]
[1,1,1,2,1,2,5]=>[1,1,1,1,2,3,4]
[1,1,1,2,1,1,6]=>[1,1,1,1,1,4,4]
[1,1,1,1,5,2,2]=>[1,2,2,1,1,1,5]
[1,1,1,1,5,1,3]=>[1,1,3,1,1,1,5]
[1,1,1,1,4,3,2]=>[1,2,1,2,1,1,5]
[1,1,1,1,4,2,3]=>[1,1,2,2,1,1,5]
[1,1,1,1,4,1,4]=>[1,1,1,3,1,1,5]
[1,1,1,1,3,4,2]=>[1,2,1,1,2,1,5]
[1,1,1,1,3,3,3]=>[1,1,2,1,2,1,5]
[1,1,1,1,3,2,4]=>[1,1,1,2,2,1,5]
[1,1,1,1,3,1,5]=>[1,1,1,1,3,1,5]
[1,1,1,1,2,5,2]=>[1,2,1,1,1,2,5]
[1,1,1,1,2,4,3]=>[1,1,2,1,1,2,5]
[1,1,1,1,2,3,4]=>[1,1,1,2,1,2,5]
[1,1,1,1,2,2,5]=>[1,1,1,1,2,2,5]
[1,1,1,1,2,1,6]=>[1,1,1,1,1,3,5]
[1,1,1,1,1,6,2]=>[1,2,1,1,1,1,6]
[1,1,1,1,1,5,3]=>[1,1,2,1,1,1,6]
[1,1,1,1,1,4,4]=>[1,1,1,2,1,1,6]
[1,1,1,1,1,3,5]=>[1,1,1,1,2,1,6]
[1,1,1,1,1,2,6]=>[1,1,1,1,1,2,6]
[1,1,1,1,1,1,7]=>[1,1,1,1,1,1,7]
click to show experimental identities
(only identities of compositions of up to three maps are shown)
Description
Properties
bijective, graded, involutive
Sage code
def mapping(elt): return elt.conjugate()
Weight
11
Created
Jan 19, 2020 at 07:28 by FindStatCrew
Updated
Jan 19, 2020 at 07:28 by Martin Rubey
searching the database
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