Identifier
Images
=>
Cc0002;cc-rep-0Cc0005;cc-rep-1
[]=>[]
[1]=>[1,0,1,0]
[2]=>[1,1,0,0,1,0]
[1,1]=>[1,0,1,1,0,0]
[3]=>[1,1,1,0,0,0,1,0]
[2,1]=>[1,0,1,0,1,0]
[1,1,1]=>[1,0,1,1,1,0,0,0]
[4]=>[1,1,1,1,0,0,0,0,1,0]
[3,1]=>[1,1,0,1,0,0,1,0]
[2,2]=>[1,1,0,0,1,1,0,0]
[2,1,1]=>[1,0,1,1,0,1,0,0]
[1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0]
[5]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[4,1]=>[1,1,1,0,1,0,0,0,1,0]
[3,2]=>[1,1,0,0,1,0,1,0]
[3,1,1]=>[1,0,1,1,0,0,1,0]
[2,2,1]=>[1,0,1,0,1,1,0,0]
[2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0]
[1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[5,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[4,2]=>[1,1,1,0,0,1,0,0,1,0]
[4,1,1]=>[1,1,0,1,1,0,0,0,1,0]
[3,3]=>[1,1,1,0,0,0,1,1,0,0]
[3,2,1]=>[1,0,1,0,1,0,1,0]
[3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0]
[2,2,2]=>[1,1,0,0,1,1,1,0,0,0]
[2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0]
[2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,1]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,2]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[4,3]=>[1,1,1,0,0,0,1,0,1,0]
[4,2,1]=>[1,1,0,1,0,1,0,0,1,0]
[4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0]
[3,3,1]=>[1,1,0,1,0,0,1,1,0,0]
[3,2,2]=>[1,1,0,0,1,1,0,1,0,0]
[3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0]
[3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0]
[2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[7,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,2]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[6,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[5,3]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[5,1,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,4]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[4,3,1]=>[1,1,0,1,0,0,1,0,1,0]
[4,2,2]=>[1,1,0,0,1,1,0,0,1,0]
[4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0]
[4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[3,3,2]=>[1,1,0,0,1,0,1,1,0,0]
[3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0]
[3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0]
[3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[9]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[8,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[7,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,1,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,3]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[6,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[6,1,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[5,4]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[5,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[4,3,2]=>[1,1,0,0,1,0,1,0,1,0]
[4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0]
[4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0]
[4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0]
[3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[9,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[8,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
[8,1,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
[7,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[7,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[7,1,1,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[6,2,2]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[6,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[6,1,1,1,1]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0]
[4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[4,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[3,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[11]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[10,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[9,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[9,1,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]
[8,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[8,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]
[8,1,1,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[7,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[7,2,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[7,2,1,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[7,1,1,1,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[6,4,1]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[6,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[6,3,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[6,2,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[6,2,1,1,1]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[6,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[5,5,1]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[5,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[5,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[4,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[4,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[4,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[3,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[3,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[3,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[12]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[11,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]
[10,1,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,3]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]
[9,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[9,1,1,1]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]
[8,3,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]
[8,2,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]
[8,2,1,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]
[8,1,1,1,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[7,4,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[7,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[7,3,1,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[7,2,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[7,2,1,1,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[7,1,1,1,1,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,5,1]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[6,4,2]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[6,4,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[6,3,3]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[6,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[6,3,1,1,1]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[6,2,2,2]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[6,2,2,1,1]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[6,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[6,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,5,2]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[5,5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[5,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[5,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[4,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[4,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[4,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[4,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[4,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[3,3,3,3]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[3,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[3,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[3,3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[3,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[3,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[13]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[12,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[11,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[11,1,1]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,1,0]
[10,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]
[10,1,1,1]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]
[9,3,1]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0]
[9,2,2]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,1,0]
[9,2,1,1]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0]
[9,1,1,1,1]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]
[8,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]
[8,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]
[8,3,1,1]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]
[8,2,2,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]
[8,2,1,1,1]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]
[8,1,1,1,1,1]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[7,5,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[7,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[7,4,1,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[7,3,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[7,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[7,3,1,1,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[7,2,2,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[7,2,2,1,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[7,2,1,1,1,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[7,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,6,1]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[6,5,2]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[6,5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[6,4,3]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[6,4,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[6,4,1,1,1]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[6,3,3,1]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[6,3,2,2]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[6,3,2,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[6,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[6,2,2,2,1]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[6,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[6,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[6,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,5,3]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[5,5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[5,5,1,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[5,4,4]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[5,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[5,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[5,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[5,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[5,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[4,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[4,4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[4,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[4,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[4,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[4,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[4,3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[4,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[4,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[4,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]
[4,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[3,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[3,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[3,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[3,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[3,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[3,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,3,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[3,3,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[3,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[3,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[3,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[3,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,2,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,2,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[14]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[12,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[12,1,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[11,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
[11,2,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[11,1,1,1]=>[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,4]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,1,0]
[10,3,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,1,0]
[10,2,2]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0]
[10,2,1,1]=>[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[10,1,1,1,1]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]
[9,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,1,0]
[9,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]
[9,3,1,1]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,1,0]
[9,2,2,1]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0]
[9,2,1,1,1]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[9,1,1,1,1,1]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]
[8,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,1,0]
[8,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]
[8,4,1,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0]
[8,3,3]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]
[8,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]
[8,3,1,1,1]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0]
[8,2,2,2]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0]
[8,2,2,1,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]
[8,2,1,1,1,1]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[8,1,1,1,1,1,1]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[7,6,1]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[7,5,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[7,5,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[7,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[7,4,2,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[7,4,1,1,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[7,3,3,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[7,3,2,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[7,3,2,1,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[7,3,1,1,1,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[7,2,2,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[7,2,2,1,1,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[7,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[7,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,6,2]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[6,6,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[6,5,3]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[6,5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[6,5,1,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[6,4,4]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[6,4,3,1]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[6,4,2,2]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[6,4,2,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[6,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[6,3,3,2]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[6,3,3,1,1]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[6,3,2,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[6,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[6,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[6,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[6,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[6,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[6,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[5,5,4]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[5,5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[5,5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[5,5,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[5,5,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[5,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[5,4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[5,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[5,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[5,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[5,3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[5,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[5,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]
[5,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[4,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[4,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[4,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[4,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[4,4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[4,4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,4,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[4,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[4,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[4,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[4,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[4,3,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[4,3,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]
[4,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[4,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[4,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]
[4,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[4,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]
[3,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[3,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[3,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[3,3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,3,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[3,3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[3,3,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[3,3,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[3,3,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[3,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[3,2,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,2,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[3,2,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]
[3,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,2,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,2,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,2,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[15]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[14,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,2]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,1,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[12,3]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[12,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[12,1,1,1]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[11,4]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0]
[11,3,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0]
[11,2,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,1,0]
[11,2,1,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[11,1,1,1,1]=>[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,1,0]
[10,4,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,1,0]
[10,3,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,0]
[10,3,1,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[10,2,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,1,0]
[10,2,1,1,1]=>[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[10,1,1,1,1,1]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]
[9,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,1,0]
[9,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,1,0]
[9,4,1,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,0]
[9,3,3]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0]
[9,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]
[9,3,1,1,1]=>[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
[9,2,2,2]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0]
[9,2,2,1,1]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
[9,2,1,1,1,1]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[9,1,1,1,1,1,1]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[8,6,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]
[8,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0]
[8,5,1,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0]
[8,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0]
[8,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]
[8,4,1,1,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]
[8,3,3,1]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0]
[8,3,2,2]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]
[8,3,2,1,1]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]
[8,3,1,1,1,1]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[8,2,2,2,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0]
[8,2,2,1,1,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[8,2,1,1,1,1,1]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[8,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,7,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]
[7,6,2]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[7,6,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[7,5,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[7,5,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[7,5,1,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[7,4,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[7,4,3,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[7,4,2,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[7,4,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[7,4,1,1,1,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[7,3,3,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[7,3,3,1,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[7,3,2,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[7,3,2,1,1,1]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[7,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[7,2,2,2,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[7,2,2,2,1,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[7,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[7,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[6,6,3]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[6,6,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[6,6,1,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[6,5,4]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[6,5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[6,5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[6,5,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[6,5,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[6,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[6,4,3,2]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[6,4,3,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[6,4,2,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[6,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[6,4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[6,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[6,3,3,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[6,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[6,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[6,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[6,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[6,3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[6,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[6,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]
[6,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[5,5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[5,5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[5,5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[5,5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[5,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[5,5,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[5,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[5,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[5,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[5,4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[5,4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[5,4,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[5,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[5,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[5,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[5,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[5,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[5,3,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[5,3,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]
[5,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[5,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[5,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]
[5,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[5,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0]
[4,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[4,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[4,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[4,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[4,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[4,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[4,4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[4,4,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[4,4,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,4,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]
[4,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[4,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[4,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[4,3,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[4,3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[4,3,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[4,3,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[4,3,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[4,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[4,2,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[4,2,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]
[4,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0]
[4,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[3,3,3,3,3]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[3,3,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,3,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[3,3,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[3,3,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,3,3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[3,3,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[3,3,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,3,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[3,3,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]
[3,3,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]
[3,2,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,2,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,2,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,2,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]
[3,2,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0]
[3,2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,2,2,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,2,2,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,2,2,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[16]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[15,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[14,2]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[14,1,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[13,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[12,4]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
[12,3,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[12,2,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[12,2,1,1]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[12,1,1,1,1]=>[1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[11,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0]
[11,4,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0]
[11,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0]
[11,3,1,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]
[11,2,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]
[11,2,1,1,1]=>[1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[11,1,1,1,1,1]=>[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,6]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0]
[10,5,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,1,0]
[10,4,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,1,0]
[10,4,1,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,0,1,0]
[10,3,3]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,1,0]
[10,3,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[10,3,1,1,1]=>[1,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[10,2,2,2]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,1,0]
[10,2,2,1,1]=>[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]
[10,2,1,1,1,1]=>[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[10,1,1,1,1,1,1]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]
[9,6,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,1,0]
[9,5,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]
[9,5,1,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,0,1,0]
[9,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,0]
[9,4,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,1,0]
[9,4,1,1,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[9,3,3,1]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,1,0]
[9,3,2,2]=>[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,1,0]
[9,3,2,1,1]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,1,0]
[9,3,1,1,1,1]=>[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
[9,2,2,2,1]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,1,0]
[9,2,2,1,1,1]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
[9,2,1,1,1,1,1]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[9,1,1,1,1,1,1,1]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[8,7,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]
[8,6,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0]
[8,6,1,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0]
[8,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0]
[8,5,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]
[8,5,1,1,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0]
[8,4,4]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,0]
[8,4,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,1,0]
[8,4,2,2]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,1,0]
[8,4,2,1,1]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,0]
[8,4,1,1,1,1]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[8,3,3,2]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0]
[8,3,3,1,1]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0]
[8,3,2,2,1]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,1,0]
[8,3,2,1,1,1]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[8,3,1,1,1,1,1]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[8,2,2,2,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,1,0]
[8,2,2,2,1,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[8,2,2,1,1,1,1]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[8,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[8,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[7,7,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]
[7,7,1,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]
[7,6,3]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[7,6,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[7,6,1,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[7,5,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[7,5,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[7,5,2,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[7,5,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[7,5,1,1,1,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[7,4,4,1]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[7,4,3,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[7,4,3,1,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[7,4,2,2,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[7,4,2,1,1,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[7,4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[7,3,3,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[7,3,3,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[7,3,3,1,1,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[7,3,2,2,2]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[7,3,2,2,1,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[7,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[7,3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[7,2,2,2,2,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[7,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[7,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[7,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]
[7,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[6,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[6,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[6,6,2,2]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[6,6,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[6,6,1,1,1,1]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[6,5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[6,5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[6,5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[6,5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[6,5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[6,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[6,5,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[6,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[6,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[6,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[6,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[6,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[6,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[6,4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[6,4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[6,4,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[6,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[6,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[6,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[6,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[6,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[6,3,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[6,3,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]
[6,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[6,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[6,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[6,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,0]
[6,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]
[6,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]
[5,5,5,1]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[5,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[5,5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[5,5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[5,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[5,5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[5,5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[5,5,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[5,5,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[5,5,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[5,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[5,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[5,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[5,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[5,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[5,4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[5,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[5,4,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[5,4,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[5,4,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]
[5,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[5,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[5,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[5,3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[5,3,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[5,3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[5,3,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[5,3,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[5,3,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]
[5,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[5,2,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[5,2,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]
[5,2,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,0]
[5,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]
[5,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[4,4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[4,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[4,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[4,4,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[4,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[4,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[4,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[4,4,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,4,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[4,4,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[4,4,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,4,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]
[4,4,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
[4,3,3,3,3]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[4,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[4,3,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[4,3,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[4,3,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[4,3,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[4,3,3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]
[4,3,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[4,3,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[4,3,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]
[4,3,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[4,3,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0]
[4,2,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[4,2,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[4,2,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0,0]
[4,2,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0]
[4,2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0]
[4,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0]
[3,3,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[3,3,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[3,3,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[3,3,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,3,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[3,3,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,3,3,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[3,3,3,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[3,3,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,3,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,3,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,3,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]
[3,3,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0]
[3,3,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0]
[3,2,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,2,2,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,2,2,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[3,2,2,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[3,2,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[3,2,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,2,2,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,2,2,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[17]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[16,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[15,2]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[15,1,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[14,3]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[14,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[14,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,4]=>[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[13,3,1]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[13,2,2]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,2,1,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[12,5]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0]
[12,4,1]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
[12,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[12,3,1,1]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[12,2,2,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[12,2,1,1,1]=>[1,1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[12,1,1,1,1,1]=>[1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[11,6]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0]
[11,5,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0]
[11,4,2]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0]
[11,4,1,1]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,0,0,1,0]
[11,3,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0]
[11,3,2,1]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]
[11,3,1,1,1]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]
[11,2,2,2]=>[1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[11,2,2,1,1]=>[1,1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]
[11,2,1,1,1,1]=>[1,1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[11,1,1,1,1,1,1]=>[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,1,0]
[10,6,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,1,0]
[10,5,2]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,1,0]
[10,5,1,1]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,0,0,1,0]
[10,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0]
[10,4,2,1]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0,1,0]
[10,4,1,1,1]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]
[10,3,3,1]=>[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0,1,0]
[10,3,2,2]=>[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0,1,0]
[10,3,2,1,1]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[10,3,1,1,1,1]=>[1,1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[10,2,2,2,1]=>[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]
[10,2,2,1,1,1]=>[1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]
[10,2,1,1,1,1,1]=>[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[10,1,1,1,1,1,1,1]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[9,7,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]
[9,6,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,1,0]
[9,6,1,1]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0,1,0]
[9,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0,1,0]
[9,5,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,1,0]
[9,5,1,1,1]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0,1,0]
[9,4,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,1,0]
[9,4,3,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,1,0]
[9,4,2,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0,1,0]
[9,4,2,1,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0,1,0]
[9,4,1,1,1,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[9,3,3,2]=>[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,1,0]
[9,3,3,1,1]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0,1,0]
[9,3,2,2,1]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,1,0]
[9,3,2,1,1,1]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]
[9,3,1,1,1,1,1]=>[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
[9,2,2,2,2]=>[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,1,0]
[9,2,2,2,1,1]=>[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]
[9,2,2,1,1,1,1]=>[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
[9,2,1,1,1,1,1,1]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[9,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,8,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]
[8,7,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]
[8,7,1,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]
[8,6,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,1,0]
[8,6,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0]
[8,6,1,1,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,1,0]
[8,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]
[8,5,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]
[8,5,2,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0]
[8,5,2,1,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]
[8,5,1,1,1,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[8,4,4,1]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,1,0]
[8,4,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]
[8,4,3,1,1]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,1,0]
[8,4,2,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,1,0]
[8,4,2,1,1,1]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[8,4,1,1,1,1,1]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[8,3,3,3]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]
[8,3,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]
[8,3,3,1,1,1]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[8,3,2,2,2]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,1,0]
[8,3,2,2,1,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[8,3,2,1,1,1,1]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[8,3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[8,2,2,2,2,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[8,2,2,2,1,1,1]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[8,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[8,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[8,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[7,7,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]
[7,7,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]
[7,7,1,1,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[7,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[7,6,2,2]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[7,6,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[7,6,1,1,1,1]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[7,5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[7,5,4,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[7,5,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[7,5,3,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[7,5,2,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[7,5,2,1,1,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[7,5,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[7,4,4,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[7,4,4,1,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[7,4,3,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[7,4,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[7,4,3,1,1,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[7,4,2,2,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[7,4,2,2,1,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[7,4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[7,4,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,3,3,3,1]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[7,3,3,2,2]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[7,3,3,2,1,1]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[7,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[7,3,2,2,2,1]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[7,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[7,3,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[7,3,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]
[7,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[7,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[7,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[7,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]
[7,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]
[7,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0]
[6,6,5]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[6,6,4,1]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[6,6,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[6,6,3,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[6,6,2,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[6,6,2,1,1,1]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[6,6,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[6,5,5,1]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[6,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[6,5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[6,5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[6,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[6,5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[6,5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[6,5,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[6,5,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[6,5,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[6,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[6,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[6,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[6,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[6,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[6,4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[6,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[6,4,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[6,4,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[6,4,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0]
[6,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[6,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[6,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[6,3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[6,3,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[6,3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[6,3,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[6,3,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]
[6,3,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[6,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[6,2,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]
[6,2,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,0,0]
[6,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0]
[6,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[5,5,5,2]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[5,5,5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[5,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[5,5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[5,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[5,5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[5,5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[5,5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[5,5,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[5,5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[5,5,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[5,5,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,5,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[5,4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[5,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[5,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[5,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[5,4,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[5,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[5,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[5,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[5,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[5,4,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[5,4,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[5,4,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[5,4,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[5,4,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]
[5,4,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0]
[5,3,3,3,3]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[5,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[5,3,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[5,3,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[5,3,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[5,3,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[5,3,3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]
[5,3,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[5,3,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[5,3,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]
[5,3,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[5,3,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0]
[5,2,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,2,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,2,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,2,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]
[5,2,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,0,0]
[5,2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0]
[5,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0]
[4,4,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[4,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[4,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[4,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[4,4,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[4,4,4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,4,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[4,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[4,4,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[4,4,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[4,4,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[4,4,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[4,4,3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]
[4,4,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[4,4,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,4,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]
[4,4,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]
[4,4,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0]
[4,3,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[4,3,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[4,3,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[4,3,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[4,3,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[4,3,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[4,3,3,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]
[4,3,3,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0]
[4,3,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[4,3,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[4,3,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]
[4,3,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[4,3,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[4,3,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[4,2,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[4,2,2,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,2,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[4,2,2,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[4,2,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[4,2,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[4,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,3,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[3,3,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[3,3,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[3,3,3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,3,3,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[3,3,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,3,3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,3,3,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,3,3,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]
[3,3,3,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0]
[3,3,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,3,2,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,3,2,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[3,3,2,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[3,3,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[3,3,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,2,2,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,2,2,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,2,2,2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[3,2,2,2,2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[3,2,2,2,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[3,2,2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,2,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,2,2,2,2,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,2,2,2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[5,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[6,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[5,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[5,5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[6,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[6,5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[5,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[5,5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[6,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[5,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[6,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[6,5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[6,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[5,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[5,5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[6,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[5,5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[6,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[6,5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[5,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[6,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[6,5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[6,5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[6,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[3,3,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[7,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[6,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[6,6,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[7,6,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[4,3,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[5,4,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[7,4,3,2,1,1]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[5,4,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[4,4,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[6,6,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[7,6,5]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[2,2,2,2,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,3,3,3,3,3]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,6,6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[10,4,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
[9,6,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0]
[8,6,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0]
[9,9]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]
[7,7,1,1,1,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,4,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[5,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[6,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[5,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[6,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[6,5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[5,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[6,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[6,5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[6,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[6,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[6,5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[6,5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[5,4,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[7,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[6,5,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[4,4,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[4,4,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[7,3,3,3,3]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[6,6,4,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[7,5,4,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[7,6,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[7,5,4,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[3,3,3,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,3,3,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,3,3,3,3,3]=>[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[7,6,6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]
[9,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,0,1,0]
[8,5,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0]
[8,5,5,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0,1,0]
[5,4,3,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[6,6,6,1]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]
[5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[6,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[6,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[6,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[6,4,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[6,5,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[4,4,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[5,5,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[6,5,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[5,4,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[6,6,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[4,4,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[7,6,3,2,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[5,4,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[7,5,4,3,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[6,6,5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[7,6,4,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[6,5,5,4]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[7,6,4,3]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[7,6,5,2]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[4,4,4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,5,5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[8,2,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[8,6,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[10,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0]
[10,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0,0,1,0]
[9,7,4]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0,1,0]
[9,5,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0,0,1,0]
[7,7,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,4,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[8,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]
[6,6,6,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]
[6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[6,3,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[6,5,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[5,5,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[6,5,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[7,5,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[7,6,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[6,5,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[5,5,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[7,5,4,3,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[7,6,5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[7,6,5,3]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[3,3,3,3,3,3,3]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,4,4,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[11,7,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0]
[8,7,6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[7,7,7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[6,5,5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]
[5,4,4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]
[4,4,4,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,5,5,5,1]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[6,4,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[5,5,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[6,5,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[6,5,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,5,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[5,5,5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[6,6,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[7,5,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[7,6,4,3,2]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[7,6,5,4]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[9,6,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,0,1,0]
[6,5,4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[5,4,3,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[5,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[6,5,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[6,5,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[6,5,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[7,6,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[6,5,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[6,6,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[7,6,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[7,6,5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[6,5,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[7,6,5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[7,6,5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[9,6,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0]
[8,6,5,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0]
[8,5,4,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[6,5,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[5,5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[6,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[6,5,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[6,5,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[6,5,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[5,5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[6,5,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[7,6,5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[6,5,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[7,6,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[7,6,5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[6,6,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[7,6,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[3,3,3,3,3,3,3,3]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,4,4,4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,6,6,6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[9,8,7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[11,7,5,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0]
[9,7,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]
[8,8,8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,0,0,0]
[6,5,4,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[7,5,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[5,4,4,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[7,7,4,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[6,5,4,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[8,5,4,3,2,1,1]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[5,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[6,5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[7,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[6,5,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[7,6,5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[6,5,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[6,6,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[7,6,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[6,5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[6,6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[7,6,5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[7,6,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[15,5,5]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[9,7,5,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[10,7,5,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0]
[5,5,5,5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[8,7,4,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[6,5,4,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[8,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]
[6,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[6,6,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[7,5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[6,6,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[6,6,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[6,6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[6,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[7,5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[7,6,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[7,6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[9,7,5,4,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,0,1,0]
[5,5,5,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[8,7,6,5]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[6,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[7,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[7,6,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[7,6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[7,6,4,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[6,5,4,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[8,7,6,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[7,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[7,7,7,7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[7,6,5,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[10,7,6,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0]
[9,7,6,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0]
[10,8,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,1,0]
[4,4,4,4,4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,5,4,3,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[6,6,6,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[6,6,5,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[7,6,5,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[7,6,5,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[8,6,5,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[10,8,6,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]
[6,5,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[8,7,6,5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[8,7,6,5,3]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]
[7,7,5,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[7,6,5,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,6,6,6,6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[15,15]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[5,5,5,5,5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[9,7,5,5,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[7,6,5,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[7,6,5,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[8,7,5,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[11,8,6,4,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0]
[10,8,6,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[7,6,5,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[8,7,6,5,4]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[9,8,7,6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[7,6,5,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[7,6,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[11,8,6,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,0]
[6,5,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[8,7,6,5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[7,7,6,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[7,6,5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[7,5,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[8,7,6,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[8,7,6,5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[7,6,5,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[7,6,6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[8,7,6,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[7,6,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[6,6,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[8,7,6,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[7,6,6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[7,6,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[7,7,6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[8,7,6,5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[8,7,6,5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[8,7,6,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[7,6,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[8,7,6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[12,9,7,5,1]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0]
[7,7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[7,7,6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[8,7,6,5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[8,7,6,5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[8,6,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[7,7,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[7,7,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[8,7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[13,9,7,5,1]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0,1,0]
[8,7,6,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[8,7,6,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[9,8,7,6,5]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[11,9,7,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[11,8,7,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,1,0,0,0,1,0]
[8,7,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[8,7,6,5,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[9,7,6,5,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[8,7,6,5,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[8,7,6,5,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[9,8,7,6,5,4]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[10,10,10,10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[8,7,6,5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[11,9,7,5,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[8,7,6,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[8,7,6,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[8,7,7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[9,7,6,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[9,8,7,6,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[8,7,7,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[8,8,7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[9,8,6,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[8,8,7,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[9,8,7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[9,8,7,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[9,8,7,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[11,9,7,7,5,3,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[9,8,8,7,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[9,9,8,7,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[10,9,8,7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[5,5,5,5,5,5,5,5,5,5,5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
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(only identities of compositions of up to three maps are shown)
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Properties
injective
Sage code
def mapping(elt): return elt.to_dyck_word()
Weight
26
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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