Identifier
Values
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [1,2,2] => [1,2] => 0
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [1,2,2] => [1,2] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [2,2,2] => [3] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [2,2,2] => [3] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [1,3,2] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [1,2,3] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [1,2,3] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [1,3,2] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [1,3,2] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [1,2,3] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [2,2,2] => [3] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [2,2,2] => [3] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [2,2,2] => [3] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [1,2,3] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [1,2,3] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [1,3,2] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [1,3,2] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [1,2,3] => [1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [2,2,2] => [3] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [2,2,2] => [3] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [1,3,2] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [1,2,3] => [1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [3,2,2] => [1,2] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [3,2,2] => [1,2] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [2,3,2] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [2,2,3] => [2,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [2,2,3] => [2,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [2,3,2] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [2,3,2] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [2,2,3] => [2,1] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => [3,2,2] => [1,2] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => [3,2,2] => [1,2] => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [3,2,2] => [1,2] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [2,2,3] => [2,1] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [2,2,3] => [2,1] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [2,3,2] => [1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [2,3,2] => [1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [2,2,3] => [2,1] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => [3,2,2] => [1,2] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [3,2,2] => [1,2] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [2,3,2] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [2,2,3] => [2,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [1,4,2] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [1,3,3] => [1,2] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [1,3,3] => [1,2] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [1,4,2] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [1,4,2] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [1,3,3] => [1,2] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [1,2,4] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [1,2,4] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [1,2,2,2] => [1,3] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [1,2,4] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [1,2,4] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [1,3,3] => [1,2] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [1,3,3] => [1,2] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [1,4,2] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [1,4,2] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [1,3,3] => [1,2] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [1,3,3] => [1,2] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [1,3,3] => [1,2] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [1,2,2,2] => [1,3] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [1,2,4] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [1,2,4] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [1,4,2] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [1,3,3] => [1,2] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [1,4,2] => [1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,3,3] => [1,2] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [1,2,4] => [1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => [2,3,2] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [2,2,3] => [2,1] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [2,2,3] => [2,1] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [2,3,2] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [2,3,2] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [2,2,3] => [2,1] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => [3,2,2] => [1,2] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => [3,2,2] => [1,2] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [3,2,2] => [1,2] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [2,2,3] => [2,1] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => [2,2,3] => [2,1] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [2,3,2] => [1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => [2,3,2] => [1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => [2,2,3] => [2,1] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [3,2,2] => [1,2] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [3,2,2] => [1,2] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => [2,3,2] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => [2,2,3] => [2,1] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [2,3,2] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [2,2,3] => [2,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [2,2,3] => [2,1] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [2,3,2] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [2,3,2] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [2,2,3] => [2,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [1,2,4] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [1,2,4] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [1,2,2,2] => [1,3] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [1,2,4] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [1,2,4] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [1,3,3] => [1,2] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [1,3,3] => [1,2] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [1,4,2] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [1,4,2] => [1,1,1] => 1
>>> Load all 360 entries. <<<
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [1,3,3] => [1,2] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [1,3,3] => [1,2] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [1,3,3] => [1,2] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [1,2,2,2] => [1,3] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [1,2,4] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [1,2,4] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [1,4,2] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [1,3,3] => [1,2] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [1,4,2] => [1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,3,3] => [1,2] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [1,2,4] => [1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => [3,2,2] => [1,2] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [2,2,3] => [2,1] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => [2,2,3] => [2,1] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [2,3,2] => [1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => [2,3,2] => [1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => [2,2,3] => [2,1] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => [3,2,2] => [1,2] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [3,2,2] => [1,2] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => [2,3,2] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [2,2,3] => [2,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [3,2,2] => [1,2] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [2,2,3] => [2,1] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [2,2,3] => [2,1] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [2,3,2] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [2,3,2] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [2,2,3] => [2,1] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [1,3,3] => [1,2] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [1,3,3] => [1,2] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [1,2,2,2] => [1,3] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [1,2,4] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [1,2,4] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [1,4,2] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [1,3,3] => [1,2] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [1,4,2] => [1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,3,3] => [1,2] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [1,2,4] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [3,2,2] => [1,2] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => [2,3,2] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => [2,2,3] => [2,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [3,2,2] => [1,2] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [2,3,2] => [1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [2,2,3] => [2,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [1,4,2] => [1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,3,3] => [1,2] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [1,2,4] => [1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7] => [4,2,2] => [1,2] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,1,7,5,8,6] => [4,2,2] => [1,2] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => [3,2,3] => [1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,7,4,8,6] => [4,2,2] => [1,2] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,8] => [3,2,3] => [1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,4,8,5,7] => [3,2,3] => [1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => [3,2,3] => [1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,3,8,7] => [2,4,2] => [1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,7,3,8,6] => [2,4,2] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [2,2,4] => [2,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => [2,2,2,2] => [4] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,8,5,7] => [2,2,4] => [2,1] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,8,7] => [2,4,2] => [1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,8,5,7] => [2,3,3] => [1,2] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => [2,2,2,2] => [4] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [2,2,4] => [2,1] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,3,8,5,6,7] => [2,2,4] => [2,1] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,4,1,5,6,3,8,7] => [3,3,2] => [2,1] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,8] => [3,2,3] => [1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,3,6,8,7] => [3,3,2] => [2,1] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,7] => [3,2,3] => [1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7] => [4,2,2] => [1,2] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,8,5] => [3,2,3] => [1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,8] => [3,2,3] => [1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,6,7,3,8,5] => [3,3,2] => [2,1] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,8,7] => [3,3,2] => [2,1] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,7] => [3,2,3] => [1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,6,1,7,3,8,5] => [4,2,2] => [1,2] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,3,7,5,8,6] => [4,2,2] => [1,2] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7] => [2,2,2,2] => [4] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,8,7] => [2,4,2] => [1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,1,5,3,7,4,8,6] => [2,2,2,2] => [4] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,5,7,3,8,4,6] => [2,3,3] => [1,2] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,1,6,7,3,8,4] => [3,3,2] => [2,1] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,5,1,7,3,4,8,6] => [3,3,2] => [2,1] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [2,3,3] => [1,2] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,6,3,7,4,8,5] => [2,2,2,2] => [4] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,6,3,7,8,4,5] => [2,2,4] => [2,1] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,1,6,3,7,4,5,8] => [2,2,4] => [2,1] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,8,7] => [2,4,2] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,1,6,3,4,8,5,7] => [2,3,3] => [1,2] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,6,1,3,7,4,8,5] => [4,2,2] => [1,2] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,6,1,7,3,8,4,5] => [3,2,3] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,4,2,6,7,8,5] => [1,3,4] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,6,7,5,8] => [1,3,4] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,6,7,2,8,5] => [1,5,2] => [1,1,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [1,3,4] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => [1,2,2,3] => [1,2,1] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,2,2,3] => [1,2,1] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,5,8,4,6,7] => [1,2,5] => [1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => [1,2,5] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,5,2,6,7,4,8] => [1,3,4] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,5,2,6,8,4,7] => [1,3,4] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,5,6,2,7,4,8] => [1,4,3] => [1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,7,4,8,6] => [1,3,2,2] => [1,1,2] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,4,6,7,8,5] => [1,3,4] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,8] => [1,2,2,3] => [1,2,1] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,7] => [1,2,2,3] => [1,2,1] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,2,6,4,5,7,8] => [1,2,5] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,6,2,4,7,8,5] => [1,4,3] => [1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,2,7,8,4,5] => [1,3,4] => [1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8] => [1,4,3] => [1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,7,4,8,5,6] => [1,2,2,3] => [1,2,1] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,3,2,7,4,5,6,8] => [1,2,5] => [1,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [1,3,4] => [1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,4,3] => [1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,3,2,4,8,5,6,7] => [1,3,4] => [1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,3,2,8,4,5,6,7] => [1,2,5] => [1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [2,2,4] => [2,1] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7] => [2,2,2,2] => [4] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,8,5,7] => [2,2,4] => [2,1] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,7,5,8,6] => [2,2,2,2] => [4] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,4,2,8,5,6,7] => [2,2,4] => [2,1] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [4,2,2] => [1,2] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,4,6,1,7,2,8,5] => [4,2,2] => [1,2] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7] => [2,2,2,2] => [4] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,5,6,2,8,4,7] => [2,3,3] => [1,2] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,8,6] => [2,2,2,2] => [4] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6,8] => [2,2,4] => [2,1] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,7,2,4,8,6] => [2,4,2] => [1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,7,2,8,4,6] => [2,3,3] => [1,2] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,5,2,8,4,6,7] => [2,2,4] => [2,1] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => [3,3,2] => [2,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,5,6,1,7,2,8,4] => [4,2,2] => [1,2] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => [3,2,3] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,6,7,4,8,5] => [3,3,2] => [2,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,6,2,7,4,8,5] => [2,2,2,2] => [4] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [3,1,6,2,7,4,5,8] => [2,2,4] => [2,1] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,8,7] => [2,4,2] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [3,1,6,2,8,4,5,7] => [2,2,4] => [2,1] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,6,1,7,2,4,8,5] => [3,3,2] => [2,1] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => [3,2,3] => [1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,7,3,8,6] => [2,4,2] => [1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,5] => [2,2,4] => [2,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => [2,2,4] => [2,1] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [2,2,4] => [2,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,3] => [1,2,5] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,4,2,5,6,7,3,8] => [1,2,5] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => [1,2,2,3] => [1,2,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,4,2,5,7,3,8,6] => [1,2,3,2] => [1,1,1,1] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,4,2,5,7,8,3,6] => [1,2,5] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => [1,2,2,3] => [1,2,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,4,2,5,8,3,6,7] => [1,2,5] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,4,2,5,3,6,7,8] => [1,2,5] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,5,2,6,7,8,3] => [1,3,4] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,5,2,6,3,8,7] => [1,3,2,2] => [1,1,2] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,5,2,6,3,7,8] => [1,3,4] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,4,5,6,2,7,3,8] => [1,4,3] => [1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,5,2,7,3,8,6] => [1,3,2,2] => [1,1,2] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => [1,5,2] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,6,7,8,5] => [1,3,4] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,8] => [1,2,2,3] => [1,2,1] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,7,8,3,5] => [1,2,5] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => [1,2,2,3] => [1,2,1] => 2
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,6,3,5,7,8] => [1,2,5] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,4,6,2,7,3,8,5] => [1,3,2,2] => [1,1,2] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,6,2,7,8,3,5] => [1,3,4] => [1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,4,6,7,2,8,3,5] => [1,4,3] => [1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2,3,5,7,6,8] => [1,4,3] => [1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2,3,7,5,6,8] => [1,3,4] => [1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,7,3,8,5,6] => [1,2,2,3] => [1,2,1] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => [1,2,5] => [1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2,7,3,5,6,8] => [1,2,5] => [1,1,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [1,4,3] => [1,1,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,2,3,8,5,6,7] => [1,3,4] => [1,1,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => [1,2,5] => [1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,5,6,3,8,7] => [3,3,2] => [2,1] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [2,2,2,2] => [4] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,5,2,6,8,3,7] => [2,2,4] => [2,1] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => [2,2,2,2] => [4] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => [2,2,4] => [2,1] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,1,5,7,2,8,3,6] => [2,3,3] => [1,2] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => [4,2,2] => [1,2] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,5,1,6,2,7,3,8] => [3,2,3] => [1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [4,5,1,6,2,8,3,7] => [3,2,3] => [1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,5,1,7,2,3,8,6] => [3,3,2] => [2,1] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [4,5,1,7,2,8,3,6] => [3,2,3] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => [4,2,2] => [1,2] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,6,7,3,8,5] => [3,3,2] => [2,1] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,8,5,7] => [3,2,3] => [1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [2,3,3] => [1,2] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => [2,2,2,2] => [4] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,8,3,5,7] => [2,2,4] => [2,1] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,3,7,5,8,6] => [4,2,2] => [1,2] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [4,1,7,2,8,3,5,6] => [2,2,4] => [2,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8] => [3,2,3] => [1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => [3,2,3] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,4] => [2,2,4] => [2,1] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,2,5,3,6,7,4,8] => [2,2,4] => [2,1] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,2,5,3,6,4,7,8] => [2,2,4] => [2,1] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,2,5,6,3,7,8,4] => [2,3,3] => [1,2] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,2,5,6,7,3,8,4] => [2,4,2] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [2,2,4] => [2,1] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,5,2,3,6,7,8,4] => [1,3,4] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,2,3,6,4,7,8] => [1,3,4] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => [1,2,2,3] => [1,2,1] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,3,8,4,7] => [1,2,2,3] => [1,2,1] => 2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,2,6,3,4,7,8] => [1,2,5] => [1,1,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,6,2,3,8,4,7] => [1,4,3] => [1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => [1,4,3] => [1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6,8] => [1,3,4] => [1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => [1,2,2,3] => [1,2,1] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6,8] => [1,2,5] => [1,1,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [1,3,4] => [1,1,1] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [1,4,3] => [1,1,1] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => [1,2,5] => [1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => [2,2,2,2] => [4] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [5,1,6,2,3,8,4,7] => [2,3,3] => [1,2] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,7,3,4,8,6] => [3,3,2] => [2,1] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => [2,2,4] => [2,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,6,4,7,8,5] => [3,2,3] => [1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,8] => [3,2,3] => [1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,2,3,6,7,4,8,5] => [3,3,2] => [2,1] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,2,3,6,4,8,5,7] => [3,2,3] => [1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,2,6,3,4,7,8,5] => [2,3,3] => [1,2] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,2,6,3,7,4,5,8] => [2,2,4] => [2,1] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,2,6,3,4,8,5,7] => [2,3,3] => [1,2] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => [1,4,3] => [1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => [1,2,2,3] => [1,2,1] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,6,2,7,3,4,5,8] => [1,2,5] => [1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,6,7,2,8,3,4,5] => [1,3,4] => [1,1,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [1,4,3] => [1,1,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,6,2,8,3,4,5,7] => [1,2,5] => [1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => [4,2,2] => [1,2] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => [3,3,2] => [2,1] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => [3,2,3] => [1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => [2,4,2] => [1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => [1,5,2] => [1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [1,4,3] => [1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,7,2,3,8,4,5,6] => [1,3,4] => [1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,7,2,8,3,4,5,6] => [1,2,5] => [1,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => [1,6,2] => [1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,8,6,9,7] => [5,2,2] => [1,2] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,8,2,9,3,4,5,6,7] => [1,2,6] => [1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8] => [3,2,2,2] => [1,3] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,9] => [2,2,2,3] => [3,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8] => [1,2,2,2,2] => [1,4] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,2,3] => [1,2,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [2,2,2,2,2] => [5] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [1,2,2,2,3] => [1,3,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,4,7,5,8,9,6] => [4,2,3] => [1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,3,6,4,7,8,9,5] => [3,2,4] => [1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,9,4] => [2,2,5] => [2,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,9,3] => [1,2,6] => [1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,9,8] => [1,2,2,2,2] => [1,4] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7,9] => [4,2,3] => [1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => [3,2,2,3] => [1,2,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => [3,2,2,3] => [1,2,1] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,7,9] => [3,2,4] => [1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7,9] => [3,3,3] => [3] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,9,8] => [3,2,2,2] => [1,3] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7,10,9] => [4,2,2,2] => [1,3] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,2,2,2,2,2] => [6] => 1
search for individual values
searching the database for the individual values of this statistic
Description
The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles.
Map
DEX composition
Description
The DEX composition of a permutation.
Let $\pi$ be a permutation in $\mathfrak S_n$. Let $\bar\pi$ be the word in the ordered set $\bar 1 < \dots < \bar n < 1 \dots < n$ obtained from $\pi$ by replacing every excedance $\pi(i) > i$ by $\overline{\pi(i)}$. Then the DEX set of $\pi$ is the set of indices $1 \leq i < n$ such that $\bar\pi(i) > \bar\pi(i+1)$. Finally, the DEX composition $c_1, \dots, c_k$ of $n$ corresponds to the DEX subset $\{c_1, c_1 + c_2, \dots, c_1 + \dots + c_{k-1}\}$.
The (quasi)symmetric function
$$ \sum_{\pi\in\mathfrak S_{\lambda, j}} F_{DEX(\pi)}, $$
where the sum is over the set of permutations of cycle type $\lambda$ with $j$ excedances, is the Eulerian quasisymmetric function.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.