Identifier
Values
[1,0] => [1] => [1] => [[1],[]] => 0
[1,0,1,0] => [1,2] => [1,1] => [[1,1],[]] => 0
[1,1,0,0] => [2,1] => [2] => [[2],[]] => 0
[1,0,1,0,1,0] => [1,2,3] => [1,1,1] => [[1,1,1],[]] => 0
[1,0,1,1,0,0] => [1,3,2] => [2,1] => [[2,1],[]] => 0
[1,1,0,0,1,0] => [2,1,3] => [2,1] => [[2,1],[]] => 0
[1,1,0,1,0,0] => [2,3,1] => [2,1] => [[2,1],[]] => 0
[1,1,1,0,0,0] => [3,2,1] => [3] => [[3],[]] => 0
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,1,1,1] => [[1,1,1,1],[]] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [2,1,1] => [[2,1,1],[]] => 0
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [2,1,1] => [[2,1,1],[]] => 0
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,1,1] => [[2,1,1],[]] => 0
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [3,1] => [[3,1],[]] => 0
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,1] => [[2,1,1],[]] => 0
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,2] => [[2,2],[]] => 1
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,1,1] => [[2,1,1],[]] => 0
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,1,1] => [[2,1,1],[]] => 0
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [3,1] => [[3,1],[]] => 0
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,1] => [[3,1],[]] => 0
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,1] => [[3,1],[]] => 0
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [3,1] => [[3,1],[]] => 0
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4] => [[4],[]] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [2,1,1,1] => [[2,1,1,1],[]] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [2,1,1,1] => [[2,1,1,1],[]] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [2,1,1,1] => [[2,1,1,1],[]] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [3,1,1] => [[3,1,1],[]] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [2,1,1,1] => [[2,1,1,1],[]] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [2,2,1] => [[2,2,1],[]] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [2,1,1,1] => [[2,1,1,1],[]] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,1,1,1] => [[2,1,1,1],[]] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [3,1,1] => [[3,1,1],[]] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [3,1,1] => [[3,1,1],[]] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [3,1,1] => [[3,1,1],[]] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [3,1,1] => [[3,1,1],[]] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [4,1] => [[4,1],[]] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,1,1] => [[2,1,1,1],[]] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,2,1] => [[2,2,1],[]] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,2,1] => [[2,2,1],[]] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,2,1] => [[2,2,1],[]] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [3,2] => [[3,2],[]] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,1,1,1] => [[2,1,1,1],[]] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [2,2,1] => [[2,2,1],[]] => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,1,1,1] => [[2,1,1,1],[]] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,1,1,1] => [[2,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [3,1,1] => [[3,1,1],[]] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,1,1] => [[3,1,1],[]] => 0
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [3,1,1] => [[3,1,1],[]] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [3,1,1] => [[3,1,1],[]] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [4,1] => [[4,1],[]] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,1,1] => [[3,1,1],[]] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [3,2] => [[3,2],[]] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,1,1] => [[3,1,1],[]] => 0
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,1,1] => [[3,1,1],[]] => 0
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [3,2] => [[3,2],[]] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [3,1,1] => [[3,1,1],[]] => 0
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [3,1,1] => [[3,1,1],[]] => 0
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [3,1,1] => [[3,1,1],[]] => 0
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [4,1] => [[4,1],[]] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,1] => [[4,1],[]] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [4,1] => [[4,1],[]] => 0
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [4,1] => [[4,1],[]] => 0
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [4,1] => [[4,1],[]] => 0
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5] => [[5],[]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [4,1,1] => [[4,1,1],[]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [3,2,1] => [[3,2,1],[]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [4,1,1] => [[4,1,1],[]] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [3,2,1] => [[3,2,1],[]] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [3,2,1] => [[3,2,1],[]] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [4,1,1] => [[4,1,1],[]] => 0
>>> Load all 625 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [4,1,1] => [[4,1,1],[]] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [4,1,1] => [[4,1,1],[]] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [4,1,1] => [[4,1,1],[]] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [4,1,1] => [[4,1,1],[]] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [5,1] => [[5,1],[]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,2,2] => [[2,2,2],[]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [4,2] => [[4,2],[]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [2,2,1,1] => [[2,2,1,1],[]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [5,1] => [[5,1],[]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [3,3] => [[3,3],[]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [4,2] => [[4,2],[]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [3,2,1] => [[3,2,1],[]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [3,1,1,1] => [[3,1,1,1],[]] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [5,1] => [[5,1],[]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [4,2] => [[4,2],[]] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [4,2] => [[4,2],[]] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [4,2] => [[4,2],[]] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [4,1,1] => [[4,1,1],[]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [5,1] => [[5,1],[]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,1] => [[5,1],[]] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [5,1] => [[5,1],[]] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [5,1] => [[5,1],[]] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [5,1] => [[5,1],[]] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [5,1] => [[5,1],[]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6] => [[6],[]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [5,1,1] => [[5,1,1],[]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [2,2,2,1] => [[2,2,2,1],[]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [4,2,1] => [[4,2,1],[]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [5,1,1] => [[5,1,1],[]] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [3,3,1] => [[3,3,1],[]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [4,2,1] => [[4,2,1],[]] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [5,1,1] => [[5,1,1],[]] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [4,2,1] => [[4,2,1],[]] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [4,2,1] => [[4,2,1],[]] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [4,2,1] => [[4,2,1],[]] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [5,1,1] => [[5,1,1],[]] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [5,1,1] => [[5,1,1],[]] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [5,1,1] => [[5,1,1],[]] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [5,1,1] => [[5,1,1],[]] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [5,1,1] => [[5,1,1],[]] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [5,1,1] => [[5,1,1],[]] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [6,1] => [[6,1],[]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,2,2,1] => [[2,2,2,1],[]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,2,2,1] => [[2,2,2,1],[]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,2,2,1] => [[2,2,2,1],[]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,2,2,1] => [[2,2,2,1],[]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [3,2,2] => [[3,2,2],[]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,2,2,1] => [[2,2,2,1],[]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [3,2,2] => [[3,2,2],[]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [3,2,2] => [[3,2,2],[]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [5,2] => [[5,2],[]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [2,2,2,1] => [[2,2,2,1],[]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,3,1] => [[3,3,1],[]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [6,1] => [[6,1],[]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [3,3,1] => [[3,3,1],[]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [3,2,2] => [[3,2,2],[]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,3,1] => [[3,3,1],[]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [3,3,1] => [[3,3,1],[]] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,3,1] => [[3,3,1],[]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [3,3,1] => [[3,3,1],[]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [4,3] => [[4,3],[]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [3,3,1] => [[3,3,1],[]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [3,2,2] => [[3,2,2],[]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [3,2,2] => [[3,2,2],[]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [5,2] => [[5,2],[]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [3,3,1] => [[3,3,1],[]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [3,2,1,1] => [[3,2,1,1],[]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [6,1] => [[6,1],[]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [4,3] => [[4,3],[]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [4,3] => [[4,3],[]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [5,2] => [[5,2],[]] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [4,2,1] => [[4,2,1],[]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [4,1,1,1] => [[4,1,1,1],[]] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [6,1] => [[6,1],[]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [5,2] => [[5,2],[]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [5,2] => [[5,2],[]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [5,2] => [[5,2],[]] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [5,2] => [[5,2],[]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [5,1,1] => [[5,1,1],[]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [6,1] => [[6,1],[]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,1] => [[6,1],[]] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [6,1] => [[6,1],[]] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [6,1] => [[6,1],[]] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [6,1] => [[6,1],[]] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [6,1] => [[6,1],[]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [6,1] => [[6,1],[]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7] => [[7],[]] => 0
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Description
The number of two-by-two squares inside a skew partition.
This is, the number of cells $(i,j)$ in a skew partition for which the box $(i+1,j+1)$ is also a cell inside the skew partition.
Map
LLPS
Description
The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
to skew partition
Description
The partition regarded as a skew partition.