Processing math: 100%

Identifier
Values
[1,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[2,2] => [2] => [1,0,1,0] => [1,2] => 1
[2,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[3,2] => [2] => [1,0,1,0] => [1,2] => 1
[3,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[2,2,1] => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 1
[2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[1,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[4,2] => [2] => [1,0,1,0] => [1,2] => 1
[4,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[3,3] => [3] => [1,0,1,0,1,0] => [1,2,3] => 2
[3,2,1] => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 1
[3,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[2,2,2] => [2,2] => [1,1,1,0,0,0] => [3,1,2] => 1
[2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 1
[2,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 1
[5,2] => [2] => [1,0,1,0] => [1,2] => 1
[5,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[4,3] => [3] => [1,0,1,0,1,0] => [1,2,3] => 2
[4,2,1] => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 1
[4,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[3,2,2] => [2,2] => [1,1,1,0,0,0] => [3,1,2] => 1
[3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 1
[3,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => 2
[2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1
[2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 1
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 1
[6,2] => [2] => [1,0,1,0] => [1,2] => 1
[6,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[5,3] => [3] => [1,0,1,0,1,0] => [1,2,3] => 2
[5,2,1] => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 1
[5,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[4,4] => [4] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 3
[4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[4,2,2] => [2,2] => [1,1,1,0,0,0] => [3,1,2] => 1
[4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 1
[4,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => 2
[3,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1
[3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => 2
[3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1
[3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 1
[2,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => 1
[2,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => 2
[2,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 1
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 1
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 1
[7,2] => [2] => [1,0,1,0] => [1,2] => 1
[7,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[6,3] => [3] => [1,0,1,0,1,0] => [1,2,3] => 2
[6,2,1] => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 1
[6,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[5,4] => [4] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 3
[5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[5,2,2] => [2,2] => [1,1,1,0,0,0] => [3,1,2] => 1
[5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 1
[5,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[4,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
[4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => 2
[4,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1
[4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => 2
[4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1
[4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 1
[3,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [3,4,1,2] => 2
[3,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => 3
[3,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 1
[3,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => 1
[3,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => 2
[3,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 1
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 1
[2,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => 2
[2,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => 2
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 1
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 1
[8,2] => [2] => [1,0,1,0] => [1,2] => 1
[8,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[7,3] => [3] => [1,0,1,0,1,0] => [1,2,3] => 2
[7,2,1] => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 1
[7,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[6,4] => [4] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 3
[6,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[6,2,2] => [2,2] => [1,1,1,0,0,0] => [3,1,2] => 1
[6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 1
[6,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[5,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 4
[5,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
[5,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => 2
[5,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1
[5,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => 2
[5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1
[5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 1
[4,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => 2
[4,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 1
[4,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [3,4,1,2] => 2
[4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => 3
[4,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 1
[4,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => 1
>>> Load all 627 entries. <<<
[4,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => 2
[4,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 1
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 1
[3,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => 1
[3,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => 2
[3,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => 1
[3,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => 2
[3,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => 2
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 1
[2,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => 2
[2,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => 2
[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => 1
[9,2] => [2] => [1,0,1,0] => [1,2] => 1
[9,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[8,3] => [3] => [1,0,1,0,1,0] => [1,2,3] => 2
[8,2,1] => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 1
[8,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[7,4] => [4] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 3
[7,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[7,2,2] => [2,2] => [1,1,1,0,0,0] => [3,1,2] => 1
[7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 1
[7,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[6,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 4
[6,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
[6,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => 2
[6,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1
[6,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => 2
[6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1
[6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 1
[5,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 1
[5,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => 2
[5,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 1
[5,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [3,4,1,2] => 2
[5,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => 3
[5,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 1
[5,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => 1
[5,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => 2
[5,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 1
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 1
[4,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => 2
[4,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => 1
[4,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => 1
[4,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => 2
[4,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => 1
[4,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => 2
[4,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => 2
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 1
[3,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => 2
[3,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => 3
[3,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => 3
[3,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => 2
[3,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => 2
[3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 1
[2,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => 1
[2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => 1
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => 1
[10,2] => [2] => [1,0,1,0] => [1,2] => 1
[10,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[9,3] => [3] => [1,0,1,0,1,0] => [1,2,3] => 2
[9,2,1] => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 1
[9,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[8,4] => [4] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 3
[8,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[8,2,2] => [2,2] => [1,1,1,0,0,0] => [3,1,2] => 1
[8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 1
[8,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[7,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 4
[7,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
[7,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => 2
[7,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1
[7,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => 2
[7,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1
[7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 1
[6,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 5
[6,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 1
[6,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => 2
[6,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 1
[6,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [3,4,1,2] => 2
[6,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => 3
[6,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 1
[6,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => 1
[6,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => 2
[6,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 1
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 1
[5,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => 2
[5,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => 2
[5,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => 1
[5,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => 1
[5,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => 2
[5,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => 1
[5,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => 2
[5,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => 2
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 1
[4,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => 2
[4,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => 1
[4,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => 3
[4,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => 1
[4,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => 2
[4,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => 3
[4,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => 3
[4,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => 2
[4,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => 2
[4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 1
[3,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => 1
[3,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => 1
[3,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => 3
[3,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => 1
[3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => 1
[2,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => 3
[2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 1
[11,2] => [2] => [1,0,1,0] => [1,2] => 1
[11,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[10,3] => [3] => [1,0,1,0,1,0] => [1,2,3] => 2
[10,2,1] => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 1
[10,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[9,4] => [4] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 3
[9,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[9,2,2] => [2,2] => [1,1,1,0,0,0] => [3,1,2] => 1
[9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 1
[9,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[8,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 4
[8,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
[8,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => 2
[8,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1
[8,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => 2
[8,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1
[8,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 1
[7,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 5
[7,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 1
[7,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => 2
[7,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 1
[7,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [3,4,1,2] => 2
[7,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => 3
[7,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 1
[7,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => 1
[7,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => 2
[7,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 1
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 1
[6,6,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 1
[6,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => 2
[6,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => 2
[6,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => 1
[6,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => 1
[6,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => 2
[6,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => 1
[6,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => 2
[6,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => 2
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 1
[5,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => 2
[5,5,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => 1
[5,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => 2
[5,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => 1
[5,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => 3
[5,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => 1
[5,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => 2
[5,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => 3
[5,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => 3
[5,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => 2
[5,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => 2
[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 1
[4,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => 1
[4,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => 3
[4,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => 4
[4,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => 1
[4,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => 1
[4,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => 3
[4,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => 1
[4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => 1
[3,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => 2
[3,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => 3
[3,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => 3
[3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => 1
[2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 1
[12,2] => [2] => [1,0,1,0] => [1,2] => 1
[12,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[11,3] => [3] => [1,0,1,0,1,0] => [1,2,3] => 2
[11,2,1] => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 1
[11,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[10,4] => [4] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 3
[10,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[10,2,2] => [2,2] => [1,1,1,0,0,0] => [3,1,2] => 1
[10,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 1
[10,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[9,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 4
[9,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
[9,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => 2
[9,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1
[9,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => 2
[9,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1
[9,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 1
[8,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 5
[8,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 1
[8,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => 2
[8,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 1
[8,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [3,4,1,2] => 2
[8,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => 3
[8,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 1
[8,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => 1
[8,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => 2
[8,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 1
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 1
[7,7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 6
[7,6,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 1
[7,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => 2
[7,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => 2
[7,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => 1
[7,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => 1
[7,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => 2
[7,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => 1
[7,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => 2
[7,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => 2
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 1
[6,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => 2
[6,5,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => 1
[6,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => 2
[6,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => 1
[6,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => 3
[6,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => 1
[6,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => 2
[6,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => 3
[6,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => 3
[6,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => 2
[6,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => 2
[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 1
[5,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => 2
[5,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => 1
[5,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => 3
[5,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => 4
[5,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => 1
[5,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => 1
[5,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => 3
[5,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => 1
[5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => 1
[4,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => 3
[4,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => 2
[4,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => 2
[4,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => 3
[4,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => 3
[4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => 1
[3,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => 1
[3,3,3,3,1,1] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => 2
[3,3,2,2,2,2] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => 3
[3,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 1
[13,2] => [2] => [1,0,1,0] => [1,2] => 1
[13,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[12,3] => [3] => [1,0,1,0,1,0] => [1,2,3] => 2
[12,2,1] => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 1
[12,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[11,4] => [4] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 3
[11,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[11,2,2] => [2,2] => [1,1,1,0,0,0] => [3,1,2] => 1
[11,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 1
[11,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[10,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 4
[10,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
[10,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => 2
[10,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1
[10,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => 2
[10,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 1
[9,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 5
[9,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 1
[9,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => 2
[9,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 1
[9,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [3,4,1,2] => 2
[9,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => 3
[9,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 1
[9,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => 1
[9,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => 2
[9,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 1
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 1
[8,7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 6
[8,6,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 1
[8,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => 2
[8,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => 2
[8,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => 1
[8,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => 1
[8,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => 2
[8,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => 1
[8,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => 2
[8,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => 2
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 1
[7,7,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 1
[7,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => 2
[7,5,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => 1
[7,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => 2
[7,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => 1
[7,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => 3
[7,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => 1
[7,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => 2
[7,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => 3
[7,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => 3
[7,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => 2
[7,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => 2
[7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 1
[6,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => 2
[6,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => 1
[6,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => 3
[6,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => 4
[6,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => 1
[6,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => 1
[6,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => 3
[6,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => 1
[6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => 1
[5,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => 2
[5,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => 3
[5,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => 2
[5,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => 2
[5,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => 3
[5,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => 3
[5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => 1
[4,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => 2
[4,4,3,3,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => 3
[4,4,3,2,2] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => 3
[4,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => 1
[4,3,3,3,1,1] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => 2
[4,3,2,2,2,2] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => 3
[4,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 1
[3,3,3,3,3] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => 1
[3,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => 2
[14,2] => [2] => [1,0,1,0] => [1,2] => 1
[14,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[13,3] => [3] => [1,0,1,0,1,0] => [1,2,3] => 2
[13,2,1] => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 1
[13,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[12,4] => [4] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 3
[12,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[12,2,2] => [2,2] => [1,1,1,0,0,0] => [3,1,2] => 1
[12,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 1
[12,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[11,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 4
[11,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
[11,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => 2
[11,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1
[11,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => 2
[11,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 1
[10,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 5
[10,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 1
[10,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => 2
[10,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 1
[10,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [3,4,1,2] => 2
[10,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => 3
[10,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 1
[10,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => 1
[10,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => 2
[10,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 1
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 1
[9,7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 6
[9,6,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 1
[9,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => 2
[9,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => 2
[9,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => 1
[9,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => 1
[9,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => 2
[9,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => 1
[9,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => 2
[9,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => 2
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 1
[8,8] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => 7
[8,7,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 1
[8,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => 2
[8,5,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => 1
[8,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => 2
[8,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => 1
[8,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => 3
[8,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => 1
[8,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => 2
[8,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => 3
[8,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => 3
[8,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => 2
[8,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => 2
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 1
[7,7,2] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => 2
[7,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => 2
[7,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => 1
[7,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => 3
[7,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => 4
[7,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => 1
[7,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => 1
[7,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => 3
[7,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => 1
[7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => 1
[6,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => 2
[6,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => 3
[6,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => 2
[6,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => 2
[6,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => 3
[6,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => 3
[6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => 1
[5,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => 2
[5,4,3,3,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => 3
[5,4,3,2,2] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => 3
[5,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => 1
[5,3,3,3,1,1] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => 2
[5,3,2,2,2,2] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => 3
[5,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 1
[4,4,4,4] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => 2
[4,4,3,3,2] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => 2
[4,3,3,3,3] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => 1
[4,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => 2
[3,3,3,3,3,1] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => 2
[15,2] => [2] => [1,0,1,0] => [1,2] => 1
[15,1,1] => [1,1] => [1,1,0,0] => [2,1] => 1
[14,3] => [3] => [1,0,1,0,1,0] => [1,2,3] => 2
[14,2,1] => [2,1] => [1,0,1,1,0,0] => [1,3,2] => 1
[14,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [2,3,1] => 1
[13,4] => [4] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 3
[13,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[13,2,2] => [2,2] => [1,1,1,0,0,0] => [3,1,2] => 1
[13,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 1
[13,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[12,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 4
[12,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
[12,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => 2
[12,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1
[12,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [3,1,4,2] => 2
[12,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 1
[11,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 5
[11,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 1
[11,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => 2
[11,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 1
[11,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [3,4,1,2] => 2
[11,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => 3
[11,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 1
[11,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [4,1,2,3] => 1
[11,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => 2
[11,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 1
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 1
[10,7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 6
[10,6,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 1
[10,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => 2
[10,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => 2
[10,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => 1
[10,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => 1
[10,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => 2
[10,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => 1
[10,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => 2
[10,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => 2
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 1
[9,8] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => 7
[9,7,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 1
[9,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => 2
[9,5,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => 1
[9,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => 2
[9,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => 1
[9,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => 3
[9,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => 1
[9,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => 2
[9,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => 3
[9,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => 3
[9,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => 2
[9,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => 2
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 1
[8,8,1] => [8,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => 1
[8,7,2] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => 2
[8,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => 2
[8,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => 1
[8,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => 3
[8,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => 4
[8,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => 1
[8,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => 1
[8,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => 3
[8,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => 1
[8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => 1
[7,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => 2
[7,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => 3
[7,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => 2
[7,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => 2
[7,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => 3
[7,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => 3
[7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => 1
[6,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => 2
[6,4,3,3,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => 3
[6,4,3,2,2] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => 3
[6,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => 1
[6,3,3,3,1,1] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => 2
[6,3,2,2,2,2] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => 3
[6,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 1
[5,5,4,3] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => 3
[5,5,3,3,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,3,4,5,8,6] => 4
[5,4,4,4] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => 2
[5,4,3,3,2] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => 2
[5,3,3,3,3] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => 1
[5,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => 2
[4,4,4,4,1] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,1,2,3,7,4] => 1
[4,4,3,3,3] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => 2
[4,3,3,3,3,1] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => 2
[3,3,3,3,3,2] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => 1
[6,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => 2
[6,4,3,3,2] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => 2
[6,5,3,3,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,3,4,5,8,6] => 4
[6,5,4,3] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => 3
[5,4,3,3,3,2] => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,2,3,8,4,5,6] => 2
[4,3,3,3,3,2] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => 1
[4,4,4,3,2,2] => [4,4,3,2,2] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,1,7,8,2,4,5] => 2
[7,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => 2
[5,4,3,3,3] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => 2
[7,3,3,3,3] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => 1
[7,5,4,3] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => 3
[3,3,3,3,3,3] => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => 2
[3,3,3,3,3,3,3,3] => [3,3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => 4
[3,3,3,3,3,3,1] => [3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,1,2,3,4,8,5] => 1
[3,3,3,3,3,3,3] => [3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => 3
[4,3,3,3,3,3] => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => 2
[4,4,4,4,4] => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => 1
[4,4,4,4,4,4] => [4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => 1
[5,5,5,5] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => 3
[6,6,6,6] => [6,6,6] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4] => 4
[6,6,6] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => 2
[7,6,6] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => 2
[10,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => 2
[10,10] => [10] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => 9
[6,6,6,6,6] => [6,6,6,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => 3
[5,5,5,5,5,5] => [5,5,5,5,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => 1
[15,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => 2
[7,7,7] => [7,7] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,1,2] => 2
[5,5,5,5,5] => [5,5,5,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => 2
[9,9] => [9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => 8
[4,4,4,4,4,4,4] => [4,4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => 2
[6,5,5,5] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => 3
[5,4,4,4,4] => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => 1
[4,4,4,4,4,1] => [4,4,4,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,8,6] => 2
search for individual values
searching the database for the individual values of this statistic
Description
The length of the exterior of a permutation.
The exterior of a permutation is the longest proper prefix that is also a suffix, when viewed as a pattern. In other words, the length of the exterior of a permutation σ of length n is the largest i<n such that the first i entries of σ are in the same relative order as the last i entries of σ.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength n in an n×n square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.