Processing math: 100%

Identifier
Values
[1] => [1,0,1,0] => [1,0,1,0] => 0
[2] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 0
[1,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 0
[3] => [1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0] => 0
[2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 0
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,0] => 0
[4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => 0
[3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 0
[2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 0
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0] => 0
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 0
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 0
[3,2] => [1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => 0
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0] => 0
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => 0
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 0
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => 0
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 0
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => 0
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 1
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 0
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => 0
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => 0
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 0
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 0
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 0
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 0
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 0
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 0
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 0
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 0
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 0
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 0
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 0
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 0
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 1
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 0
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 0
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 0
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 0
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 0
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 0
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 0
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 0
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 0
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 0
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 1
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 0
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 0
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 0
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 0
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 0
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 0
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 0
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 0
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 0
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 0
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 0
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 0
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
>>> Load all 428 entries. <<<
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 0
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 0
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 0
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 0
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 0
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 1
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 1
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 0
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 0
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 0
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 0
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 0
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 0
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 0
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 0
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 1
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 0
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 1
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 0
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 0
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 0
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 0
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 1
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 0
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 0
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 0
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 0
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 0
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 1
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 0
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 0
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 1
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 0
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 1
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 0
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 0
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 0
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 0
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 0
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 0
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 0
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 0
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 0
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 0
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 0
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 0
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 0
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 1
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 0
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 1
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 0
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 1
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 0
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 0
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 0
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 0
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 0
[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 0
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 0
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 0
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 0
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 1
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 1
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 1
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 1
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 1
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 0
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 0
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 0
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 0
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 0
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 0
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 0
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 0
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 0
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 1
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 1
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 0
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 1
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 1
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 1
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 1
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 0
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 0
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 1
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 0
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 1
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 1
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 1
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 1
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 1
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 1
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 0
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 0
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 0
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 0
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
Number of simple modules with projective dimension 4 in the Nakayama algebra corresponding to the Dyck path.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
Cori-Le Borgne involution
Description
The Cori-Le Borgne involution on Dyck paths.
Append an additional down step to the Dyck path and consider its (literal) reversal. The image of the involution is then the unique rotation of this word which is a Dyck word followed by an additional down step. Alternatively, it is the composite ζ∘rev∘ζ(−1), where ζ is Mp00030zeta map.