Identifier
Images
=>
Cc0002;cc-rep-0Cc0005;cc-rep-1
[]=>[]
[1]=>[1,0]
[2]=>[1,0,1,0]
[1,1]=>[1,1,0,0]
[3]=>[1,0,1,0,1,0]
[2,1]=>[1,0,1,1,0,0]
[1,1,1]=>[1,1,0,1,0,0]
[4]=>[1,0,1,0,1,0,1,0]
[3,1]=>[1,0,1,0,1,1,0,0]
[2,2]=>[1,1,1,0,0,0]
[2,1,1]=>[1,0,1,1,0,1,0,0]
[1,1,1,1]=>[1,1,0,1,0,1,0,0]
[5]=>[1,0,1,0,1,0,1,0,1,0]
[4,1]=>[1,0,1,0,1,0,1,1,0,0]
[3,2]=>[1,0,1,1,1,0,0,0]
[3,1,1]=>[1,0,1,0,1,1,0,1,0,0]
[2,2,1]=>[1,1,1,0,0,1,0,0]
[2,1,1,1]=>[1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,0]
[6]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2]=>[1,0,1,0,1,1,1,0,0,0]
[4,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,3]=>[1,1,1,0,1,0,0,0]
[3,2,1]=>[1,0,1,1,1,0,0,1,0,0]
[3,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,2,2]=>[1,1,1,1,0,0,0,0]
[2,2,1,1]=>[1,1,1,0,0,1,0,1,0,0]
[2,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[6,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[5,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[4,3]=>[1,0,1,1,1,0,1,0,0,0]
[4,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[4,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[3,3,1]=>[1,1,1,0,1,0,0,1,0,0]
[3,2,2]=>[1,0,1,1,1,1,0,0,0,0]
[3,2,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[2,2,2,1]=>[1,1,1,1,0,0,0,1,0,0]
[2,2,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[7,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[6,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[6,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[5,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[5,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[4,4]=>[1,1,1,0,1,0,1,0,0,0]
[4,3,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,2,2]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[4,2,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[4,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[3,3,2]=>[1,1,1,0,1,1,0,0,0,0]
[3,3,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[3,2,2,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[3,2,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[3,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2]=>[1,1,1,1,0,1,0,0,0,0]
[2,2,2,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[2,2,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[8,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[7,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[7,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[6,3]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[6,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[6,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[5,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[5,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[5,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[5,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[5,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[4,4,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[4,3,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[4,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[4,2,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[4,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[3,3,3]=>[1,1,1,1,1,0,0,0,0,0]
[3,3,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,3,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[3,2,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[3,2,2,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[3,2,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[3,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[2,2,2,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[2,2,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[10]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[9,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[8,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[8,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[7,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[7,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[7,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[6,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[6,3,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[6,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[6,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[6,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[5,5]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[5,4,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[5,3,2]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[5,3,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[5,2,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[5,2,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[5,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[4,4,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[4,4,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[4,3,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[4,3,2,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[4,3,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[4,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[4,2,2,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[4,2,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[4,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,3,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[3,3,2,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,3,2,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[3,3,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[3,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[3,2,2,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[3,2,1,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[2,2,2,2,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[2,2,2,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[2,2,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[11]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[10,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[9,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[9,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[8,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[8,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[8,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[7,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[7,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[7,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[7,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[7,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[6,5]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[6,4,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[6,3,2]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[6,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[6,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[6,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[6,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[5,5,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[5,4,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[5,4,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[5,3,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[5,3,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[5,3,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[5,2,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[5,2,2,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[5,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[5,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,3]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[4,4,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[4,4,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[4,3,3,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[4,3,2,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[4,3,2,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[4,3,1,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[4,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[4,2,2,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[4,2,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[3,3,3,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[3,3,2,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[3,3,2,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[3,3,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,2,2,2,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[3,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,2,1,1,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[2,2,2,2,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[2,2,2,1,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,1,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[12]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[11,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[10,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[10,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[9,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[9,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[9,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[8,4]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[8,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[8,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[8,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[8,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[7,5]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[7,4,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[7,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[7,3,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[7,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[7,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[7,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[6,6]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[6,5,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[6,4,2]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[6,4,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[6,3,3]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[6,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[6,3,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[6,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[6,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[6,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[6,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,5,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[5,5,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[5,4,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[5,4,2,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[5,4,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[5,3,3,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[5,3,2,2]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[5,3,2,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[5,3,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[5,2,2,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[5,2,2,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[5,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[4,4,3,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[4,4,2,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[4,4,2,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[4,4,1,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[4,3,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[4,3,3,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[4,3,2,2,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[4,3,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[4,3,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[4,2,2,2,1,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[4,2,2,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[4,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,3,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[3,3,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[3,3,3,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[3,3,2,2,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[3,3,2,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[3,3,2,1,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,3,1,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[3,2,2,2,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[3,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[2,2,2,2,2,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[2,2,2,2,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[2,2,2,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,1,1,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[13]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[12,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[11,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[11,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[10,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[10,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[10,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[9,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[9,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[9,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[9,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[9,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[8,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[8,4,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[8,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[8,3,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[8,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[8,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[8,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[7,6]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[7,5,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[7,4,2]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[7,4,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[7,3,3]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[7,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[7,3,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[7,2,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[7,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[7,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[7,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,6,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[6,5,2]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[6,5,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[6,4,3]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[6,4,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[6,4,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[6,3,3,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[6,3,2,2]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[6,3,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[6,3,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[6,2,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[6,2,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[6,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[6,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,5,3]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[5,5,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[5,5,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[5,4,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[5,4,3,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[5,4,2,2]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[5,4,2,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[5,4,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[5,3,3,2]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[5,3,3,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[5,3,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[5,3,2,1,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[5,3,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,2,2,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[5,2,2,2,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[5,2,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[5,2,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[4,4,3,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[4,4,3,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[4,4,2,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[4,4,2,1,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[4,4,1,1,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,3,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,3,3,2,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[4,3,3,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[4,3,2,2,2]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[4,3,2,2,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[4,3,2,1,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[4,3,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[4,2,2,2,1,1,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[4,2,2,1,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,3,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,3,3,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[3,3,3,2,1,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[3,3,3,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[3,3,2,2,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[3,3,2,2,1,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[3,3,2,1,1,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,1,1,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[3,2,2,2,2,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[3,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,2,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[2,2,2,2,2,1,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[2,2,2,2,1,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,1,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,1,1,1,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[14]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[13,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[12,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[12,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[11,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[11,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[11,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[10,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[10,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[10,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[10,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[10,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[9,5]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[9,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[9,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[9,3,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[9,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[9,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[9,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[8,6]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[8,5,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[8,4,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[8,4,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[8,3,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[8,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[8,3,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[8,2,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[8,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[8,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[8,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[7,7]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[7,6,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[7,5,2]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[7,5,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[7,4,3]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[7,4,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[7,4,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[7,3,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[7,3,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[7,3,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[7,3,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[7,2,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[7,2,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[7,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[7,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,6,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[6,6,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[6,5,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[6,5,2,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[6,5,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[6,4,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[6,4,3,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[6,4,2,2]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[6,4,2,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[6,4,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[6,3,3,2]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[6,3,3,1,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[6,3,2,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[6,3,2,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[6,3,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[6,2,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[6,2,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[6,2,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[6,2,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[5,5,3,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[5,5,2,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[5,5,2,1,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[5,5,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[5,4,4,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[5,4,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[5,4,3,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[5,4,2,2,1]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[5,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[5,4,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,3,3,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,3,3,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[5,3,3,1,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[5,3,2,2,2]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[5,3,2,2,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[5,3,2,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[5,3,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,2,2,2,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[5,2,2,2,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[5,2,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,2,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[4,4,4,1,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[4,4,3,3]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[4,4,3,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[4,4,3,1,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[4,4,2,2,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[4,4,2,2,1,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[4,4,2,1,1,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[4,4,1,1,1,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,3,3,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[4,3,3,2,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[4,3,3,2,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[4,3,3,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[4,3,2,2,2,1]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[4,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[4,3,2,1,1,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,2,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[4,2,2,2,2,1,1]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[4,2,2,2,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[4,2,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,3,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,3,3,3,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[3,3,3,2,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[3,3,3,2,1,1,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]
[3,3,3,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,2,2,2,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[3,3,2,2,2,1,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[3,3,2,2,1,1,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,3,2,1,1,1,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,1,1,1,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,2,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[3,2,2,2,2,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[3,2,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[2,2,2,2,2,2,1,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[2,2,2,2,2,1,1,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,1,1,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,1,1,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[15]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[14,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[13,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[13,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[12,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[12,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[12,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[11,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[11,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[11,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[11,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[11,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[10,5]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[10,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[10,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[10,3,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[10,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[10,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[10,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[9,6]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[9,5,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[9,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[9,4,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[9,3,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[9,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[9,3,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[9,2,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[9,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[9,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[9,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[8,7]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[8,6,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[8,5,2]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[8,5,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[8,4,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[8,4,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[8,4,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[8,3,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[8,3,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[8,3,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[8,3,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[8,2,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[8,2,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[8,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[8,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[7,7,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[7,6,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[7,6,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[7,5,3]=>[1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[7,5,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[7,5,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[7,4,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[7,4,3,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[7,4,2,2]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[7,4,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[7,4,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[7,3,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[7,3,3,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[7,3,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[7,3,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[7,3,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[7,2,2,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[7,2,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[7,2,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[7,2,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[7,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,6,3]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[6,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[6,6,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[6,5,4]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[6,5,3,1]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[6,5,2,2]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[6,5,2,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[6,5,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[6,4,4,1]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[6,4,3,2]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[6,4,3,1,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[6,4,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[6,4,2,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[6,4,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[6,3,3,3]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[6,3,3,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[6,3,2,2,2]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[6,3,2,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[6,3,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[6,3,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,2,2,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[6,2,2,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[6,2,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[6,2,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,5,5]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[5,5,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[5,5,3,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[5,5,3,1,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[5,5,2,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[5,5,2,1,1,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[5,5,1,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,4,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[5,4,4,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[5,4,3,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[5,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[5,4,3,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[5,4,2,2,2]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[5,4,2,2,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[5,4,2,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[5,4,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,3,3,3,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,3,3,2,2]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[5,3,3,2,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[5,3,3,1,1,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[5,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[5,3,2,2,1,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[5,3,2,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,3,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,2,2,2,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[5,2,2,2,2,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[5,2,2,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[5,2,2,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,2,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[4,4,4,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[4,4,4,1,1,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]
[4,4,3,3,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[4,4,3,2,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[4,4,3,2,1,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[4,4,3,1,1,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[4,4,2,2,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[4,4,2,2,1,1,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[4,4,2,1,1,1,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,1,1,1,1,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,3,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[4,3,3,3,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,3,3,2,2,1]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[4,3,3,2,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]
[4,3,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,2,2,2,2]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[4,3,2,2,2,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[4,3,2,2,1,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[4,3,2,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[4,2,2,2,2,1,1,1]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[4,2,2,2,1,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,2,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,3,3,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,3,3,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[3,3,3,3,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[3,3,3,2,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[3,3,3,2,2,1,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0]
[3,3,3,2,1,1,1,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,3,3,1,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,2,2,2,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[3,3,2,2,2,1,1,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[3,3,2,2,1,1,1,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,2,1,1,1,1,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,1,1,1,1,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,2,2,2,2,2,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[3,2,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,2,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,2,2,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[2,2,2,2,2,2,1,1,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[2,2,2,2,2,1,1,1,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,1,1,1,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[16]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[15,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[14,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[14,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[13,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[13,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[13,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[12,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[12,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[12,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[12,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[12,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[11,5]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[11,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[11,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[11,3,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[11,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[11,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[11,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[10,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[10,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[10,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[10,4,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[10,3,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[10,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[10,3,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[10,2,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[10,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[10,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[10,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[9,7]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[9,6,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[9,5,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[9,5,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[9,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[9,4,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[9,4,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[9,3,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[9,3,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[9,3,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[9,3,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[9,2,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[9,2,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[9,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[9,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[8,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[8,7,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[8,6,2]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[8,6,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[8,5,3]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[8,5,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[8,5,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[8,4,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[8,4,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[8,4,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[8,4,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[8,4,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[8,3,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[8,3,3,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[8,3,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[8,3,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[8,3,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[8,2,2,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[8,2,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[8,2,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[8,2,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[8,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[7,7,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[7,7,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[7,6,3]=>[1,0,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[7,6,2,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[7,6,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[7,5,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[7,5,3,1]=>[1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[7,5,2,2]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[7,5,2,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[7,5,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[7,4,4,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[7,4,3,2]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[7,4,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[7,4,2,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[7,4,2,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[7,4,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[7,3,3,3]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[7,3,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[7,3,3,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[7,3,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[7,3,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[7,3,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[7,3,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[7,2,2,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[7,2,2,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[7,2,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[7,2,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[7,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,6,4]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[6,6,3,1]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[6,6,2,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[6,6,2,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[6,6,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[6,5,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[6,5,4,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[6,5,3,2]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[6,5,3,1,1]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[6,5,2,2,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[6,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[6,5,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[6,4,4,2]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[6,4,4,1,1]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[6,4,3,3]=>[1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[6,4,3,2,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[6,4,3,1,1,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[6,4,2,2,2]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[6,4,2,2,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[6,4,2,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[6,4,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,3,3,3,1]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,3,3,2,2]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[6,3,3,2,1,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[6,3,3,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[6,3,2,2,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[6,3,2,2,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[6,3,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[6,3,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,2,2,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[6,2,2,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[6,2,2,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[6,2,2,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,2,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,5,5,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[5,5,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[5,5,4,1,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[5,5,3,3]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[5,5,3,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[5,5,3,1,1,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[5,5,2,2,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[5,5,2,2,1,1]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[5,5,2,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[5,5,1,1,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,4,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[5,4,4,2,1]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[5,4,4,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]
[5,4,3,3,1]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[5,4,3,2,2]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[5,4,3,2,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[5,4,3,1,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[5,4,2,2,2,1]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[5,4,2,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[5,4,2,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,4,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,3,3,3,2]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,3,3,3,1,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,3,3,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[5,3,3,2,1,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]
[5,3,3,1,1,1,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,3,2,2,2,2]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[5,3,2,2,2,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[5,3,2,2,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[5,3,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,3,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,2,2,2,2,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[5,2,2,2,2,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[5,2,2,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,2,2,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,4,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,4,4,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[4,4,4,2,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[4,4,4,2,1,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
[4,4,4,1,1,1,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[4,4,3,3,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[4,4,3,3,1,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[4,4,3,2,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[4,4,3,2,1,1,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]
[4,4,3,1,1,1,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,2,2,2,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[4,4,2,2,2,1,1]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[4,4,2,2,1,1,1,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[4,4,2,1,1,1,1,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,1,1,1,1,1,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,3,3,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[4,3,3,3,2,1]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[4,3,3,3,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[4,3,3,2,2,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[4,3,3,2,2,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0]
[4,3,3,2,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[4,3,3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,2,2,2,2,1]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[4,3,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[4,3,2,2,1,1,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,2,2,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[4,2,2,2,2,2,1,1]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[4,2,2,2,2,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[4,2,2,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,2,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,3,3,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[3,3,3,3,2,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[3,3,3,3,2,1,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0]
[3,3,3,3,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]
[3,3,3,2,2,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,0]
[3,3,3,2,2,1,1,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[3,3,3,2,1,1,1,1,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,3,1,1,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,2,2,2,2,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,3,2,2,2,2,1,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[3,3,2,2,2,1,1,1,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,3,2,2,1,1,1,1,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,2,1,1,1,1,1,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,2,2,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[3,2,2,2,2,2,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[3,2,2,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,2,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[2,2,2,2,2,2,2,1,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[2,2,2,2,2,2,1,1,1,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,2,1,1,1,1,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,1,1,1,1,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[17]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[16,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[15,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[15,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[14,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[14,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[14,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[13,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[13,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[13,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[13,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[13,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[12,5]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[12,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[12,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[12,3,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[12,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[12,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[12,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[11,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[11,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[11,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[11,4,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[11,3,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[11,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[11,3,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[11,2,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[11,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[11,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[11,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[10,7]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[10,6,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[10,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[10,5,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[10,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[10,4,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[10,4,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[10,3,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[10,3,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[10,3,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[10,3,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[10,2,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[10,2,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[10,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[10,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[9,8]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[9,7,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[9,6,2]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[9,6,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[9,5,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[9,5,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[9,5,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[9,4,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[9,4,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[9,4,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[9,4,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[9,4,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[9,3,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[9,3,3,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[9,3,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[9,3,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[9,3,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[9,2,2,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[9,2,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[9,2,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[9,2,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[9,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[8,8,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[8,7,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[8,7,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[8,6,3]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[8,6,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[8,6,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[8,5,4]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[8,5,3,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[8,5,2,2]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[8,5,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[8,5,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[8,4,4,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[8,4,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[8,4,3,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[8,4,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[8,4,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[8,4,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[8,3,3,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[8,3,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[8,3,3,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[8,3,2,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[8,3,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[8,3,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[8,3,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[8,2,2,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[8,2,2,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[8,2,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[8,2,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[8,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[7,7,3]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[7,7,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[7,7,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[7,6,4]=>[1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[7,6,3,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[7,6,2,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[7,6,2,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[7,6,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[7,5,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[7,5,4,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[7,5,3,2]=>[1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[7,5,3,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[7,5,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[7,5,2,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[7,5,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[7,4,4,2]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[7,4,4,1,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[7,4,3,3]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[7,4,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[7,4,3,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[7,4,2,2,2]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[7,4,2,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[7,4,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[7,4,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[7,3,3,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[7,3,3,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[7,3,3,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[7,3,3,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[7,3,2,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[7,3,2,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[7,3,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[7,3,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[7,2,2,2,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[7,2,2,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[7,2,2,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[7,2,2,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[7,2,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[7,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,6,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[6,6,4,1]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[6,6,3,2]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[6,6,3,1,1]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[6,6,2,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[6,6,2,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[6,6,1,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[6,5,5,1]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[6,5,4,2]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[6,5,4,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[6,5,3,3]=>[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[6,5,3,2,1]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[6,5,3,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[6,5,2,2,2]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[6,5,2,2,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[6,5,2,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[6,5,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,4,4,3]=>[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[6,4,4,2,1]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[6,4,4,1,1,1]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]
[6,4,3,3,1]=>[1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[6,4,3,2,2]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[6,4,3,2,1,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[6,4,3,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[6,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[6,4,2,2,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[6,4,2,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[6,4,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,3,3,3,2]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[6,3,3,3,1,1]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[6,3,3,2,2,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[6,3,3,2,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]
[6,3,3,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[6,3,2,2,2,2]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[6,3,2,2,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[6,3,2,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[6,3,2,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,3,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,2,2,2,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[6,2,2,2,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[6,2,2,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[6,2,2,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,5,5,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[5,5,5,1,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,0]
[5,5,4,3]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[5,5,4,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[5,5,4,1,1,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]
[5,5,3,3,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[5,5,3,2,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[5,5,3,2,1,1]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[5,5,3,1,1,1,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[5,5,2,2,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[5,5,2,2,1,1,1]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[5,5,2,1,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,5,1,1,1,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,4,4,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,4,4,3,1]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[5,4,4,2,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[5,4,4,2,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
[5,4,4,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[5,4,3,3,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[5,4,3,3,1,1]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,4,3,2,2,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[5,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]
[5,4,3,1,1,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,4,2,2,2,2]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[5,4,2,2,2,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[5,4,2,2,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[5,4,2,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,4,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,3,3,3,3]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[5,3,3,3,2,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[5,3,3,3,1,1,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[5,3,3,2,2,2]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[5,3,3,2,2,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0]
[5,3,3,2,1,1,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[5,3,3,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,3,2,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[5,3,2,2,2,1,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[5,3,2,2,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[5,3,2,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,3,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,2,2,2,2,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[5,2,2,2,2,2,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[5,2,2,2,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[5,2,2,2,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,2,2,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[5,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,4,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[4,4,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[4,4,4,3,1,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
[4,4,4,2,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
[4,4,4,2,1,1,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,1,0,0]
[4,4,4,1,1,1,1,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,3,3,3]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[4,4,3,3,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[4,4,3,3,1,1,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[4,4,3,2,2,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[4,4,3,2,2,1,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0]
[4,4,3,2,1,1,1,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[4,4,3,1,1,1,1,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,2,2,2,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[4,4,2,2,2,1,1,1]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[4,4,2,2,1,1,1,1,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,2,1,1,1,1,1,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,4,1,1,1,1,1,1,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,3,3,3,1]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[4,3,3,3,2,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[4,3,3,3,2,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0]
[4,3,3,3,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]
[4,3,3,2,2,2,1]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,0]
[4,3,3,2,2,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[4,3,3,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,3,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,2,2,2,2,2]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[4,3,2,2,2,2,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[4,3,2,2,2,1,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[4,3,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,3,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[4,2,2,2,2,2,1,1,1]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[4,2,2,2,2,1,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,2,2,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[4,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,3,3,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[3,3,3,3,3,1,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]
[3,3,3,3,2,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0]
[3,3,3,3,2,1,1,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0,0]
[3,3,3,3,1,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,3,2,2,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]
[3,3,3,2,2,2,1,1]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[3,3,3,2,2,1,1,1,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,3,3,2,1,1,1,1,1,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,3,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,2,2,2,2,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[3,3,2,2,2,2,1,1,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[3,3,2,2,2,1,1,1,1,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,2,2,1,1,1,1,1,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,2,1,1,1,1,1,1,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,3,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,2,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[3,2,2,2,2,2,2,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]
[3,2,2,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,2,2,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,2,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,2,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,2,2,2,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[2,2,2,2,2,2,2,1,1,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
[2,2,2,2,2,2,1,1,1,1,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,2,1,1,1,1,1,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
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Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Properties
injective
Sage code
def mapping(la): if not la: return ParallelogramPolyomino([[1],[1]]).to_dyck_word() lower_path = [0]*la[0] + [1]*len(la) upper_path = [] la = list(la) + [0] for i in range(len(la)-1): upper_path.extend([1]+[0]*(la[i]-la[i+1])) return ParallelogramPolyomino([lower_path, upper_path]).to_dyck_word()
Weight
26
Created
May 07, 2021 at 14:19 by Martin Rubey
Updated
May 07, 2021 at 14:19 by Martin Rubey
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