Identifier
-
Mp00024:
Dyck paths
—to 321-avoiding permutation⟶
Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
St001462: Standard tableaux ⟶ ℤ
Values
[1,0] => [1] => [1] => [[1]] => 1
[1,0,1,0] => [2,1] => [2,1] => [[1],[2]] => 1
[1,1,0,0] => [1,2] => [1,2] => [[1,2]] => 2
[1,0,1,0,1,0] => [2,1,3] => [2,1,3] => [[1,3],[2]] => 2
[1,0,1,1,0,0] => [2,3,1] => [3,2,1] => [[1],[2],[3]] => 1
[1,1,0,0,1,0] => [3,1,2] => [3,2,1] => [[1],[2],[3]] => 1
[1,1,0,1,0,0] => [1,3,2] => [1,3,2] => [[1,2],[3]] => 2
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [[1,2,3]] => 3
[1,0,1,0,1,0,1,0] => [2,1,4,3] => [2,1,4,3] => [[1,3],[2,4]] => 2
[1,0,1,0,1,1,0,0] => [2,4,1,3] => [3,4,1,2] => [[1,2],[3,4]] => 1
[1,0,1,1,0,0,1,0] => [2,1,3,4] => [2,1,3,4] => [[1,3,4],[2]] => 3
[1,0,1,1,0,1,0,0] => [2,3,1,4] => [3,2,1,4] => [[1,4],[2],[3]] => 2
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [4,2,3,1] => [[1,3],[2],[4]] => 1
[1,1,0,0,1,0,1,0] => [3,1,4,2] => [4,2,3,1] => [[1,3],[2],[4]] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [4,3,2,1] => [[1],[2],[3],[4]] => 1
[1,1,0,1,0,0,1,0] => [3,1,2,4] => [3,2,1,4] => [[1,4],[2],[3]] => 2
[1,1,0,1,0,1,0,0] => [1,3,2,4] => [1,3,2,4] => [[1,2,4],[3]] => 3
[1,1,0,1,1,0,0,0] => [1,3,4,2] => [1,4,3,2] => [[1,2],[3],[4]] => 2
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [4,2,3,1] => [[1,3],[2],[4]] => 1
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,4,3,2] => [[1,2],[3],[4]] => 2
[1,1,1,0,1,0,0,0] => [1,2,4,3] => [1,2,4,3] => [[1,2,3],[4]] => 3
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [[1,2,3,4]] => 4
[1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => [[1,3,5],[2,4]] => 3
[1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => [3,4,1,2,5] => [[1,2,5],[3,4]] => 2
[1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [2,1,5,4,3] => [[1,3],[2,4],[5]] => 2
[1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => [3,5,1,4,2] => [[1,2],[3,4],[5]] => 1
[1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => [4,5,3,1,2] => [[1,2],[3,5],[4]] => 1
[1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [2,1,5,4,3] => [[1,3],[2,4],[5]] => 2
[1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => [3,5,1,4,2] => [[1,2],[3,4],[5]] => 1
[1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => [2,1,3,5,4] => [[1,3,4],[2,5]] => 3
[1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => [3,2,1,5,4] => [[1,4],[2,5],[3]] => 2
[1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => [4,2,5,1,3] => [[1,3],[2,5],[4]] => 1
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[1,3,4,5],[2]] => 4
[1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => [3,2,1,4,5] => [[1,4,5],[2],[3]] => 3
[1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => [4,2,3,1,5] => [[1,3,5],[2],[4]] => 2
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => [[1,3,4],[2],[5]] => 1
[1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => [4,2,3,1,5] => [[1,3,5],[2],[4]] => 2
[1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => [4,3,2,1,5] => [[1,5],[2],[3],[4]] => 2
[1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => [5,2,3,4,1] => [[1,3,4],[2],[5]] => 1
[1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => [5,3,2,4,1] => [[1,4],[2],[3],[5]] => 1
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]] => 1
[1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => [4,2,5,1,3] => [[1,3],[2,5],[4]] => 1
[1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => [4,5,3,1,2] => [[1,2],[3,5],[4]] => 1
[1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => [3,2,1,5,4] => [[1,4],[2,5],[3]] => 2
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [[1,2,4],[3,5]] => 3
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,4,5,2,3] => [[1,2,3],[4,5]] => 2
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => [3,2,1,4,5] => [[1,4,5],[2],[3]] => 3
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => [[1,2,4,5],[3]] => 4
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => [1,4,3,2,5] => [[1,2,5],[3],[4]] => 3
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => [1,5,3,4,2] => [[1,2,4],[3],[5]] => 2
[1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => [5,2,4,3,1] => [[1,3],[2],[4],[5]] => 1
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]] => 1
[1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => [5,2,3,4,1] => [[1,3,4],[2],[5]] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => [1,5,3,4,2] => [[1,2,4],[3],[5]] => 2
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => [4,2,3,1,5] => [[1,3,5],[2],[4]] => 2
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => [1,4,3,2,5] => [[1,2,5],[3],[4]] => 3
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => [[1,2,3,5],[4]] => 4
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => [1,2,5,4,3] => [[1,2,3],[4],[5]] => 3
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [5,2,3,4,1] => [[1,3,4],[2],[5]] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => [1,5,3,4,2] => [[1,2,4],[3],[5]] => 2
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => [1,2,5,4,3] => [[1,2,3],[4],[5]] => 3
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [[1,2,3,4],[5]] => 4
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [[1,2,3,4,5]] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => 3
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => [3,4,1,2,6,5] => [[1,2,5],[3,4,6]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [2,1,5,6,3,4] => [[1,3,4],[2,5,6]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => [3,5,1,6,2,4] => [[1,2,4],[3,5,6]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => [4,5,6,1,2,3] => [[1,2,3],[4,5,6]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => [3,4,1,2,5,6] => [[1,2,5,6],[3,4]] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [[1,3,6],[2,4],[5]] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => [3,5,1,4,2,6] => [[1,2,6],[3,4],[5]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [4,5,3,1,2,6] => [[1,2,6],[3,5],[4]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [[1,3,5],[2,4],[6]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => [3,6,1,4,5,2] => [[1,2,5],[3,4],[6]] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => [4,6,3,1,5,2] => [[1,2],[3,5],[4,6]] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => [5,6,3,4,1,2] => [[1,2],[3,4],[5,6]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [2,1,6,4,5,3] => [[1,3,5],[2,4],[6]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [3,6,1,4,5,2] => [[1,2,5],[3,4],[6]] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => [3,6,1,5,4,2] => [[1,2],[3,4],[5],[6]] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => [4,6,5,1,3,2] => [[1,2],[3,5],[4],[6]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [2,1,5,4,3,6] => [[1,3,6],[2,4],[5]] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => [3,5,1,4,2,6] => [[1,2,6],[3,4],[5]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [[1,4,6],[2,5],[3]] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [4,2,5,1,3,6] => [[1,3,6],[2,5],[4]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [[1,3,4],[2,5],[6]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => [4,2,6,1,5,3] => [[1,3],[2,5],[4,6]] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => [5,2,6,4,1,3] => [[1,3],[2,4],[5,6]] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [2,1,6,4,5,3] => [[1,3,5],[2,4],[6]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => [3,6,1,4,5,2] => [[1,2,5],[3,4],[6]] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => [2,1,3,6,5,4] => [[1,3,4],[2,5],[6]] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => [4,2,6,1,5,3] => [[1,3],[2,5],[4,6]] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [[1,3,4,5],[2,6]] => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [[1,4,5],[2,6],[3]] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [[1,3,5],[2,6],[4]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => [5,2,3,6,1,4] => [[1,3,4],[2,6],[5]] => 1
>>> Load all 1640 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => 5
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [[1,3,5,6],[2],[4]] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [[1,3,4,6],[2],[5]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => [4,2,3,1,6,5] => [[1,3,5],[2,6],[4]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => [4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => [5,2,3,6,1,4] => [[1,3,4],[2,6],[5]] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => [5,3,2,6,1,4] => [[1,4],[2,6],[3],[5]] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => [5,4,6,2,1,3] => [[1,3],[2,6],[4],[5]] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [4,2,3,1,5,6] => [[1,3,5,6],[2],[4]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => [4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [5,2,3,4,1,6] => [[1,3,4,6],[2],[5]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => [5,3,2,4,1,6] => [[1,4,6],[2],[3],[5]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => [6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => [6,3,2,4,5,1] => [[1,4,5],[2],[3],[6]] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => [6,4,3,2,5,1] => [[1,5],[2],[3],[4],[6]] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [6,5,3,4,2,1] => [[1,4],[2],[3],[5],[6]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => [4,2,6,1,5,3] => [[1,3],[2,5],[4,6]] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => [4,6,3,1,5,2] => [[1,2],[3,5],[4,6]] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => [5,2,6,4,1,3] => [[1,3],[2,4],[5,6]] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => [5,6,3,4,1,2] => [[1,2],[3,4],[5,6]] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => [5,6,4,3,1,2] => [[1,2],[3,6],[4],[5]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => [4,2,5,1,3,6] => [[1,3,6],[2,5],[4]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => [4,5,3,1,2,6] => [[1,2,6],[3,5],[4]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => [3,2,1,5,4,6] => [[1,4,6],[2,5],[3]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [[1,2,4,6],[3,5]] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,4,5,2,3,6] => [[1,2,3,6],[4,5]] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [[1,2,4],[3,5],[6]] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => [1,4,6,2,5,3] => [[1,2,3],[4,5],[6]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => [1,5,6,4,2,3] => [[1,2,3],[4,6],[5]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => [4,2,6,1,5,3] => [[1,3],[2,5],[4,6]] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => [4,6,3,1,5,2] => [[1,2],[3,5],[4,6]] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => [1,3,2,6,5,4] => [[1,2,4],[3,5],[6]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => [1,4,6,2,5,3] => [[1,2,3],[4,5],[6]] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => [3,2,1,4,6,5] => [[1,4,5],[2,6],[3]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [[1,2,4,5],[3,6]] => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [[1,2,5],[3,6],[4]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => [1,5,3,6,2,4] => [[1,2,4],[3,6],[5]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [[1,2,5,6],[3],[4]] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [[1,2,4,6],[3],[5]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [[1,2,4,5],[3],[6]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => [6,2,4,3,5,1] => [[1,3,5],[2],[4],[6]] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => [6,4,3,2,5,1] => [[1,5],[2],[3],[4],[6]] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => [6,2,5,4,3,1] => [[1,3],[2],[4],[5],[6]] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => [6,5,3,4,2,1] => [[1,4],[2],[3],[5],[6]] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => [5,2,4,3,1,6] => [[1,3,6],[2],[4],[5]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => [5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => [5,2,3,4,1,6] => [[1,3,4,6],[2],[5]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => [1,5,3,4,2,6] => [[1,2,4,6],[3],[5]] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [1,5,4,3,2,6] => [[1,2,6],[3],[4],[5]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => [6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => [1,6,3,4,5,2] => [[1,2,4,5],[3],[6]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => [1,6,4,3,5,2] => [[1,2,5],[3],[4],[6]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => [5,2,6,4,1,3] => [[1,3],[2,4],[5,6]] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => [5,6,3,4,1,2] => [[1,2],[3,4],[5,6]] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => [5,2,3,6,1,4] => [[1,3,4],[2,6],[5]] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => [1,5,3,6,2,4] => [[1,2,4],[3,6],[5]] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => [1,5,6,4,2,3] => [[1,2,3],[4,6],[5]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => [4,2,3,1,6,5] => [[1,3,5],[2,6],[4]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => [1,4,3,2,6,5] => [[1,2,5],[3,6],[4]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [[1,2,3,5],[4,6]] => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => [1,2,5,6,3,4] => [[1,2,3,4],[5,6]] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => [4,2,3,1,5,6] => [[1,3,5,6],[2],[4]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => [1,4,3,2,5,6] => [[1,2,5,6],[3],[4]] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => 5
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [[1,2,3,6],[4],[5]] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [[1,2,3,5],[4],[6]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => [6,2,5,4,3,1] => [[1,3],[2],[4],[5],[6]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [6,5,3,4,2,1] => [[1,4],[2],[3],[5],[6]] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => [6,2,3,5,4,1] => [[1,3,4],[2],[5],[6]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => [1,6,3,5,4,2] => [[1,2,4],[3],[5],[6]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => [6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => [1,6,3,4,5,2] => [[1,2,4,5],[3],[6]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => [1,2,6,4,5,3] => [[1,2,3,5],[4],[6]] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => [1,2,6,5,4,3] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => [5,2,3,4,1,6] => [[1,3,4,6],[2],[5]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => [1,5,3,4,2,6] => [[1,2,4,6],[3],[5]] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => [1,2,5,4,3,6] => [[1,2,3,6],[4],[5]] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => 5
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => [1,6,3,4,5,2] => [[1,2,4,5],[3],[6]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [1,2,6,4,5,3] => [[1,2,3,5],[4],[6]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [[1,3,5,7],[2,4,6]] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7] => [3,4,1,2,6,5,7] => [[1,2,5,7],[3,4,6]] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,7] => [2,1,5,6,3,4,7] => [[1,3,4,7],[2,5,6]] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7] => [3,5,1,6,2,4,7] => [[1,2,4,7],[3,5,6]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7] => [4,5,6,1,2,3,7] => [[1,2,3,7],[4,5,6]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [[1,3,5],[2,4,6],[7]] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,7,5] => [3,4,1,2,7,6,5] => [[1,2,5],[3,4,6],[7]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [2,1,5,7,3,6,4] => [[1,3,4],[2,5,6],[7]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5] => [3,5,1,7,2,6,4] => [[1,2,4],[3,5,6],[7]] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5] => [4,5,7,1,2,6,3] => [[1,2,3],[4,5,6],[7]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,7,3,5] => [2,1,6,7,5,3,4] => [[1,3,4],[2,5,7],[6]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,7,3,5] => [3,6,1,7,5,2,4] => [[1,2,4],[3,5,7],[6]] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,7,3,5] => [4,6,7,1,5,2,3] => [[1,2,3],[4,5,7],[6]] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5] => [5,6,7,4,1,2,3] => [[1,2,3],[4,6,7],[5]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [2,1,4,3,7,6,5] => [[1,3,5],[2,4,6],[7]] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,7,5,6] => [3,4,1,2,7,6,5] => [[1,2,5],[3,4,6],[7]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,7,3,5,6] => [2,1,5,7,3,6,4] => [[1,3,4],[2,5,6],[7]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,7,3,5,6] => [3,5,1,7,2,6,4] => [[1,2,4],[3,5,6],[7]] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,7,1,3,5,6] => [4,5,7,1,2,6,3] => [[1,2,3],[4,5,6],[7]] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [[1,3,5,6],[2,4,7]] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,3,5,7,6] => [3,4,1,2,5,7,6] => [[1,2,5,6],[3,4,7]] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [[1,3,6],[2,4,7],[5]] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6] => [3,5,1,4,2,7,6] => [[1,2,6],[3,4,7],[5]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6] => [4,5,3,1,2,7,6] => [[1,2,6],[3,5,7],[4]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,3,6] => [2,1,6,4,7,3,5] => [[1,3,5],[2,4,7],[6]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,6] => [3,6,1,4,7,2,5] => [[1,2,5],[3,4,7],[6]] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6] => [4,6,3,1,7,2,5] => [[1,2,5],[3,6,7],[4]] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [5,6,3,7,1,2,4] => [[1,2,4],[3,6,7],[5]] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [[1,3,5,6,7],[2,4]] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7] => [3,4,1,2,5,6,7] => [[1,2,5,6,7],[3,4]] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [[1,3,6,7],[2,4],[5]] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7] => [3,5,1,4,2,6,7] => [[1,2,6,7],[3,4],[5]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7] => [4,5,3,1,2,6,7] => [[1,2,6,7],[3,5],[4]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [[1,3,5,7],[2,4],[6]] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7] => [3,6,1,4,5,2,7] => [[1,2,5,7],[3,4],[6]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7] => [4,6,3,1,5,2,7] => [[1,2,7],[3,5],[4,6]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7] => [5,6,3,4,1,2,7] => [[1,2,7],[3,4],[5,6]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [[1,3,5,6],[2,4],[7]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3] => [3,7,1,4,5,6,2] => [[1,2,5,6],[3,4],[7]] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3] => [4,7,3,1,5,6,2] => [[1,2,6],[3,5],[4,7]] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3] => [5,7,3,4,1,6,2] => [[1,2,6],[3,4],[5,7]] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3] => [6,7,3,4,5,1,2] => [[1,2,5],[3,4],[6,7]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [2,1,6,4,5,3,7] => [[1,3,5,7],[2,4],[6]] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7] => [3,6,1,4,5,2,7] => [[1,2,5,7],[3,4],[6]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7] => [2,1,6,5,4,3,7] => [[1,3,7],[2,4],[5],[6]] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7] => [3,6,1,5,4,2,7] => [[1,2,7],[3,4],[5],[6]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,7] => [4,6,5,1,3,2,7] => [[1,2,7],[3,5],[4],[6]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [2,1,7,4,5,6,3] => [[1,3,5,6],[2,4],[7]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,7,4] => [3,7,1,4,5,6,2] => [[1,2,5,6],[3,4],[7]] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [2,1,7,5,4,6,3] => [[1,3,6],[2,4],[5],[7]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4] => [3,7,1,5,4,6,2] => [[1,2,6],[3,4],[5],[7]] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4] => [4,7,5,1,3,6,2] => [[1,2,6],[3,5],[4],[7]] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4] => [3,7,1,6,5,4,2] => [[1,2],[3,4],[5],[6],[7]] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4] => [4,7,6,1,5,3,2] => [[1,2],[3,5],[4],[6],[7]] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,5,6,7,1,3,4] => [5,7,6,4,1,3,2] => [[1,2],[3,6],[4],[5],[7]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [2,1,6,4,7,3,5] => [[1,3,5],[2,4,7],[6]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6] => [3,6,1,4,7,2,5] => [[1,2,5],[3,4,7],[6]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,5,7,3,4,6] => [2,1,6,7,5,3,4] => [[1,3,4],[2,5,7],[6]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,5,1,7,3,4,6] => [3,6,1,7,5,2,4] => [[1,2,4],[3,5,7],[6]] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,5,7,1,3,4,6] => [4,6,7,1,5,2,3] => [[1,2,3],[4,5,7],[6]] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => [2,1,5,4,3,7,6] => [[1,3,6],[2,4,7],[5]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [3,5,1,4,2,7,6] => [[1,2,6],[3,4,7],[5]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [[1,3,4,6],[2,5,7]] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [[1,4,6],[2,5,7],[3]] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6] => [4,2,5,1,3,7,6] => [[1,3,6],[2,5,7],[4]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,3,5,7,4,6] => [2,1,3,6,7,4,5] => [[1,3,4,5],[2,6,7]] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,4,6] => [3,2,1,6,7,4,5] => [[1,4,5],[2,6,7],[3]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,1,7,4,6] => [4,2,6,1,7,3,5] => [[1,3,5],[2,6,7],[4]] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [5,2,6,7,1,3,4] => [[1,3,4],[2,6,7],[5]] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [2,1,5,4,3,6,7] => [[1,3,6,7],[2,4],[5]] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7] => [3,5,1,4,2,6,7] => [[1,2,6,7],[3,4],[5]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [[1,3,4,6,7],[2,5]] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [[1,4,6,7],[2,5],[3]] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7] => [4,2,5,1,3,6,7] => [[1,3,6,7],[2,5],[4]] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [[1,3,4,7],[2,5],[6]] => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [[1,4,7],[2,5],[3,6]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7] => [4,2,6,1,5,3,7] => [[1,3,7],[2,5],[4,6]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7] => [5,2,6,4,1,3,7] => [[1,3,7],[2,4],[5,6]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [[1,3,4,6],[2,5],[7]] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [[1,4,6],[2,5],[3,7]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,6,7,4] => [4,2,7,1,5,6,3] => [[1,3,6],[2,5],[4,7]] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4] => [5,2,7,4,1,6,3] => [[1,3,6],[2,4],[5,7]] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4] => [6,2,7,4,5,1,3] => [[1,3,5],[2,4],[6,7]] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,7,4,5] => [2,1,7,4,6,5,3] => [[1,3,5],[2,4],[6],[7]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,6,1,3,7,4,5] => [3,7,1,4,6,5,2] => [[1,2,5],[3,4],[6],[7]] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,6,7,3,4,5] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5] => [3,7,1,6,5,4,2] => [[1,2],[3,4],[5],[6],[7]] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,5] => [4,7,6,1,5,3,2] => [[1,2],[3,5],[4],[6],[7]] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => [2,1,7,4,5,6,3] => [[1,3,5,6],[2,4],[7]] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,1,3,4,7,5] => [3,7,1,4,5,6,2] => [[1,2,5,6],[3,4],[7]] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [2,1,3,7,5,6,4] => [[1,3,4,6],[2,5],[7]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5] => [3,2,1,7,5,6,4] => [[1,4,6],[2,5],[3,7]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,6,1,4,7,5] => [4,2,7,1,5,6,3] => [[1,3,6],[2,5],[4,7]] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,6,7,4,5] => [2,1,3,7,6,5,4] => [[1,3,4],[2,5],[6],[7]] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,7,4,5] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,7,4,5] => [4,2,7,1,6,5,3] => [[1,3],[2,5],[4,6],[7]] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,6,7,1,4,5] => [5,2,7,6,1,4,3] => [[1,3],[2,4],[5,6],[7]] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => [2,1,6,4,5,3,7] => [[1,3,5,7],[2,4],[6]] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7] => [3,6,1,4,5,2,7] => [[1,2,5,7],[3,4],[6]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,7] => [2,1,3,6,5,4,7] => [[1,3,4,7],[2,5],[6]] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7] => [3,2,1,6,5,4,7] => [[1,4,7],[2,5],[3,6]] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7] => [4,2,6,1,5,3,7] => [[1,3,7],[2,5],[4,6]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [[1,3,4,5,7],[2,6]] => 5
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [[1,4,5,7],[2,6],[3]] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [[1,3,5,7],[2,6],[4]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7] => [5,2,3,6,1,4,7] => [[1,3,4,7],[2,6],[5]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [[1,3,4,5],[2,6],[7]] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [[1,4,5],[2,6],[3,7]] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5] => [5,2,3,7,1,6,4] => [[1,3,4],[2,6],[5,7]] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5] => [6,2,3,7,5,1,4] => [[1,3,4],[2,5],[6,7]] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => [2,1,7,4,5,6,3] => [[1,3,5,6],[2,4],[7]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6] => [3,7,1,4,5,6,2] => [[1,2,5,6],[3,4],[7]] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,7,4,5,6] => [2,1,3,7,5,6,4] => [[1,3,4,6],[2,5],[7]] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,7,4,5,6] => [3,2,1,7,5,6,4] => [[1,4,6],[2,5],[3,7]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6] => [4,2,7,1,5,6,3] => [[1,3,6],[2,5],[4,7]] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6] => [2,1,3,4,7,6,5] => [[1,3,4,5],[2,6],[7]] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6] => [3,2,1,4,7,6,5] => [[1,4,5],[2,6],[3,7]] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,7,5,6] => [4,2,3,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [5,2,3,7,1,6,4] => [[1,3,4],[2,6],[5,7]] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]] => 5
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [[1,4,5,6],[2,7],[3]] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [[1,3,5,6],[2,7],[4]] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [[1,3,4,6],[2,7],[5]] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6] => [6,2,3,4,7,1,5] => [[1,3,4,5],[2,7],[6]] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]] => 6
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [[1,3,4,6,7],[2],[5]] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [[1,3,4,5,7],[2],[6]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7] => [4,2,3,1,6,5,7] => [[1,3,5,7],[2,6],[4]] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7] => [4,3,2,1,6,5,7] => [[1,5,7],[2,6],[3],[4]] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,7] => [5,2,3,6,1,4,7] => [[1,3,4,7],[2,6],[5]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,7] => [5,3,2,6,1,4,7] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,7] => [5,4,6,2,1,3,7] => [[1,3,7],[2,6],[4],[5]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [4,2,3,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,7,5] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [5,2,3,7,1,6,4] => [[1,3,4],[2,6],[5,7]] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5] => [5,3,2,7,1,6,4] => [[1,4],[2,6],[3,7],[5]] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,4,6,1,2,7,5] => [5,4,7,2,1,6,3] => [[1,3],[2,6],[4,7],[5]] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,7,2,5] => [6,2,3,7,5,1,4] => [[1,3,4],[2,5],[6,7]] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,7,2,5] => [6,3,2,7,5,1,4] => [[1,4],[2,5],[3,7],[6]] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,4,6,1,7,2,5] => [6,4,7,2,5,1,3] => [[1,3],[2,5],[4,7],[6]] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,7,1,2,5] => [6,5,7,4,2,1,3] => [[1,3],[2,7],[4],[5],[6]] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6] => [4,2,3,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,7,5,6] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,7,2,5,6] => [5,2,3,7,1,6,4] => [[1,3,4],[2,6],[5,7]] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,4,1,7,2,5,6] => [5,3,2,7,1,6,4] => [[1,4],[2,6],[3,7],[5]] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,4,7,1,2,5,6] => [5,4,7,2,1,6,3] => [[1,3],[2,6],[4,7],[5]] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,5,7,6] => [4,2,3,1,5,7,6] => [[1,3,5,6],[2,7],[4]] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6] => [4,3,2,1,5,7,6] => [[1,5,6],[2,7],[3],[4]] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6] => [5,2,3,4,1,7,6] => [[1,3,4,6],[2,7],[5]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6] => [5,3,2,4,1,7,6] => [[1,4,6],[2,7],[3],[5]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,7,6] => [5,4,3,2,1,7,6] => [[1,6],[2,7],[3],[4],[5]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,5,7,2,6] => [6,2,3,4,7,1,5] => [[1,3,4,5],[2,7],[6]] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,6] => [6,3,2,4,7,1,5] => [[1,4,5],[2,7],[3],[6]] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,5,1,7,2,6] => [6,4,3,2,7,1,5] => [[1,5],[2,7],[3],[4],[6]] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [6,5,3,7,2,1,4] => [[1,4],[2,7],[3],[5],[6]] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7] => [4,2,3,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7] => [4,3,2,1,5,6,7] => [[1,5,6,7],[2],[3],[4]] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7] => [5,2,3,4,1,6,7] => [[1,3,4,6,7],[2],[5]] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7] => [5,3,2,4,1,6,7] => [[1,4,6,7],[2],[3],[5]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7] => [5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7] => [6,2,3,4,5,1,7] => [[1,3,4,5,7],[2],[6]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7] => [6,3,2,4,5,1,7] => [[1,4,5,7],[2],[3],[6]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7] => [6,4,3,2,5,1,7] => [[1,5,7],[2],[3],[4],[6]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7] => [6,5,3,4,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2] => [7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2] => [7,3,2,4,5,6,1] => [[1,4,5,6],[2],[3],[7]] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2] => [7,4,3,2,5,6,1] => [[1,5,6],[2],[3],[4],[7]] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2] => [7,5,3,4,2,6,1] => [[1,4,6],[2],[3],[5],[7]] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [7,6,3,4,5,2,1] => [[1,4,5],[2],[3],[6],[7]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,7] => [4,2,6,1,5,3,7] => [[1,3,7],[2,5],[4,6]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,7] => [4,6,3,1,5,2,7] => [[1,2,7],[3,5],[4,6]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7] => [5,2,6,4,1,3,7] => [[1,3,7],[2,4],[5,6]] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7] => [5,6,3,4,1,2,7] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7] => [5,6,4,3,1,2,7] => [[1,2,7],[3,6],[4],[5]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [4,2,7,1,5,6,3] => [[1,3,6],[2,5],[4,7]] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4] => [4,7,3,1,5,6,2] => [[1,2,6],[3,5],[4,7]] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [5,2,7,4,1,6,3] => [[1,3,6],[2,4],[5,7]] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4] => [5,7,3,4,1,6,2] => [[1,2,6],[3,4],[5,7]] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4] => [5,7,4,3,1,6,2] => [[1,2],[3,6],[4,7],[5]] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,6,7,2,4] => [6,2,7,4,5,1,3] => [[1,3,5],[2,4],[6,7]] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4] => [6,7,3,4,5,1,2] => [[1,2,5],[3,4],[6,7]] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4] => [6,7,4,3,5,1,2] => [[1,2],[3,5],[4,7],[6]] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4] => [6,7,5,4,3,1,2] => [[1,2],[3,7],[4],[5],[6]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6] => [4,2,6,1,7,3,5] => [[1,3,5],[2,6,7],[4]] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6] => [4,6,3,1,7,2,5] => [[1,2,5],[3,6,7],[4]] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6] => [5,2,6,7,1,3,4] => [[1,3,4],[2,6,7],[5]] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6] => [5,6,3,7,1,2,4] => [[1,2,4],[3,6,7],[5]] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6] => [5,6,7,4,1,2,3] => [[1,2,3],[4,6,7],[5]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6] => [4,2,5,1,3,7,6] => [[1,3,6],[2,5,7],[4]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [4,5,3,1,2,7,6] => [[1,2,6],[3,5,7],[4]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6] => [3,2,1,5,4,7,6] => [[1,4,6],[2,5,7],[3]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [[1,2,4,6],[3,5,7]] => 4
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6] => [1,4,5,2,3,7,6] => [[1,2,3,6],[4,5,7]] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6] => [3,2,1,6,7,4,5] => [[1,4,5],[2,6,7],[3]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6] => [1,3,2,6,7,4,5] => [[1,2,4,5],[3,6,7]] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6] => [1,4,6,2,7,3,5] => [[1,2,3,5],[4,6,7]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [1,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [4,2,5,1,3,6,7] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7] => [4,5,3,1,2,6,7] => [[1,2,6,7],[3,5],[4]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,5,4,6,7] => [3,2,1,5,4,6,7] => [[1,4,6,7],[2,5],[3]] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [[1,2,4,6,7],[3,5]] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7] => [1,4,5,2,3,6,7] => [[1,2,3,6,7],[4,5]] => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,6,4,7] => [3,2,1,6,5,4,7] => [[1,4,7],[2,5],[3,6]] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [[1,2,4,7],[3,5],[6]] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7] => [1,4,6,2,5,3,7] => [[1,2,3,7],[4,5],[6]] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7] => [1,5,6,4,2,3,7] => [[1,2,3,7],[4,6],[5]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4] => [3,2,1,7,5,6,4] => [[1,4,6],[2,5],[3,7]] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [[1,2,4,6],[3,5],[7]] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4] => [1,4,7,2,5,6,3] => [[1,2,3,6],[4,5],[7]] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4] => [1,5,7,4,2,6,3] => [[1,2,3],[4,6],[5,7]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4] => [1,6,7,4,5,2,3] => [[1,2,3],[4,5],[6,7]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5] => [4,2,7,1,6,5,3] => [[1,3],[2,5],[4,6],[7]] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,6,1,2,7,4,5] => [4,7,3,1,6,5,2] => [[1,2],[3,5],[4,6],[7]] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5] => [5,2,7,6,1,4,3] => [[1,3],[2,4],[5,6],[7]] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,6,1,7,2,4,5] => [5,7,3,6,1,4,2] => [[1,2],[3,4],[5,6],[7]] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,6,7,1,2,4,5] => [5,7,6,4,1,3,2] => [[1,2],[3,6],[4],[5],[7]] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5] => [4,2,7,1,5,6,3] => [[1,3,6],[2,5],[4,7]] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5] => [4,7,3,1,5,6,2] => [[1,2,6],[3,5],[4,7]] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [3,2,1,7,5,6,4] => [[1,4,6],[2,5],[3,7]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5] => [1,3,2,7,5,6,4] => [[1,2,4,6],[3,5],[7]] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5] => [1,4,7,2,5,6,3] => [[1,2,3,6],[4,5],[7]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,7,4,5] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5] => [1,3,2,7,6,5,4] => [[1,2,4],[3,5],[6],[7]] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5] => [1,4,7,2,6,5,3] => [[1,2,3],[4,5],[6],[7]] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5] => [1,5,7,6,2,4,3] => [[1,2,3],[4,6],[5],[7]] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7] => [4,2,6,1,5,3,7] => [[1,3,7],[2,5],[4,6]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7] => [4,6,3,1,5,2,7] => [[1,2,7],[3,5],[4,6]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5,7] => [3,2,1,6,5,4,7] => [[1,4,7],[2,5],[3,6]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7] => [1,3,2,6,5,4,7] => [[1,2,4,7],[3,5],[6]] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7] => [1,4,6,2,5,3,7] => [[1,2,3,7],[4,5],[6]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,7] => [3,2,1,4,6,5,7] => [[1,4,5,7],[2,6],[3]] => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [[1,2,4,5,7],[3,6]] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [[1,2,5,7],[3,6],[4]] => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7] => [1,5,3,6,2,4,7] => [[1,2,4,7],[3,6],[5]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5] => [3,2,1,4,7,6,5] => [[1,4,5],[2,6],[3,7]] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [[1,2,4,5],[3,6],[7]] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [[1,2,5],[3,6],[4,7]] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5] => [1,5,3,7,2,6,4] => [[1,2,4],[3,6],[5,7]] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5] => [1,6,3,7,5,2,4] => [[1,2,4],[3,5],[6,7]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6] => [4,2,7,1,5,6,3] => [[1,3,6],[2,5],[4,7]] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6] => [4,7,3,1,5,6,2] => [[1,2,6],[3,5],[4,7]] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6] => [3,2,1,7,5,6,4] => [[1,4,6],[2,5],[3,7]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6] => [1,3,2,7,5,6,4] => [[1,2,4,6],[3,5],[7]] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6] => [1,4,7,2,5,6,3] => [[1,2,3,6],[4,5],[7]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6] => [3,2,1,4,7,6,5] => [[1,4,5],[2,6],[3,7]] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,7,6,5] => [[1,2,4,5],[3,6],[7]] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,4,2,7,5,6] => [1,4,3,2,7,6,5] => [[1,2,5],[3,6],[4,7]] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [1,5,3,7,2,6,4] => [[1,2,4],[3,6],[5,7]] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [3,2,1,4,5,7,6] => [[1,4,5,6],[2,7],[3]] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]] => 5
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [[1,2,5,6],[3,7],[4]] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [[1,2,4,6],[3,7],[5]] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6] => [1,6,3,4,7,2,5] => [[1,2,4,5],[3,7],[6]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7] => [3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 6
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [[1,2,5,6,7],[3],[4]] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [[1,2,4,6,7],[3],[5]] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [[1,2,4,5,7],[3],[6]] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [[1,2,4,5,6],[3],[7]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7] => [6,2,4,3,5,1,7] => [[1,3,5,7],[2],[4],[6]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,7] => [6,4,3,2,5,1,7] => [[1,5,7],[2],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7] => [6,2,5,4,3,1,7] => [[1,3,7],[2],[4],[5],[6]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7] => [6,5,3,4,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7] => [6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [7,2,4,3,5,6,1] => [[1,3,5,6],[2],[4],[7]] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3] => [7,4,3,2,5,6,1] => [[1,5,6],[2],[3],[4],[7]] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [7,2,5,4,3,6,1] => [[1,3,6],[2],[4],[5],[7]] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3] => [7,5,3,4,2,6,1] => [[1,4,6],[2],[3],[5],[7]] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3] => [7,5,4,3,2,6,1] => [[1,6],[2],[3],[4],[5],[7]] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3] => [7,2,6,4,5,3,1] => [[1,3,5],[2],[4],[6],[7]] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3] => [7,6,3,4,5,2,1] => [[1,4,5],[2],[3],[6],[7]] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3] => [7,6,4,3,5,2,1] => [[1,5],[2],[3],[4],[6],[7]] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6] => [6,2,4,3,7,1,5] => [[1,3,5],[2,7],[4],[6]] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6] => [6,4,3,2,7,1,5] => [[1,5],[2,7],[3],[4],[6]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,7,2,3,6] => [6,2,5,7,3,1,4] => [[1,3,4],[2,7],[5],[6]] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,5,1,7,2,3,6] => [6,5,3,7,2,1,4] => [[1,4],[2,7],[3],[5],[6]] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,5,7,1,2,3,6] => [6,5,7,4,2,1,3] => [[1,3],[2,7],[4],[5],[6]] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6] => [5,2,4,3,1,7,6] => [[1,3,6],[2,7],[4],[5]] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [5,4,3,2,1,7,6] => [[1,6],[2,7],[3],[4],[5]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6] => [5,2,3,4,1,7,6] => [[1,3,4,6],[2,7],[5]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6] => [1,5,3,4,2,7,6] => [[1,2,4,6],[3,7],[5]] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6] => [1,5,4,3,2,7,6] => [[1,2,6],[3,7],[4],[5]] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [6,2,3,4,7,1,5] => [[1,3,4,5],[2,7],[6]] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6] => [1,6,3,4,7,2,5] => [[1,2,4,5],[3,7],[6]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6] => [1,6,4,3,7,2,5] => [[1,2,5],[3,7],[4],[6]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [1,6,5,7,3,2,4] => [[1,2,4],[3,7],[5],[6]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [5,2,4,3,1,6,7] => [[1,3,6,7],[2],[4],[5]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7] => [5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7] => [5,2,3,4,1,6,7] => [[1,3,4,6,7],[2],[5]] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7] => [1,5,3,4,2,6,7] => [[1,2,4,6,7],[3],[5]] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7] => [1,5,4,3,2,6,7] => [[1,2,6,7],[3],[4],[5]] => 4
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7] => [6,2,3,4,5,1,7] => [[1,3,4,5,7],[2],[6]] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7] => [1,6,3,4,5,2,7] => [[1,2,4,5,7],[3],[6]] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7] => [1,6,4,3,5,2,7] => [[1,2,5,7],[3],[4],[6]] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7] => [1,6,5,4,3,2,7] => [[1,2,7],[3],[4],[5],[6]] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3] => [7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3] => [1,7,3,4,5,6,2] => [[1,2,4,5,6],[3],[7]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3] => [1,7,4,3,5,6,2] => [[1,2,5,6],[3],[4],[7]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3] => [1,7,5,4,3,6,2] => [[1,2,6],[3],[4],[5],[7]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3] => [1,7,6,4,5,3,2] => [[1,2,5],[3],[4],[6],[7]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5] => [6,2,7,4,5,1,3] => [[1,3,5],[2,4],[6,7]] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5] => [6,7,3,4,5,1,2] => [[1,2,5],[3,4],[6,7]] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5] => [6,2,7,5,4,1,3] => [[1,3],[2,4],[5,7],[6]] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5] => [6,7,3,5,4,1,2] => [[1,2],[3,4],[5,7],[6]] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5] => [6,7,5,4,3,1,2] => [[1,2],[3,7],[4],[5],[6]] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5] => [5,2,7,4,1,6,3] => [[1,3,6],[2,4],[5,7]] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5] => [5,7,3,4,1,6,2] => [[1,2,6],[3,4],[5,7]] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [5,2,3,7,1,6,4] => [[1,3,4],[2,6],[5,7]] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5] => [1,5,3,7,2,6,4] => [[1,2,4],[3,6],[5,7]] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5] => [1,5,7,4,2,6,3] => [[1,2,3],[4,6],[5,7]] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5] => [6,2,3,7,5,1,4] => [[1,3,4],[2,5],[6,7]] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5] => [1,6,3,7,5,2,4] => [[1,2,4],[3,5],[6,7]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5] => [1,6,7,4,5,2,3] => [[1,2,3],[4,5],[6,7]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5] => [1,6,7,5,4,2,3] => [[1,2,3],[4,7],[5],[6]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7] => [5,2,6,4,1,3,7] => [[1,3,7],[2,4],[5,6]] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7] => [5,6,3,4,1,2,7] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,7] => [5,2,3,6,1,4,7] => [[1,3,4,7],[2,6],[5]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7] => [1,5,3,6,2,4,7] => [[1,2,4,7],[3,6],[5]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7] => [1,5,6,4,2,3,7] => [[1,2,3,7],[4,6],[5]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7] => [4,2,3,1,6,5,7] => [[1,3,5,7],[2,6],[4]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7] => [1,4,3,2,6,5,7] => [[1,2,5,7],[3,6],[4]] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [[1,2,3,5,7],[4,6]] => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7] => [1,2,5,6,3,4,7] => [[1,2,3,4,7],[5,6]] => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5] => [4,2,3,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5] => [1,4,3,2,7,6,5] => [[1,2,5],[3,6],[4,7]] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [[1,2,3,5],[4,6],[7]] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5] => [1,2,5,7,3,6,4] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5] => [1,2,6,7,5,3,4] => [[1,2,3,4],[5,7],[6]] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6] => [5,2,7,4,1,6,3] => [[1,3,6],[2,4],[5,7]] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6] => [5,7,3,4,1,6,2] => [[1,2,6],[3,4],[5,7]] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6] => [5,2,3,7,1,6,4] => [[1,3,4],[2,6],[5,7]] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6] => [1,5,3,7,2,6,4] => [[1,2,4],[3,6],[5,7]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6] => [1,5,7,4,2,6,3] => [[1,2,3],[4,6],[5,7]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6] => [4,2,3,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,4,3,2,7,6,5] => [[1,2,5],[3,6],[4,7]] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,7,6,5] => [[1,2,3,5],[4,6],[7]] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [1,2,5,7,3,6,4] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [4,2,3,1,5,7,6] => [[1,3,5,6],[2,7],[4]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6] => [1,4,3,2,5,7,6] => [[1,2,5,6],[3,7],[4]] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]] => 5
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [[1,2,3,6],[4,7],[5]] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6] => [1,2,6,4,7,3,5] => [[1,2,3,5],[4,7],[6]] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7] => [4,2,3,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7] => [1,4,3,2,5,6,7] => [[1,2,5,6,7],[3],[4]] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => 6
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [[1,2,3,6,7],[4],[5]] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [[1,2,3,5,7],[4],[6]] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [[1,2,3,5,6],[4],[7]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4] => [7,2,6,4,5,3,1] => [[1,3,5],[2],[4],[6],[7]] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,6,1,2,7,3,4] => [7,6,3,4,5,2,1] => [[1,4,5],[2],[3],[6],[7]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,1,6,7,2,3,4] => [7,2,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4] => [7,6,3,5,4,2,1] => [[1,4],[2],[3],[5],[6],[7]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4] => [7,2,5,4,3,6,1] => [[1,3,6],[2],[4],[5],[7]] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,7,4] => [7,5,3,4,2,6,1] => [[1,4,6],[2],[3],[5],[7]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [7,2,3,5,4,6,1] => [[1,3,4,6],[2],[5],[7]] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4] => [1,7,3,5,4,6,2] => [[1,2,4,6],[3],[5],[7]] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,7,4] => [1,7,5,4,3,6,2] => [[1,2,6],[3],[4],[5],[7]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4] => [7,2,3,6,5,4,1] => [[1,3,4],[2],[5],[6],[7]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4] => [1,7,3,6,5,4,2] => [[1,2,4],[3],[5],[6],[7]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4] => [1,7,6,4,5,3,2] => [[1,2,5],[3],[4],[6],[7]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7] => [6,2,5,4,3,1,7] => [[1,3,7],[2],[4],[5],[6]] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7] => [6,5,3,4,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7] => [6,2,3,5,4,1,7] => [[1,3,4,7],[2],[5],[6]] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7] => [1,6,3,5,4,2,7] => [[1,2,4,7],[3],[5],[6]] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7] => [1,6,5,4,3,2,7] => [[1,2,7],[3],[4],[5],[6]] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7] => [6,2,3,4,5,1,7] => [[1,3,4,5,7],[2],[6]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7] => [1,6,3,4,5,2,7] => [[1,2,4,5,7],[3],[6]] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7] => [1,2,6,4,5,3,7] => [[1,2,3,5,7],[4],[6]] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7] => [1,2,6,5,4,3,7] => [[1,2,3,7],[4],[5],[6]] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4] => [7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4] => [1,7,3,4,5,6,2] => [[1,2,4,5,6],[3],[7]] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4] => [1,2,7,4,5,6,3] => [[1,2,3,5,6],[4],[7]] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4] => [1,2,7,5,4,6,3] => [[1,2,3,6],[4],[5],[7]] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,6,7,3,4] => [1,2,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6] => [6,2,7,4,5,1,3] => [[1,3,5],[2,4],[6,7]] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6] => [6,7,3,4,5,1,2] => [[1,2,5],[3,4],[6,7]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6] => [6,2,3,7,5,1,4] => [[1,3,4],[2,5],[6,7]] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6] => [1,6,3,7,5,2,4] => [[1,2,4],[3,5],[6,7]] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6] => [1,6,7,4,5,2,3] => [[1,2,3],[4,5],[6,7]] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6] => [6,2,3,4,7,1,5] => [[1,3,4,5],[2,7],[6]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,6,3,4,7,2,5] => [[1,2,4,5],[3,7],[6]] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6] => [1,2,6,4,7,3,5] => [[1,2,3,5],[4,7],[6]] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [1,2,6,7,5,3,4] => [[1,2,3,4],[5,7],[6]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [5,2,3,4,1,7,6] => [[1,3,4,6],[2,7],[5]] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6] => [1,5,3,4,2,7,6] => [[1,2,4,6],[3,7],[5]] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6] => [1,2,5,4,3,7,6] => [[1,2,3,6],[4,7],[5]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [[1,2,3,4,6],[5,7]] => 5
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6] => [1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7] => [5,2,3,4,1,6,7] => [[1,3,4,6,7],[2],[5]] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7] => [1,5,3,4,2,6,7] => [[1,2,4,6,7],[3],[5]] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7] => [1,2,5,4,3,6,7] => [[1,2,3,6,7],[4],[5]] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => 6
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [[1,2,3,4,7],[5],[6]] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [[1,2,3,4,6],[5],[7]] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5] => [7,2,6,4,5,3,1] => [[1,3,5],[2],[4],[6],[7]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [7,6,3,4,5,2,1] => [[1,4,5],[2],[3],[6],[7]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5] => [7,2,3,6,5,4,1] => [[1,3,4],[2],[5],[6],[7]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5] => [1,7,3,6,5,4,2] => [[1,2,4],[3],[5],[6],[7]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5] => [1,7,6,4,5,3,2] => [[1,2,5],[3],[4],[6],[7]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5] => [7,2,3,4,6,5,1] => [[1,3,4,5],[2],[6],[7]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,7,3,4,6,5,2] => [[1,2,4,5],[3],[6],[7]] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5] => [1,2,7,4,6,5,3] => [[1,2,3,5],[4],[6],[7]] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5] => [1,2,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [1,7,3,4,5,6,2] => [[1,2,4,5,6],[3],[7]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5] => [1,2,7,4,5,6,3] => [[1,2,3,5,6],[4],[7]] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5] => [1,2,3,7,5,6,4] => [[1,2,3,4,6],[5],[7]] => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5] => [1,2,3,7,6,5,4] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [6,2,3,4,5,1,7] => [[1,3,4,5,7],[2],[6]] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7] => [1,6,3,4,5,2,7] => [[1,2,4,5,7],[3],[6]] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7] => [1,2,6,4,5,3,7] => [[1,2,3,5,7],[4],[6]] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7] => [1,2,3,6,5,4,7] => [[1,2,3,4,7],[5],[6]] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6] => [1,7,3,4,5,6,2] => [[1,2,4,5,6],[3],[7]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6] => [1,2,7,4,5,6,3] => [[1,2,3,5,6],[4],[7]] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,7,5,6,4] => [[1,2,3,4,6],[5],[7]] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,7,6,5] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [3,4,1,2,6,5,8,7] => [[1,2,5,7],[3,4,6,8]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,8,7] => [2,1,5,6,3,4,8,7] => [[1,3,4,7],[2,5,6,8]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7] => [3,5,1,6,2,4,8,7] => [[1,2,4,7],[3,5,6,8]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,8,7] => [4,5,6,1,2,3,8,7] => [[1,2,3,7],[4,5,6,8]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,8,5,7] => [2,1,4,3,7,8,5,6] => [[1,3,5,6],[2,4,7,8]] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,8,5,7] => [3,4,1,2,7,8,5,6] => [[1,2,5,6],[3,4,7,8]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,8,5,7] => [2,1,5,7,3,8,4,6] => [[1,3,4,6],[2,5,7,8]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7] => [3,5,1,7,2,8,4,6] => [[1,2,4,6],[3,5,7,8]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => [4,5,7,1,2,8,3,6] => [[1,2,3,6],[4,5,7,8]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,8,3,5,7] => [2,1,6,7,8,3,4,5] => [[1,3,4,5],[2,6,7,8]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,8,3,5,7] => [3,6,1,7,8,2,4,5] => [[1,2,4,5],[3,6,7,8]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [4,6,7,1,8,2,3,5] => [[1,2,3,5],[4,6,7,8]] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [5,6,7,8,1,2,3,4] => [[1,2,3,4],[5,6,7,8]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [[1,3,5,7,8],[2,4,6]] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7,8] => [3,4,1,2,6,5,7,8] => [[1,2,5,7,8],[3,4,6]] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7,8] => [3,5,1,6,2,4,7,8] => [[1,2,4,7,8],[3,5,6]] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7,8] => [4,5,6,1,2,3,7,8] => [[1,2,3,7,8],[4,5,6]] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5,8] => [4,5,7,1,2,6,3,8] => [[1,2,3,8],[4,5,6],[7]] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [5,6,7,4,1,2,3,8] => [[1,2,3,8],[4,6,7],[5]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [[1,3,5,7],[2,4,6],[8]] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,7,8,5] => [3,4,1,2,8,6,7,5] => [[1,2,5,7],[3,4,6],[8]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,6,3,7,8,5] => [2,1,5,8,3,6,7,4] => [[1,3,4,7],[2,5,6],[8]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,4,6,1,3,7,8,5] => [4,5,8,1,2,6,7,3] => [[1,2,3,7],[4,5,6],[8]] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,6,7,3,8,5] => [2,1,6,8,5,3,7,4] => [[1,3,4],[2,5,7],[6,8]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,6,7,3,8,5] => [3,6,1,8,5,2,7,4] => [[1,2,4],[3,5,7],[6,8]] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,6,1,7,3,8,5] => [4,6,8,1,5,2,7,3] => [[1,2,3],[4,5,7],[6,8]] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,8,5] => [5,6,8,4,1,2,7,3] => [[1,2,3],[4,6,7],[5,8]] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,6,7,8,3,5] => [2,1,7,8,5,6,3,4] => [[1,3,4],[2,5,6],[7,8]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,6,7,8,3,5] => [3,7,1,8,5,6,2,4] => [[1,2,4],[3,5,6],[7,8]] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,4,6,1,7,8,3,5] => [4,7,8,1,5,6,2,3] => [[1,2,3],[4,5,6],[7,8]] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,6,7,1,8,3,5] => [5,7,8,4,1,6,2,3] => [[1,2,3],[4,6,8],[5,7]] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,6,7,8,1,3,5] => [6,7,8,4,5,1,2,3] => [[1,2,3],[4,5,8],[6,7]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,7,5,8,6] => [2,1,4,3,8,6,7,5] => [[1,3,5,7],[2,4,6],[8]] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,3,7,5,8,6] => [3,4,1,2,8,6,7,5] => [[1,2,5,7],[3,4,6],[8]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,7,3,5,8,6] => [2,1,5,8,3,6,7,4] => [[1,3,4,7],[2,5,6],[8]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,4,7,1,3,5,8,6] => [4,5,8,1,2,6,7,3] => [[1,2,3,7],[4,5,6],[8]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,7,8,5,6] => [2,1,4,3,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8]] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,7,8,5,6] => [3,4,1,2,8,7,6,5] => [[1,2,5],[3,4,6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,4,1,7,3,8,5,6] => [3,5,1,8,2,7,6,4] => [[1,2,4],[3,5,6],[7],[8]] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,7,1,3,8,5,6] => [4,5,8,1,2,7,6,3] => [[1,2,3],[4,5,6],[7],[8]] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,7,8,3,5,6] => [2,1,6,8,7,3,5,4] => [[1,3,4],[2,5,7],[6],[8]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,8,3,5,6] => [3,6,1,8,7,2,5,4] => [[1,2,4],[3,5,7],[6],[8]] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,4,7,1,8,3,5,6] => [4,6,8,1,7,2,5,3] => [[1,2,3],[4,5,7],[6],[8]] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [5,6,8,7,1,2,4,3] => [[1,2,3],[4,6,7],[5],[8]] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6,8] => [4,6,3,1,7,2,5,8] => [[1,2,5,8],[3,6,7],[4]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,7,6] => [[1,3,5,6],[2,4,7],[8]] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,7,8,6] => [3,4,1,2,5,8,7,6] => [[1,2,5,6],[3,4,7],[8]] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,7,8,6] => [3,5,1,4,2,8,7,6] => [[1,2,6],[3,4,7],[5,8]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,7,8,6] => [4,5,3,1,2,8,7,6] => [[1,2,6],[3,5,7],[4,8]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,4,5,7,3,8,6] => [2,1,6,4,8,3,7,5] => [[1,3,5],[2,4,7],[6,8]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,1,7,3,8,6] => [4,6,3,1,8,2,7,5] => [[1,2,5],[3,6,7],[4,8]] => 1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,8,6] => [5,6,3,8,1,2,7,4] => [[1,2,4],[3,6,7],[5,8]] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,4,5,7,8,3,6] => [2,1,7,4,8,6,3,5] => [[1,3,5],[2,4,6],[7,8]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,7,8,3,6] => [4,7,3,1,8,6,2,5] => [[1,2,5],[3,6,8],[4,7]] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,5,7,1,8,3,6] => [5,7,3,8,1,6,2,4] => [[1,2,4],[3,6,8],[5,7]] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,7,8,1,3,6] => [6,7,3,8,5,1,2,4] => [[1,2,4],[3,5,8],[6,7]] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,4,3,8,5,6,7] => [2,1,4,3,8,6,7,5] => [[1,3,5,7],[2,4,6],[8]] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,8,5,6,7] => [3,4,1,2,8,6,7,5] => [[1,2,5,7],[3,4,6],[8]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,4,8,3,5,6,7] => [2,1,5,8,3,6,7,4] => [[1,3,4,7],[2,5,6],[8]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,4,8,1,3,5,6,7] => [4,5,8,1,2,6,7,3] => [[1,2,3,7],[4,5,6],[8]] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,4,3,5,8,6,7] => [2,1,4,3,5,8,7,6] => [[1,3,5,6],[2,4,7],[8]] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,3,8,6,7] => [3,5,1,4,2,8,7,6] => [[1,2,6],[3,4,7],[5,8]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,4,5,8,3,6,7] => [2,1,6,4,8,3,7,5] => [[1,3,5],[2,4,7],[6,8]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [4,6,3,1,8,2,7,5] => [[1,2,5],[3,6,7],[4,8]] => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,4,5,8,1,3,6,7] => [5,6,3,8,1,2,7,4] => [[1,2,4],[3,6,7],[5,8]] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [[1,3,5,6,7],[2,4,8]] => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,8,7] => [3,5,1,4,2,6,8,7] => [[1,2,6,7],[3,4,8],[5]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [[1,3,5,7],[2,4,8],[6]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,8,7] => [3,6,1,4,5,2,8,7] => [[1,2,5,7],[3,4,8],[6]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,8,7] => [4,6,3,1,5,2,8,7] => [[1,2,7],[3,5,8],[4,6]] => 2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,8,7] => [5,6,3,4,1,2,8,7] => [[1,2,7],[3,4,8],[5,6]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,4,5,6,8,3,7] => [2,1,7,4,5,8,3,6] => [[1,3,5,6],[2,4,8],[7]] => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,4,5,6,8,1,3,7] => [6,7,3,4,8,1,2,5] => [[1,2,5],[3,4,8],[6,7]] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4]] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7,8] => [3,4,1,2,5,6,7,8] => [[1,2,5,6,7,8],[3,4]] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7,8] => [2,1,5,4,3,6,7,8] => [[1,3,6,7,8],[2,4],[5]] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7,8] => [3,5,1,4,2,6,7,8] => [[1,2,6,7,8],[3,4],[5]] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7,8] => [3,6,1,4,5,2,7,8] => [[1,2,5,7,8],[3,4],[6]] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7,8] => [4,6,3,1,5,2,7,8] => [[1,2,7,8],[3,5],[4,6]] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3,8] => [3,7,1,4,5,6,2,8] => [[1,2,5,6,8],[3,4],[7]] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3,8] => [4,7,3,1,5,6,2,8] => [[1,2,6,8],[3,5],[4,7]] => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3,8] => [5,7,3,4,1,6,2,8] => [[1,2,6,8],[3,4],[5,7]] => 2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3,8] => [6,7,3,4,5,1,2,8] => [[1,2,5,8],[3,4],[6,7]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,3] => [2,1,8,4,5,6,7,3] => [[1,3,5,6,7],[2,4],[8]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,5,6,7,8,3] => [3,8,1,4,5,6,7,2] => [[1,2,5,6,7],[3,4],[8]] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,4,5,1,6,7,8,3] => [4,8,3,1,5,6,7,2] => [[1,2,6,7],[3,5],[4,8]] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,4,5,6,1,7,8,3] => [5,8,3,4,1,6,7,2] => [[1,2,6,7],[3,4],[5,8]] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,4,5,6,7,1,8,3] => [6,8,3,4,5,1,7,2] => [[1,2,5,7],[3,4],[6,8]] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,3] => [7,8,3,4,5,6,1,2] => [[1,2,5,6],[3,4],[7,8]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,8,7] => [2,1,6,4,5,3,8,7] => [[1,3,5,7],[2,4,8],[6]] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,8,7] => [3,6,1,4,5,2,8,7] => [[1,2,5,7],[3,4,8],[6]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,8,7] => [2,1,6,5,4,3,8,7] => [[1,3,7],[2,4,8],[5],[6]] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,8,7] => [3,6,1,5,4,2,8,7] => [[1,2,7],[3,4,8],[5],[6]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,8,7] => [4,6,5,1,3,2,8,7] => [[1,2,7],[3,5,8],[4],[6]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,8,4,7] => [2,1,7,4,5,8,3,6] => [[1,3,5,6],[2,4,8],[7]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,5,1,6,3,8,4,7] => [3,7,1,5,4,8,2,6] => [[1,2,6],[3,4,8],[5],[7]] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,8,4,7] => [4,7,5,1,3,8,2,6] => [[1,2,6],[3,5,8],[4],[7]] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,5,6,8,3,4,7] => [2,1,7,6,8,4,3,5] => [[1,3,5],[2,4,8],[6],[7]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,5,1,6,8,3,4,7] => [3,7,1,6,8,4,2,5] => [[1,2,5],[3,4,8],[6],[7]] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => [5,7,6,8,1,3,2,4] => [[1,2,4],[3,6,8],[5],[7]] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7,8] => [3,6,1,4,5,2,7,8] => [[1,2,5,7,8],[3,4],[6]] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7,8] => [3,6,1,5,4,2,7,8] => [[1,2,7,8],[3,4],[5],[6]] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4,8] => [3,7,1,5,4,6,2,8] => [[1,2,6,8],[3,4],[5],[7]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4,8] => [2,1,7,6,5,4,3,8] => [[1,3,8],[2,4],[5],[6],[7]] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [2,1,8,4,5,6,7,3] => [[1,3,5,6,7],[2,4],[8]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,5,1,3,6,7,8,4] => [3,8,1,4,5,6,7,2] => [[1,2,5,6,7],[3,4],[8]] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,6,3,7,8,4] => [2,1,8,5,4,6,7,3] => [[1,3,6,7],[2,4],[5],[8]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5,1,6,3,7,8,4] => [3,8,1,5,4,6,7,2] => [[1,2,6,7],[3,4],[5],[8]] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5,6,1,3,7,8,4] => [4,8,5,1,3,6,7,2] => [[1,2,6,7],[3,5],[4],[8]] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,7,3,8,4] => [2,1,8,6,5,4,7,3] => [[1,3,7],[2,4],[5],[6],[8]] => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5,6,7,1,3,8,4] => [5,8,6,4,1,3,7,2] => [[1,2,7],[3,6],[4],[5],[8]] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,5,6,7,8,3,4] => [2,1,8,7,5,6,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5,1,6,7,8,3,4] => [3,8,1,7,5,6,4,2] => [[1,2,6],[3,4],[5],[7],[8]] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5,6,1,7,8,3,4] => [4,8,7,1,5,6,3,2] => [[1,2,6],[3,5],[4],[7],[8]] => 1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5,6,7,1,8,3,4] => [5,8,7,4,1,6,3,2] => [[1,2],[3,6],[4,7],[5],[8]] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5,6,7,8,1,3,4] => [6,8,7,4,5,1,3,2] => [[1,2],[3,5],[4,7],[6],[8]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,7,4,8,6] => [2,1,6,4,8,3,7,5] => [[1,3,5],[2,4,7],[6,8]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,7,3,4,8,6] => [2,1,6,8,5,3,7,4] => [[1,3,4],[2,5,7],[6,8]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,7,3,4,8,6] => [3,6,1,8,5,2,7,4] => [[1,2,4],[3,5,7],[6,8]] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,5,7,1,3,4,8,6] => [4,6,8,1,5,2,7,3] => [[1,2,3],[4,5,7],[6,8]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,7,8,4,6] => [2,1,7,4,8,6,3,5] => [[1,3,5],[2,4,6],[7,8]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,7,3,8,4,6] => [2,1,7,8,5,6,3,4] => [[1,3,4],[2,5,6],[7,8]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,5,1,7,3,8,4,6] => [3,7,1,8,5,6,2,4] => [[1,2,4],[3,5,6],[7,8]] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,5,7,1,3,8,4,6] => [4,7,8,1,5,6,2,3] => [[1,2,3],[4,5,6],[7,8]] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,7,8,3,4,6] => [2,1,7,8,6,5,3,4] => [[1,3,4],[2,5,8],[6],[7]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,7,8,3,4,6] => [3,7,1,8,6,5,2,4] => [[1,2,4],[3,5,8],[6],[7]] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,5,7,1,8,3,4,6] => [4,7,8,1,6,5,2,3] => [[1,2,3],[4,5,8],[6],[7]] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [5,7,8,6,1,4,2,3] => [[1,2,3],[4,6,8],[5],[7]] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6,8] => [3,6,1,4,7,2,5,8] => [[1,2,5,8],[3,4,7],[6]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [[1,4,6,8],[2,5,7],[3]] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6,8] => [4,2,5,1,3,7,6,8] => [[1,3,6,8],[2,5,7],[4]] => 3
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,7,1,4,6,8] => [5,2,6,7,1,3,4,8] => [[1,3,4,8],[2,6,7],[5]] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,7,8,6] => [2,1,3,5,4,8,7,6] => [[1,3,4,6],[2,5,7],[8]] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,7,4,8,6] => [4,2,6,1,8,3,7,5] => [[1,3,5],[2,6,7],[4,8]] => 1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,8,6] => [5,2,6,8,1,3,7,4] => [[1,3,4],[2,6,7],[5,8]] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,7,8,4,6] => [3,2,1,7,8,6,4,5] => [[1,4,5],[2,6,8],[3,7]] => 2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,7,1,8,4,6] => [5,2,7,8,1,6,3,4] => [[1,3,4],[2,6,8],[5,7]] => 1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,7,8,1,4,6] => [6,2,7,8,5,1,3,4] => [[1,3,4],[2,5,8],[6,7]] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,8,4,6,7] => [2,1,6,4,8,3,7,5] => [[1,3,5],[2,4,7],[6,8]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,8,3,4,6,7] => [2,1,6,8,5,3,7,4] => [[1,3,4],[2,5,7],[6,8]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,5,1,8,3,4,6,7] => [3,6,1,8,5,2,7,4] => [[1,2,4],[3,5,7],[6,8]] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,5,8,1,3,4,6,7] => [4,6,8,1,5,2,7,3] => [[1,2,3],[4,5,7],[6,8]] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,3,5,1,4,8,6,7] => [4,2,5,1,3,8,7,6] => [[1,3,6],[2,5,7],[4,8]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => [4,2,6,1,8,3,7,5] => [[1,3,5],[2,6,7],[4,8]] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,8,1,4,6,7] => [5,2,6,8,1,3,7,4] => [[1,3,4],[2,6,7],[5,8]] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,8,7] => [4,2,6,1,5,3,8,7] => [[1,3,7],[2,5,8],[4,6]] => 2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,8,7] => [5,2,6,4,1,3,8,7] => [[1,3,7],[2,4,8],[5,6]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,5,6,8,4,7] => [2,1,3,7,5,8,4,6] => [[1,3,4,6],[2,5,8],[7]] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,5,6,8,4,7] => [3,2,1,7,5,8,4,6] => [[1,4,6],[2,5,8],[3,7]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,1,6,8,4,7] => [4,2,7,1,5,8,3,6] => [[1,3,6],[2,5,8],[4,7]] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,6,1,8,4,7] => [5,2,7,4,1,8,3,6] => [[1,3,6],[2,4,8],[5,7]] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,6,8,1,4,7] => [6,2,7,4,8,1,3,5] => [[1,3,5],[2,4,8],[6,7]] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => [2,1,5,4,3,6,7,8] => [[1,3,6,7,8],[2,4],[5]] => 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7,8] => [3,5,1,4,2,6,7,8] => [[1,2,6,7,8],[3,4],[5]] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7,8] => [4,2,5,1,3,6,7,8] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7,8] => [4,2,6,1,5,3,7,8] => [[1,3,7,8],[2,5],[4,6]] => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => [5,2,6,4,1,3,7,8] => [[1,3,7,8],[2,4],[5,6]] => 3
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4,8] => [5,2,7,4,1,6,3,8] => [[1,3,6,8],[2,4],[5,7]] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4,8] => [6,2,7,4,5,1,3,8] => [[1,3,5,8],[2,4],[6,7]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,5,6,7,4] => [[1,3,4,6,7],[2,5],[8]] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [[1,4,6,7],[2,5],[3,8]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,5,1,6,7,8,4] => [4,2,8,1,5,6,7,3] => [[1,3,6,7],[2,5],[4,8]] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,5,6,1,7,8,4] => [5,2,8,4,1,6,7,3] => [[1,3,6,7],[2,4],[5,8]] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,5,6,7,1,8,4] => [6,2,8,4,5,1,7,3] => [[1,3,5,7],[2,4],[6,8]] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,6,7,8,1,4] => [7,2,8,4,5,6,1,3] => [[1,3,5,6],[2,4],[7,8]] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,6,3,7,4,8,5] => [2,1,8,4,6,5,7,3] => [[1,3,5,7],[2,4],[6],[8]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,6,7,3,4,8,5] => [2,1,8,6,5,4,7,3] => [[1,3,7],[2,4],[5],[6],[8]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => [4,8,6,1,5,3,7,2] => [[1,2,7],[3,5],[4],[6],[8]] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,6,3,7,8,4,5] => [2,1,8,4,7,6,5,3] => [[1,3,5],[2,4],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,6,1,3,7,8,4,5] => [3,8,1,4,7,6,5,2] => [[1,2,5],[3,4],[6],[7],[8]] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,1,6,7,3,8,4,5] => [2,1,8,7,5,6,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,6,1,7,3,8,4,5] => [3,8,1,7,5,6,4,2] => [[1,2,6],[3,4],[5],[7],[8]] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,6,7,1,3,8,4,5] => [4,8,7,1,5,6,3,2] => [[1,2,6],[3,5],[4],[7],[8]] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,6,7,8,3,4,5] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,6,1,7,8,3,4,5] => [3,8,1,7,6,5,4,2] => [[1,2],[3,4],[5],[6],[7],[8]] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,6,7,1,8,3,4,5] => [4,8,7,1,6,5,3,2] => [[1,2],[3,5],[4],[6],[7],[8]] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => [5,8,7,6,1,4,3,2] => [[1,2],[3,6],[4],[5],[7],[8]] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,6,1,3,4,7,5,8] => [3,7,1,4,5,6,2,8] => [[1,2,5,6,8],[3,4],[7]] => 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,3,6,7,1,4,5,8] => [5,2,7,6,1,4,3,8] => [[1,3,8],[2,4],[5,6],[7]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [2,1,8,4,5,6,7,3] => [[1,3,5,6,7],[2,4],[8]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,7,8,5] => [3,8,1,4,5,6,7,2] => [[1,2,5,6,7],[3,4],[8]] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [4,2,8,1,5,6,7,3] => [[1,3,6,7],[2,5],[4,8]] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,4,8,5] => [2,1,3,8,6,5,7,4] => [[1,3,4,7],[2,5],[6],[8]] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,3,6,7,8,4,5] => [2,1,3,8,7,6,5,4] => [[1,3,4],[2,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,3,1,6,7,8,4,5] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,8,4,5] => [4,2,8,1,7,6,5,3] => [[1,3],[2,5],[4,6],[7],[8]] => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,8,4,5] => [5,2,8,7,1,6,4,3] => [[1,3],[2,4],[5,6],[7],[8]] => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,3,6,7,8,1,4,5] => [6,2,8,7,5,1,4,3] => [[1,3],[2,4],[5,7],[6],[8]] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,8,4,5,7] => [2,1,7,4,8,6,3,5] => [[1,3,5],[2,4,6],[7,8]] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,1,6,8,3,4,5,7] => [2,1,7,8,5,6,3,4] => [[1,3,4],[2,5,6],[7,8]] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,6,1,8,3,4,5,7] => [3,7,1,8,5,6,2,4] => [[1,2,4],[3,5,6],[7,8]] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,6,8,1,3,4,5,7] => [4,7,8,1,5,6,2,3] => [[1,2,3],[4,5,6],[7,8]] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,8,5,7] => [2,1,7,4,5,8,3,6] => [[1,3,5,6],[2,4,8],[7]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,8,5,7] => [2,1,3,7,5,8,4,6] => [[1,3,4,6],[2,5,8],[7]] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,8,5,7] => [3,2,1,7,5,8,4,6] => [[1,4,6],[2,5,8],[3,7]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,3,6,1,4,8,5,7] => [4,2,7,1,5,8,3,6] => [[1,3,6],[2,5,8],[4,7]] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,8,4,5,7] => [3,2,1,7,8,6,4,5] => [[1,4,5],[2,6,8],[3,7]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,8,4,5,7] => [4,2,7,1,8,6,3,5] => [[1,3,5],[2,6,8],[4,7]] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,3,6,8,1,4,5,7] => [5,2,7,8,1,6,3,4] => [[1,3,4],[2,6,8],[5,7]] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,8,7] => [2,1,6,4,5,3,8,7] => [[1,3,5,7],[2,4,8],[6]] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,8,7] => [3,6,1,4,5,2,8,7] => [[1,2,5,7],[3,4,8],[6]] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,8,7] => [4,2,6,1,5,3,8,7] => [[1,3,7],[2,5,8],[4,6]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => 5
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,8,5,7] => [4,2,3,1,7,8,5,6] => [[1,3,5,6],[2,7,8],[4]] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,8,5,7] => [5,2,3,7,1,8,4,6] => [[1,3,4,6],[2,7,8],[5]] => 1
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,8,1,5,7] => [6,2,3,7,8,1,4,5] => [[1,3,4,5],[2,7,8],[6]] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7,8] => [3,6,1,4,5,2,7,8] => [[1,2,5,7,8],[3,4],[6]] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7,8] => [4,2,6,1,5,3,7,8] => [[1,3,7,8],[2,5],[4,6]] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => 6
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]] => 4
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5,8] => [6,2,3,7,5,1,4,8] => [[1,3,4,8],[2,5],[6,7]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,6,7,5] => [[1,3,4,5,7],[2,6],[8]] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => [[1,4,5,7],[2,6],[3,8]] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,3,4,6,1,7,8,5] => [5,2,3,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,6,7,8,1,5] => [7,2,3,8,5,6,1,4] => [[1,3,4,6],[2,5],[7,8]] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,7,3,8,4,5,6] => [2,1,8,4,7,6,5,3] => [[1,3,5],[2,4],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,7,1,3,8,4,5,6] => [3,8,1,4,7,6,5,2] => [[1,2,5],[3,4],[6],[7],[8]] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,7,8,3,4,5,6] => [2,1,8,7,5,6,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => [3,8,1,7,5,6,4,2] => [[1,2,6],[3,4],[5],[7],[8]] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,7,8,1,3,4,5,6] => [4,8,7,1,5,6,3,2] => [[1,2,6],[3,5],[4],[7],[8]] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,1,7,3,4,8,5,6] => [2,1,8,4,5,7,6,3] => [[1,3,5,6],[2,4],[7],[8]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,1,3,7,4,8,5,6] => [2,1,3,8,5,7,6,4] => [[1,3,4,6],[2,5],[7],[8]] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,7,4,8,5,6] => [3,2,1,8,5,7,6,4] => [[1,4,6],[2,5],[3,7],[8]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,1,4,8,5,6] => [4,2,8,1,5,7,6,3] => [[1,3,6],[2,5],[4,7],[8]] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,1,3,7,8,4,5,6] => [2,1,3,8,7,6,5,4] => [[1,3,4],[2,5],[6],[7],[8]] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,1,7,8,4,5,6] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [5,2,8,7,1,6,4,3] => [[1,3],[2,4],[5,6],[7],[8]] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,7,3,4,5,8,6] => [2,1,8,4,5,6,7,3] => [[1,3,5,6,7],[2,4],[8]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [3,8,1,4,5,6,7,2] => [[1,2,5,6,7],[3,4],[8]] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,3,1,7,4,5,8,6] => [3,2,1,8,5,6,7,4] => [[1,4,6,7],[2,5],[3,8]] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,3,7,1,4,5,8,6] => [4,2,8,1,5,6,7,3] => [[1,3,6,7],[2,5],[4,8]] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,3,4,7,5,8,6] => [2,1,3,4,8,6,7,5] => [[1,3,4,5,7],[2,6],[8]] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,4,1,7,5,8,6] => [4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,8,6] => [5,2,3,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,3,4,7,8,5,6] => [2,1,3,4,8,7,6,5] => [[1,3,4,5],[2,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,1,4,7,8,5,6] => [3,2,1,4,8,7,6,5] => [[1,4,5],[2,6],[3,7],[8]] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,4,1,7,8,5,6] => [4,2,3,1,8,7,6,5] => [[1,3,5],[2,6],[4,7],[8]] => 2
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,3,4,7,8,1,5,6] => [6,2,3,8,7,1,5,4] => [[1,3,4],[2,5],[6,7],[8]] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6,8] => [3,7,1,4,5,6,2,8] => [[1,2,5,6,8],[3,4],[7]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6,8] => [3,2,1,4,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6,8] => [4,2,3,1,5,7,6,8] => [[1,3,5,6,8],[2,7],[4]] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,7,6] => [[1,3,4,5,6],[2,7],[8]] => 5
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => 4
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,5,7,8,1,6] => [7,2,3,4,8,6,1,5] => [[1,3,4,5],[2,6],[7,8]] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,8,3,4,5,6,7] => [2,1,8,4,5,6,7,3] => [[1,3,5,6,7],[2,4],[8]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,8,1,3,4,5,6,7] => [3,8,1,4,5,6,7,2] => [[1,2,5,6,7],[3,4],[8]] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,8,4,5,6,7] => [2,1,3,8,5,6,7,4] => [[1,3,4,6,7],[2,5],[8]] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,1,8,4,5,6,7] => [3,2,1,8,5,6,7,4] => [[1,4,6,7],[2,5],[3,8]] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,8,1,4,5,6,7] => [4,2,8,1,5,6,7,3] => [[1,3,6,7],[2,5],[4,8]] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,1,3,4,8,5,6,7] => [2,1,3,4,8,6,7,5] => [[1,3,4,5,7],[2,6],[8]] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,1,4,8,5,6,7] => [3,2,1,4,8,6,7,5] => [[1,4,5,7],[2,6],[3,8]] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => 2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [5,2,3,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,3,4,5,8,6,7] => [2,1,3,4,5,8,7,6] => [[1,3,4,5,6],[2,7],[8]] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => [3,2,1,4,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => 4
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,3,4,5,1,8,6,7] => [5,2,3,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => 5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,8,7] => [5,2,3,4,1,6,8,7] => [[1,3,4,6,7],[2,8],[5]] => 3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => [[1,3,4,5,7],[2,8],[6]] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,7] => [7,2,3,4,5,8,1,6] => [[1,3,4,5,6],[2,8],[7]] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 5
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 4
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7] => [4,2,3,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [4,3,2,1,6,5,8,7] => [[1,5,7],[2,6,8],[3],[4]] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,8,7] => [5,2,3,6,1,4,8,7] => [[1,3,4,7],[2,6,8],[5]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,8,7] => [5,3,2,6,1,4,8,7] => [[1,4,7],[2,6,8],[3],[5]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,8,7] => [5,4,6,2,1,3,8,7] => [[1,3,7],[2,6,8],[4],[5]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,8,5,7] => [4,2,3,1,7,8,5,6] => [[1,3,5,6],[2,7,8],[4]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,8,5,7] => [4,3,2,1,7,8,5,6] => [[1,5,6],[2,7,8],[3],[4]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [5,2,3,7,1,8,4,6] => [[1,3,4,6],[2,7,8],[5]] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,8,5,7] => [5,3,2,7,1,8,4,6] => [[1,4,6],[2,7,8],[3],[5]] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,8,2,5,7] => [6,2,3,7,8,1,4,5] => [[1,3,4,5],[2,7,8],[6]] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,8,2,5,7] => [6,3,2,7,8,1,4,5] => [[1,4,5],[2,7,8],[3],[6]] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [6,5,7,8,2,1,3,4] => [[1,3,4],[2,7,8],[5],[6]] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7,8] => [4,3,2,1,6,5,7,8] => [[1,5,7,8],[2,6],[3],[4]] => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [3,4,1,2,6,7,5,8] => [4,3,2,1,7,6,5,8] => [[1,5,8],[2,6],[3,7],[4]] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5,8] => [5,3,2,7,1,6,4,8] => [[1,4,8],[2,6],[3,7],[5]] => 2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,6,7,1,2,5,8] => [6,5,7,4,2,1,3,8] => [[1,3,8],[2,7],[4],[5],[6]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,7,8,5] => [4,3,2,1,8,6,7,5] => [[1,5,7],[2,6],[3,8],[4]] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,6,2,7,8,5] => [5,2,3,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,6,2,7,8,5] => [5,3,2,8,1,6,7,4] => [[1,4,7],[2,6],[3,8],[5]] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,6,7,2,8,5] => [6,2,3,8,5,1,7,4] => [[1,3,4,7],[2,5],[6,8]] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,6,7,2,8,5] => [6,3,2,8,5,1,7,4] => [[1,4,7],[2,5],[3,8],[6]] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [3,4,6,1,7,2,8,5] => [6,4,8,2,5,1,7,3] => [[1,3,7],[2,5],[4,8],[6]] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,6,7,1,2,8,5] => [6,5,8,4,2,1,7,3] => [[1,3],[2,7],[4,8],[5],[6]] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,6,7,8,2,5] => [7,2,3,8,5,6,1,4] => [[1,3,4,6],[2,5],[7,8]] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,6,7,8,2,5] => [7,3,2,8,5,6,1,4] => [[1,4,6],[2,5],[3,8],[7]] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [3,4,6,1,7,8,2,5] => [7,4,8,2,5,6,1,3] => [[1,3,6],[2,5],[4,8],[7]] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,4,6,7,1,8,2,5] => [7,5,8,4,2,6,1,3] => [[1,3],[2,6],[4,8],[5],[7]] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,6,7,8,1,2,5] => [7,6,8,4,5,2,1,3] => [[1,3],[2,5],[4,8],[6],[7]] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,8,6] => [4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,7,5,8,6] => [4,3,2,1,8,6,7,5] => [[1,5,7],[2,6],[3,8],[4]] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,7,2,5,8,6] => [5,2,3,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,7,2,5,8,6] => [5,3,2,8,1,6,7,4] => [[1,4,7],[2,6],[3,8],[5]] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,7,8,5,6] => [4,2,3,1,8,7,6,5] => [[1,3,5],[2,6],[4,7],[8]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,7,8,5,6] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [6,4,8,2,7,1,5,3] => [[1,3],[2,5],[4,7],[6,8]] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => [6,5,8,7,2,1,4,3] => [[1,3],[2,4],[5,7],[6,8]] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,2,7,5,6,8] => [4,3,2,1,7,6,5,8] => [[1,5,8],[2,6],[3,7],[4]] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6,8] => [4,3,2,1,5,7,6,8] => [[1,5,6,8],[2,7],[3],[4]] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6,8] => [5,3,2,4,1,7,6,8] => [[1,4,6,8],[2,7],[3],[5]] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,1,7,2,6,8] => [6,4,3,2,7,1,5,8] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6,8] => [6,5,3,7,2,1,4,8] => [[1,4,8],[2,7],[3],[5],[6]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,7,8,6] => [4,3,2,1,5,8,7,6] => [[1,5,6],[2,7],[3,8],[4]] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,7,8,6] => [5,2,3,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,7,8,6] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,8,6] => [6,5,3,8,2,1,7,4] => [[1,4],[2,7],[3,8],[5],[6]] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,8,2,6] => [7,2,3,4,8,6,1,5] => [[1,3,4,5],[2,6],[7,8]] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,5,7,8,2,6] => [7,3,2,4,8,6,1,5] => [[1,4,5],[2,6],[3,8],[7]] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [3,4,5,1,7,8,2,6] => [7,4,3,2,8,6,1,5] => [[1,5],[2,6],[3,8],[4],[7]] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,7,1,8,2,6] => [7,5,3,8,2,6,1,4] => [[1,4],[2,6],[3,8],[5],[7]] => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,7,8,1,2,6] => [7,6,3,8,5,2,1,4] => [[1,4],[2,5],[3,8],[6],[7]] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,2,8,5,6,7] => [4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,8,5,6,7] => [4,3,2,1,8,6,7,5] => [[1,5,7],[2,6],[3,8],[4]] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,8,2,5,6,7] => [5,2,3,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,4,1,8,2,5,6,7] => [5,3,2,8,1,6,7,4] => [[1,4,7],[2,6],[3,8],[5]] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,2,5,8,6,7] => [4,3,2,1,5,8,7,6] => [[1,5,6],[2,7],[3,8],[4]] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,2,8,6,7] => [5,3,2,4,1,8,7,6] => [[1,4,6],[2,7],[3,8],[5]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,4,5,1,2,8,6,7] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [6,5,3,8,2,1,7,4] => [[1,4],[2,7],[3,8],[5],[6]] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,8,7] => [4,3,2,1,5,6,8,7] => [[1,5,6,7],[2,8],[3],[4]] => 4
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,8,7] => [5,4,3,2,1,6,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,8,7] => [6,2,3,4,5,1,8,7] => [[1,3,4,5,7],[2,8],[6]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,8,7] => [6,4,3,2,5,1,8,7] => [[1,5,7],[2,8],[3],[4],[6]] => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,8,7] => [6,5,3,4,2,1,8,7] => [[1,4,7],[2,8],[3],[5],[6]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [7,2,3,4,5,8,1,6] => [[1,3,4,5,6],[2,8],[7]] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,4,5,6,1,8,2,7] => [7,5,3,4,2,8,1,6] => [[1,4,6],[2,8],[3],[5],[7]] => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,6,8,1,2,7] => [7,6,3,4,8,2,1,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8] => [4,3,2,1,5,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7,8] => [5,2,3,4,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7,8] => [5,3,2,4,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7,8] => [5,4,3,2,1,6,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7,8] => [6,2,3,4,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7,8] => [6,4,3,2,5,1,7,8] => [[1,5,7,8],[2],[3],[4],[6]] => 3
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [6,5,3,4,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2,8] => [7,2,3,4,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2,8] => [7,5,3,4,2,6,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [7,6,3,4,5,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,2] => [8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1,5,6,7,8,2] => [8,3,2,4,5,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,4,5,1,6,7,8,2] => [8,4,3,2,5,6,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,4,5,6,1,7,8,2] => [8,5,3,4,2,6,7,1] => [[1,4,6,7],[2],[3],[5],[8]] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,4,5,6,7,1,8,2] => [8,6,3,4,5,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [8,7,3,4,5,6,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7] => [4,2,6,1,5,3,8,7] => [[1,3,7],[2,5,8],[4,6]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,8,7] => [4,6,3,1,5,2,8,7] => [[1,2,7],[3,5,8],[4,6]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,8,7] => [5,2,6,4,1,3,8,7] => [[1,3,7],[2,4,8],[5,6]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,8,7] => [5,6,3,4,1,2,8,7] => [[1,2,7],[3,4,8],[5,6]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,8,7] => [5,6,4,3,1,2,8,7] => [[1,2,7],[3,6,8],[4],[5]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,8,4,7] => [4,2,7,1,5,8,3,6] => [[1,3,6],[2,5,8],[4,7]] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,8,4,7] => [5,2,7,4,1,8,3,6] => [[1,3,6],[2,4,8],[5,7]] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,8,4,7] => [5,7,4,3,1,8,2,6] => [[1,2,6],[3,7,8],[4],[5]] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,5,6,8,2,4,7] => [6,2,7,4,8,1,3,5] => [[1,3,5],[2,4,8],[6,7]] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,5,1,6,8,2,4,7] => [6,7,3,4,8,1,2,5] => [[1,2,5],[3,4,8],[6,7]] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [6,7,4,3,8,1,2,5] => [[1,2,5],[3,7,8],[4],[6]] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [6,7,5,8,3,1,2,4] => [[1,2,4],[3,7,8],[5],[6]] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7,8] => [5,2,6,4,1,3,7,8] => [[1,3,7,8],[2,4],[5,6]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [4,7,3,1,5,6,2,8] => [[1,2,6,8],[3,5],[4,7]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4,8] => [5,7,3,4,1,6,2,8] => [[1,2,6,8],[3,4],[5,7]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4,8] => [6,7,3,4,5,1,2,8] => [[1,2,5,8],[3,4],[6,7]] => 2
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => [6,7,5,4,3,1,2,8] => [[1,2,8],[3,7],[4],[5],[6]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,5,2,6,7,8,4] => [4,2,8,1,5,6,7,3] => [[1,3,6,7],[2,5],[4,8]] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,5,1,2,6,7,8,4] => [4,8,3,1,5,6,7,2] => [[1,2,6,7],[3,5],[4,8]] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,5,6,2,7,8,4] => [5,2,8,4,1,6,7,3] => [[1,3,6,7],[2,4],[5,8]] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5,1,6,2,7,8,4] => [5,8,3,4,1,6,7,2] => [[1,2,6,7],[3,4],[5,8]] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5,6,1,2,7,8,4] => [5,8,4,3,1,6,7,2] => [[1,2,7],[3,6],[4,8],[5]] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,5,6,7,2,8,4] => [6,2,8,4,5,1,7,3] => [[1,3,5,7],[2,4],[6,8]] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5,1,6,7,2,8,4] => [6,8,3,4,5,1,7,2] => [[1,2,5,7],[3,4],[6,8]] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5,6,1,7,2,8,4] => [6,8,4,3,5,1,7,2] => [[1,2,7],[3,5],[4,8],[6]] => 1
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,8,4] => [6,8,5,4,3,1,7,2] => [[1,2],[3,7],[4,8],[5],[6]] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,5,6,7,8,2,4] => [7,2,8,4,5,6,1,3] => [[1,3,5,6],[2,4],[7,8]] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5,1,6,7,8,2,4] => [7,8,3,4,5,6,1,2] => [[1,2,5,6],[3,4],[7,8]] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5,6,1,7,8,2,4] => [7,8,4,3,5,6,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5,6,7,1,8,2,4] => [7,8,5,4,3,6,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5,6,7,8,1,2,4] => [7,8,6,4,5,3,1,2] => [[1,2],[3,5],[4,8],[6],[7]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6] => [4,2,6,1,8,3,7,5] => [[1,3,5],[2,6,7],[4,8]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,7,4,8,6] => [4,6,3,1,8,2,7,5] => [[1,2,5],[3,6,7],[4,8]] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,7,2,4,8,6] => [5,2,6,8,1,3,7,4] => [[1,3,4],[2,6,7],[5,8]] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,7,2,4,8,6] => [5,6,3,8,1,2,7,4] => [[1,2,4],[3,6,7],[5,8]] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,7,1,2,4,8,6] => [5,6,8,4,1,2,7,3] => [[1,2,3],[4,6,7],[5,8]] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,7,8,4,6] => [4,2,7,1,8,6,3,5] => [[1,3,5],[2,6,8],[4,7]] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,7,8,4,6] => [4,7,3,1,8,6,2,5] => [[1,2,5],[3,6,8],[4,7]] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,7,2,8,4,6] => [5,2,7,8,1,6,3,4] => [[1,3,4],[2,6,8],[5,7]] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,7,2,8,4,6] => [5,7,3,8,1,6,2,4] => [[1,2,4],[3,6,8],[5,7]] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,5,7,1,2,8,4,6] => [5,7,8,4,1,6,2,3] => [[1,2,3],[4,6,8],[5,7]] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,7,8,2,4,6] => [6,2,7,8,5,1,3,4] => [[1,3,4],[2,5,8],[6,7]] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,7,8,2,4,6] => [6,7,3,8,5,1,2,4] => [[1,2,4],[3,5,8],[6,7]] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [6,7,8,5,4,1,2,3] => [[1,2,3],[4,7,8],[5],[6]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6,8] => [4,2,6,1,7,3,5,8] => [[1,3,5,8],[2,6,7],[4]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6,8] => [4,6,3,1,7,2,5,8] => [[1,2,5,8],[3,6,7],[4]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6,8] => [5,2,6,7,1,3,4,8] => [[1,3,4,8],[2,6,7],[5]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6,8] => [5,6,3,7,1,2,4,8] => [[1,2,4,8],[3,6,7],[5]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6,8] => [5,6,7,4,1,2,3,8] => [[1,2,3,8],[4,6,7],[5]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,8] => [4,2,5,1,3,7,6,8] => [[1,3,6,8],[2,5,7],[4]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [[1,4,6,8],[2,5,7],[3]] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,8] => [1,4,5,2,3,7,6,8] => [[1,2,3,6,8],[4,5,7]] => 4
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,8] => [3,2,1,6,7,4,5,8] => [[1,4,5,8],[2,6,7],[3]] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6,8] => [1,3,2,6,7,4,5,8] => [[1,2,4,5,8],[3,6,7]] => 4
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6,8] => [1,4,6,2,7,3,5,8] => [[1,2,3,5,8],[4,6,7]] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => [1,5,6,7,2,3,4,8] => [[1,2,3,4,8],[5,6,7]] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,7,8,6] => [4,2,5,1,3,8,7,6] => [[1,3,6],[2,5,7],[4,8]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,7,8,6] => [4,5,3,1,2,8,7,6] => [[1,2,6],[3,5,7],[4,8]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,7,6] => [[1,2,4,6],[3,5,7],[8]] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,7,4,8,6] => [1,3,2,6,8,4,7,5] => [[1,2,4,5],[3,6,7],[8]] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,7,4,8,6] => [1,4,6,2,8,3,7,5] => [[1,2,3,5],[4,6,7],[8]] => 2
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,8,6] => [1,5,6,8,2,3,7,4] => [[1,2,3,4],[5,6,7],[8]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,7,8,4,6] => [3,2,1,7,8,6,4,5] => [[1,4,5],[2,6,8],[3,7]] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,7,2,8,4,6] => [1,5,7,8,2,6,3,4] => [[1,2,3,4],[5,6,8],[7]] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,7,8,2,4,6] => [1,6,7,8,5,2,3,4] => [[1,2,3,4],[5,7,8],[6]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [4,2,6,1,8,3,7,5] => [[1,3,5],[2,6,7],[4,8]] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,8,4,6,7] => [4,6,3,1,8,2,7,5] => [[1,2,5],[3,6,7],[4,8]] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,8,2,4,6,7] => [5,2,6,8,1,3,7,4] => [[1,3,4],[2,6,7],[5,8]] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,5,1,8,2,4,6,7] => [5,6,3,8,1,2,7,4] => [[1,2,4],[3,6,7],[5,8]] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,4,8,6,7] => [4,2,5,1,3,8,7,6] => [[1,3,6],[2,5,7],[4,8]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,5,1,2,4,8,6,7] => [4,5,3,1,2,8,7,6] => [[1,2,6],[3,5,7],[4,8]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,3,2,5,4,8,7,6] => [[1,2,4,6],[3,5,7],[8]] => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,5,8,4,6,7] => [1,3,2,6,8,4,7,5] => [[1,2,4,5],[3,6,7],[8]] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [1,4,6,2,8,3,7,5] => [[1,2,3,5],[4,6,7],[8]] => 2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [1,5,6,8,2,3,7,4] => [[1,2,3,4],[5,6,7],[8]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,8,7] => [4,2,5,1,3,6,8,7] => [[1,3,6,7],[2,5,8],[4]] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,8,7] => [4,5,3,1,2,6,8,7] => [[1,2,6,7],[3,5,8],[4]] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,8,7] => [1,3,2,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]] => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,5,6,8,4,7] => [3,2,1,7,5,8,4,6] => [[1,4,6],[2,5,8],[3,7]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,2,6,8,4,7] => [1,4,7,2,5,8,3,6] => [[1,2,3,6],[4,5,8],[7]] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,6,2,8,4,7] => [1,5,7,4,2,8,3,6] => [[1,2,3,6],[4,7,8],[5]] => 2
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,6,8,2,4,7] => [1,6,7,4,8,2,3,5] => [[1,2,3,5],[4,7,8],[6]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7,8] => [4,2,5,1,3,6,7,8] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => 6
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7,8] => [1,4,5,2,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 5
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7,8] => [1,3,2,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]] => 5
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7,8] => [1,4,6,2,5,3,7,8] => [[1,2,3,7,8],[4,5],[6]] => 4
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [1,5,6,4,2,3,7,8] => [[1,2,3,7,8],[4,6],[5]] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4,8] => [1,4,7,2,5,6,3,8] => [[1,2,3,6,8],[4,5],[7]] => 3
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4,8] => [1,5,7,4,2,6,3,8] => [[1,2,3,8],[4,6],[5,7]] => 3
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4,8] => [1,6,7,4,5,2,3,8] => [[1,2,3,8],[4,5],[6,7]] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [[1,4,6,7],[2,5],[3,8]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,5,2,6,7,8,4] => [1,4,8,2,5,6,7,3] => [[1,2,3,6,7],[4,5],[8]] => 2
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,5,6,2,7,8,4] => [1,5,8,4,2,6,7,3] => [[1,2,3,7],[4,6],[5,8]] => 2
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,5,6,7,2,8,4] => [1,6,8,4,5,2,7,3] => [[1,2,3,7],[4,5],[6,8]] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5,6,7,8,2,4] => [1,7,8,4,5,6,2,3] => [[1,2,3,6],[4,5],[7,8]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5] => [4,2,8,1,6,5,7,3] => [[1,3,7],[2,5],[4,6],[8]] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,6,1,2,7,4,8,5] => [4,8,3,1,6,5,7,2] => [[1,2,7],[3,5],[4,6],[8]] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,6,1,7,2,4,8,5] => [5,8,3,6,1,4,7,2] => [[1,2,7],[3,4],[5,6],[8]] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,6,7,1,2,4,8,5] => [5,8,6,4,1,3,7,2] => [[1,2,7],[3,6],[4],[5],[8]] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,6,1,2,7,8,4,5] => [4,8,3,1,7,6,5,2] => [[1,2],[3,5],[4,6],[7],[8]] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,6,7,2,8,4,5] => [5,2,8,7,1,6,4,3] => [[1,3],[2,4],[5,6],[7],[8]] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,6,1,7,2,8,4,5] => [5,8,3,7,1,6,4,2] => [[1,2],[3,4],[5,6],[7],[8]] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,6,7,1,2,8,4,5] => [5,8,7,4,1,6,3,2] => [[1,2],[3,6],[4,7],[5],[8]] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,6,1,7,8,2,4,5] => [6,8,3,7,5,1,4,2] => [[1,2],[3,4],[5,7],[6],[8]] => 1
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [6,8,7,5,4,1,3,2] => [[1,2],[3,7],[4],[5],[6],[8]] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5,8] => [5,2,7,6,1,4,3,8] => [[1,3,8],[2,4],[5,6],[7]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => [4,7,3,1,5,6,2,8] => [[1,2,6,8],[3,5],[4,7]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5,8] => [1,4,7,2,5,6,3,8] => [[1,2,3,6,8],[4,5],[7]] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5,8] => [1,3,2,7,6,5,4,8] => [[1,2,4,8],[3,5],[6],[7]] => 4
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5,8] => [1,4,7,2,6,5,3,8] => [[1,2,3,8],[4,5],[6],[7]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,7,8,5] => [4,2,8,1,5,6,7,3] => [[1,3,6,7],[2,5],[4,8]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,7,8,5] => [4,8,3,1,5,6,7,2] => [[1,2,6,7],[3,5],[4,8]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,7,8,5] => [3,2,1,8,5,6,7,4] => [[1,4,6,7],[2,5],[3,8]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,7,8,5] => [1,4,8,2,5,6,7,3] => [[1,2,3,6,7],[4,5],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,6,7,4,8,5] => [3,2,1,8,6,5,7,4] => [[1,4,7],[2,5],[3,6],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,4,8,5] => [1,3,2,8,6,5,7,4] => [[1,2,4,7],[3,5],[6],[8]] => 3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,6,7,2,4,8,5] => [1,5,8,6,2,4,7,3] => [[1,2,3,7],[4,6],[5],[8]] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,2,6,7,8,4,5] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,3,2,6,7,8,4,5] => [1,3,2,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]] => 3
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,3,6,7,8,2,4,5] => [1,6,8,7,5,2,4,3] => [[1,2,3],[4,7],[5],[6],[8]] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,8,4,5,7] => [4,2,7,1,8,6,3,5] => [[1,3,5],[2,6,8],[4,7]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,6,1,2,8,4,5,7] => [4,7,3,1,8,6,2,5] => [[1,2,5],[3,6,8],[4,7]] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,6,8,2,4,5,7] => [5,2,7,8,1,6,3,4] => [[1,3,4],[2,6,8],[5,7]] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,6,1,8,2,4,5,7] => [5,7,3,8,1,6,2,4] => [[1,2,4],[3,6,8],[5,7]] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,6,8,1,2,4,5,7] => [5,7,8,4,1,6,2,3] => [[1,2,3],[4,6,8],[5,7]] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,8,5,7] => [4,2,7,1,5,8,3,6] => [[1,3,6],[2,5,8],[4,7]] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,8,5,7] => [1,3,2,7,5,8,4,6] => [[1,2,4,6],[3,5,8],[7]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,8,5,7] => [1,4,7,2,5,8,3,6] => [[1,2,3,6],[4,5,8],[7]] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,8,4,5,7] => [3,2,1,7,8,6,4,5] => [[1,4,5],[2,6,8],[3,7]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,8,7] => [4,2,6,1,5,3,8,7] => [[1,3,7],[2,5,8],[4,6]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,8,7] => [4,6,3,1,5,2,8,7] => [[1,2,7],[3,5,8],[4,6]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => 5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,8,5,7] => [3,2,1,4,7,8,5,6] => [[1,4,5,6],[2,7,8],[3]] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,8,5,7] => [1,3,2,4,7,8,5,6] => [[1,2,4,5,6],[3,7,8]] => 4
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,8,2,5,7] => [1,6,3,7,8,2,4,5] => [[1,2,4,5],[3,7,8],[6]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7,8] => [4,2,6,1,5,3,7,8] => [[1,3,7,8],[2,5],[4,6]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7,8] => [4,6,3,1,5,2,7,8] => [[1,2,7,8],[3,5],[4,6]] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7,8] => [1,3,2,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]] => 5
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7,8] => [1,4,6,2,5,3,7,8] => [[1,2,3,7,8],[4,5],[6]] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [[1,2,4,5,7,8],[3,6]] => 6
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7,8] => [1,5,3,6,2,4,7,8] => [[1,2,4,7,8],[3,6],[5]] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5,8] => [1,3,2,4,7,6,5,8] => [[1,2,4,5,8],[3,6],[7]] => 5
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [[1,2,5,8],[3,6],[4,7]] => 4
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5,8] => [1,5,3,7,2,6,4,8] => [[1,2,4,8],[3,6],[5,7]] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5,8] => [1,6,3,7,5,2,4,8] => [[1,2,4,8],[3,5],[6,7]] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => [[1,4,5,7],[2,6],[3,8]] => 3
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,4,6,7,2,8,5] => [1,6,3,8,5,2,7,4] => [[1,2,4,7],[3,5],[6,8]] => 2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,4,6,7,8,2,5] => [1,7,3,8,5,6,2,4] => [[1,2,4,6],[3,5],[7,8]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,7,2,8,4,5,6] => [4,2,8,1,7,6,5,3] => [[1,3],[2,5],[4,6],[7],[8]] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [3,7,1,2,8,4,5,6] => [4,8,3,1,7,6,5,2] => [[1,2],[3,5],[4,6],[7],[8]] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,7,8,2,4,5,6] => [5,2,8,7,1,6,4,3] => [[1,3],[2,4],[5,6],[7],[8]] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [3,7,1,8,2,4,5,6] => [5,8,3,7,1,6,4,2] => [[1,2],[3,4],[5,6],[7],[8]] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,7,8,1,2,4,5,6] => [5,8,7,4,1,6,3,2] => [[1,2],[3,6],[4,7],[5],[8]] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [3,7,1,2,4,8,5,6] => [4,8,3,1,5,7,6,2] => [[1,2,6],[3,5],[4,7],[8]] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,7,4,8,5,6] => [3,2,1,8,5,7,6,4] => [[1,4,6],[2,5],[3,7],[8]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,3,2,7,4,8,5,6] => [1,3,2,8,5,7,6,4] => [[1,2,4,6],[3,5],[7],[8]] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [3,1,2,7,8,4,5,6] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,3,7,8,2,4,5,6] => [1,5,8,7,2,6,4,3] => [[1,2,3],[4,6],[5],[7],[8]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [3,1,7,2,4,5,8,6] => [4,2,8,1,5,6,7,3] => [[1,3,6,7],[2,5],[4,8]] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,7,1,2,4,5,8,6] => [4,8,3,1,5,6,7,2] => [[1,2,6,7],[3,5],[4,8]] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,3,7,2,4,5,8,6] => [1,4,8,2,5,6,7,3] => [[1,2,3,6,7],[4,5],[8]] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [3,1,2,4,7,5,8,6] => [3,2,1,4,8,6,7,5] => [[1,4,5,7],[2,6],[3,8]] => 3
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,8,6] => [1,5,3,8,2,6,7,4] => [[1,2,4,7],[3,6],[5,8]] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,2,4,7,8,5,6] => [3,2,1,4,8,7,6,5] => [[1,4,5],[2,6],[3,7],[8]] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,3,2,4,7,8,5,6] => [1,3,2,4,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,3,4,2,7,8,5,6] => [1,4,3,2,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => 3
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,3,4,7,8,2,5,6] => [1,6,3,8,7,2,5,4] => [[1,2,4],[3,5],[6,7],[8]] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6,8] => [4,7,3,1,5,6,2,8] => [[1,2,6,8],[3,5],[4,7]] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6,8] => [1,4,7,2,5,6,3,8] => [[1,2,3,6,8],[4,5],[7]] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => [3,2,1,4,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]] => 4
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => [1,5,3,7,2,6,4,8] => [[1,2,4,8],[3,6],[5,7]] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => 6
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6,8] => [1,4,3,2,5,7,6,8] => [[1,2,5,6,8],[3,7],[4]] => 5
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,7,6] => [[1,2,4,5,6],[3,7],[8]] => 5
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,7,8,6] => [1,4,3,2,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => 4
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,7,8,6] => [1,5,3,4,2,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,4,5,7,2,8,6] => [1,6,3,4,8,2,7,5] => [[1,2,4,5],[3,7],[6,8]] => 2
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,3,4,5,7,8,2,6] => [1,7,3,4,8,6,2,5] => [[1,2,4,5],[3,6],[7,8]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [4,2,8,1,5,6,7,3] => [[1,3,6,7],[2,5],[4,8]] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,8,1,2,4,5,6,7] => [4,8,3,1,5,6,7,2] => [[1,2,6,7],[3,5],[4,8]] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,8,4,5,6,7] => [3,2,1,8,5,6,7,4] => [[1,4,6,7],[2,5],[3,8]] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,3,8,2,4,5,6,7] => [1,4,8,2,5,6,7,3] => [[1,2,3,6,7],[4,5],[8]] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,2,4,8,5,6,7] => [3,2,1,4,8,6,7,5] => [[1,4,5,7],[2,6],[3,8]] => 3
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [1,5,3,8,2,6,7,4] => [[1,2,4,7],[3,6],[5,8]] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,2,4,5,8,6,7] => [3,2,1,4,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,8,7,6] => [[1,2,4,5,6],[3,7],[8]] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,3,4,2,5,8,6,7] => [1,4,3,2,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => 4
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,3,4,5,2,8,6,7] => [1,5,3,4,2,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => 3
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,3,4,5,8,2,6,7] => [1,6,3,4,8,2,7,5] => [[1,2,4,5],[3,7],[6,8]] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => 5
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => 6
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => [[1,2,5,6,7],[3,8],[4]] => 5
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,3,4,5,6,8,2,7] => [1,7,3,4,5,8,2,6] => [[1,2,4,5,6],[3,8],[7]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => 6
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [1,5,3,4,2,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 5
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7,8] => [1,6,3,4,5,2,7,8] => [[1,2,4,5,7,8],[3],[6]] => 4
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,8] => [1,7,3,4,5,6,2,8] => [[1,2,4,5,6,8],[3],[7]] => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,2] => [1,8,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3],[8]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7] => [6,2,4,3,5,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => [6,4,3,2,5,1,8,7] => [[1,5,7],[2,8],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,8,7] => [6,2,5,4,3,1,8,7] => [[1,3,7],[2,8],[4],[5],[6]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,8,7] => [6,5,3,4,2,1,8,7] => [[1,4,7],[2,8],[3],[5],[6]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,8,7] => [6,5,4,3,2,1,8,7] => [[1,7],[2,8],[3],[4],[5],[6]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,8,3,7] => [7,2,4,3,5,8,1,6] => [[1,3,5,6],[2,8],[4],[7]] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,8,3,7] => [7,4,3,2,5,8,1,6] => [[1,5,6],[2,8],[3],[4],[7]] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,8,3,7] => [7,2,5,4,3,8,1,6] => [[1,3,6],[2,8],[4],[5],[7]] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,8,3,7] => [7,5,3,4,2,8,1,6] => [[1,4,6],[2,8],[3],[5],[7]] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,8,3,7] => [7,5,4,3,2,8,1,6] => [[1,6],[2,8],[3],[4],[5],[7]] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,5,6,8,2,3,7] => [7,2,6,4,8,3,1,5] => [[1,3,5],[2,8],[4],[6],[7]] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [4,5,1,6,8,2,3,7] => [7,6,3,4,8,2,1,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [7,6,4,3,8,2,1,5] => [[1,5],[2,8],[3],[4],[6],[7]] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [7,6,5,8,3,2,1,4] => [[1,4],[2,8],[3],[5],[6],[7]] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7,8] => [6,5,3,4,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7,8] => [6,5,4,3,2,1,7,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3,8] => [7,5,3,4,2,6,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3,8] => [7,5,4,3,2,6,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3,8] => [7,2,6,4,5,3,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3,8] => [7,6,3,4,5,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3,8] => [7,6,4,3,5,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => 2
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [7,6,5,4,3,2,1,8] => [[1,8],[2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,6,7,8,3] => [8,4,3,2,5,6,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [4,5,1,6,2,7,8,3] => [8,5,3,4,2,6,7,1] => [[1,4,6,7],[2],[3],[5],[8]] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [4,5,6,1,2,7,8,3] => [8,5,4,3,2,6,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [4,1,5,6,7,2,8,3] => [8,2,6,4,5,3,7,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [4,5,1,6,7,2,8,3] => [8,6,3,4,5,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5,6,1,7,2,8,3] => [8,6,4,3,5,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,8,3] => [8,6,5,4,3,2,7,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,1,5,6,7,8,2,3] => [8,2,7,4,5,6,3,1] => [[1,3,5,6],[2],[4],[7],[8]] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,5,1,6,7,8,2,3] => [8,7,3,4,5,6,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [4,5,6,1,7,8,2,3] => [8,7,4,3,5,6,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5,6,7,1,8,2,3] => [8,7,5,4,3,6,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [8,7,6,4,5,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,7,3,8,6] => [6,2,4,3,8,1,7,5] => [[1,3,5],[2,7],[4,8],[6]] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,7,3,8,6] => [6,4,3,2,8,1,7,5] => [[1,5],[2,7],[3,8],[4],[6]] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [4,5,1,7,2,3,8,6] => [6,5,3,8,2,1,7,4] => [[1,4],[2,7],[3,8],[5],[6]] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [4,5,7,1,2,3,8,6] => [6,5,8,4,2,1,7,3] => [[1,3],[2,7],[4,8],[5],[6]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,7,8,3,6] => [7,2,4,3,8,6,1,5] => [[1,3,5],[2,6],[4,8],[7]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,7,8,3,6] => [7,4,3,2,8,6,1,5] => [[1,5],[2,6],[3,8],[4],[7]] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,1,5,7,2,8,3,6] => [7,2,5,8,3,6,1,4] => [[1,3,4],[2,6],[5,8],[7]] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,5,1,7,2,8,3,6] => [7,5,3,8,2,6,1,4] => [[1,4],[2,6],[3,8],[5],[7]] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,5,7,1,2,8,3,6] => [7,5,8,4,2,6,1,3] => [[1,3],[2,6],[4,8],[5],[7]] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,5,1,7,8,2,3,6] => [7,6,3,8,5,2,1,4] => [[1,4],[2,5],[3,8],[6],[7]] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [7,6,8,5,4,2,1,3] => [[1,3],[2,8],[4],[5],[6],[7]] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6,8] => [6,4,3,2,7,1,5,8] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [4,5,1,7,2,3,6,8] => [6,5,3,7,2,1,4,8] => [[1,4,8],[2,7],[3],[5],[6]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6,8] => [5,2,4,3,1,7,6,8] => [[1,3,6,8],[2,7],[4],[5]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6,8] => [5,4,3,2,1,7,6,8] => [[1,6,8],[2,7],[3],[4],[5]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6,8] => [1,5,4,3,2,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => 4
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6,8] => [1,6,4,3,7,2,5,8] => [[1,2,5,8],[3,7],[4],[6]] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => [5,2,4,3,1,8,7,6] => [[1,3,6],[2,7],[4,8],[5]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,7,8,6] => [5,2,3,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,7,8,6] => [1,5,3,4,2,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,7,8,6] => [1,5,4,3,2,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => [1,6,3,4,8,2,7,5] => [[1,2,4,5],[3,7],[6,8]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,7,3,8,6] => [1,6,4,3,8,2,7,5] => [[1,2,5],[3,7],[4,8],[6]] => 2
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,8,6] => [1,6,5,8,3,2,7,4] => [[1,2,4],[3,7],[5,8],[6]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,7,8,3,6] => [7,2,3,4,8,6,1,5] => [[1,3,4,5],[2,6],[7,8]] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,7,8,3,6] => [1,7,3,4,8,6,2,5] => [[1,2,4,5],[3,6],[7,8]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,7,8,3,6] => [1,7,4,3,8,6,2,5] => [[1,2,5],[3,6],[4,8],[7]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,8,3,6,7] => [6,2,4,3,8,1,7,5] => [[1,3,5],[2,7],[4,8],[6]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,8,3,6,7] => [6,4,3,2,8,1,7,5] => [[1,5],[2,7],[3,8],[4],[6]] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,8,2,3,6,7] => [6,5,3,8,2,1,7,4] => [[1,4],[2,7],[3,8],[5],[6]] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [4,5,8,1,2,3,6,7] => [6,5,8,4,2,1,7,3] => [[1,3],[2,7],[4,8],[5],[6]] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,8,6,7] => [5,2,4,3,1,8,7,6] => [[1,3,6],[2,7],[4,8],[5]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,8,6,7] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,8,6,7] => [5,2,3,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,8,6,7] => [1,5,3,4,2,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => [1,5,4,3,2,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,8,3,6,7] => [1,6,3,4,8,2,7,5] => [[1,2,4,5],[3,7],[6,8]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => [1,6,4,3,8,2,7,5] => [[1,2,5],[3,7],[4,8],[6]] => 2
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,8,2,3,6,7] => [1,6,5,8,3,2,7,4] => [[1,2,4],[3,7],[5,8],[6]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,8,7] => [5,4,3,2,1,6,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,8,7] => [6,2,3,4,5,1,8,7] => [[1,3,4,5,7],[2,8],[6]] => 2
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,8,7] => [1,6,5,4,3,2,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [7,2,3,4,5,8,1,6] => [[1,3,4,5,6],[2,8],[7]] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,5,6,8,3,7] => [1,7,3,4,5,8,2,6] => [[1,2,4,5,6],[3,8],[7]] => 2
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,5,6,2,8,3,7] => [1,7,5,4,3,8,2,6] => [[1,2,6],[3,8],[4],[5],[7]] => 2
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,5,6,8,2,3,7] => [1,7,6,4,8,3,2,5] => [[1,2,5],[3,8],[4],[6],[7]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7,8] => [5,2,4,3,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7,8] => [5,4,3,2,1,6,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7,8] => [5,2,3,4,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7,8] => [1,5,3,4,2,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7,8] => [1,5,4,3,2,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => 5
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7,8] => [6,2,3,4,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7,8] => [1,6,4,3,5,2,7,8] => [[1,2,5,7,8],[3],[4],[6]] => 4
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7,8] => [1,6,5,4,3,2,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3,8] => [7,2,3,4,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3,8] => [1,7,3,4,5,6,2,8] => [[1,2,4,5,6,8],[3],[7]] => 3
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3,8] => [1,7,6,4,5,3,2,8] => [[1,2,5,8],[3],[4],[6],[7]] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [4,1,2,5,6,7,8,3] => [8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,3] => [1,8,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3],[8]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,5,2,6,7,8,3] => [1,8,4,3,5,6,7,2] => [[1,2,5,6,7],[3],[4],[8]] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,5,6,2,7,8,3] => [1,8,5,4,3,6,7,2] => [[1,2,6,7],[3],[4],[5],[8]] => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,5,6,7,2,8,3] => [1,8,6,4,5,3,7,2] => [[1,2,5,7],[3],[4],[6],[8]] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,5,6,7,8,2,3] => [1,8,7,4,5,6,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5] => [6,2,8,4,5,1,7,3] => [[1,3,5,7],[2,4],[6,8]] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,6,7,2,3,8,5] => [6,2,8,5,4,1,7,3] => [[1,3,7],[2,4],[5,8],[6]] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,6,1,7,2,3,8,5] => [6,8,3,5,4,1,7,2] => [[1,2,7],[3,4],[5,8],[6]] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,6,7,1,2,3,8,5] => [6,8,5,4,3,1,7,2] => [[1,2],[3,7],[4,8],[5],[6]] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,6,1,2,7,8,3,5] => [7,8,3,4,5,6,1,2] => [[1,2,5,6],[3,4],[7,8]] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,6,7,2,8,3,5] => [7,2,8,5,4,6,1,3] => [[1,3,6],[2,4],[5,8],[7]] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,6,1,7,2,8,3,5] => [7,8,3,5,4,6,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,6,7,1,2,8,3,5] => [7,8,5,4,3,6,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,6,7,8,2,3,5] => [7,2,8,6,5,4,1,3] => [[1,3],[2,4],[5,8],[6],[7]] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,6,1,7,8,2,3,5] => [7,8,3,6,5,4,1,2] => [[1,2],[3,4],[5,8],[6],[7]] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [7,8,6,4,5,3,1,2] => [[1,2],[3,5],[4,8],[6],[7]] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [7,8,6,5,4,3,1,2] => [[1,2],[3,8],[4],[5],[6],[7]] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5,8] => [6,2,7,4,5,1,3,8] => [[1,3,5,8],[2,4],[6,7]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5,8] => [6,7,3,4,5,1,2,8] => [[1,2,5,8],[3,4],[6,7]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5,8] => [6,7,3,5,4,1,2,8] => [[1,2,8],[3,4],[5,7],[6]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5,8] => [6,7,5,4,3,1,2,8] => [[1,2,8],[3,7],[4],[5],[6]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5,8] => [5,2,7,4,1,6,3,8] => [[1,3,6,8],[2,4],[5,7]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [5,7,3,4,1,6,2,8] => [[1,2,6,8],[3,4],[5,7]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5,8] => [1,5,3,7,2,6,4,8] => [[1,2,4,8],[3,6],[5,7]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5,8] => [6,2,3,7,5,1,4,8] => [[1,3,4,8],[2,5],[6,7]] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5,8] => [1,6,3,7,5,2,4,8] => [[1,2,4,8],[3,5],[6,7]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5,8] => [1,6,7,4,5,2,3,8] => [[1,2,3,8],[4,5],[6,7]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [5,2,8,4,1,6,7,3] => [[1,3,6,7],[2,4],[5,8]] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,7,8,5] => [5,2,3,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,6,2,3,7,8,5] => [1,5,8,4,2,6,7,3] => [[1,2,3,7],[4,6],[5,8]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,6,7,3,8,5] => [6,2,3,8,5,1,7,4] => [[1,3,4,7],[2,5],[6,8]] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,2,7,3,8,5] => [1,6,8,4,5,2,7,3] => [[1,2,3,7],[4,5],[6,8]] => 2
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,8,5] => [1,6,8,5,4,2,7,3] => [[1,2,3],[4,7],[5,8],[6]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,6,7,8,3,5] => [1,7,3,8,5,6,2,4] => [[1,2,4,6],[3,5],[7,8]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,6,2,7,8,3,5] => [1,7,8,4,5,6,2,3] => [[1,2,3,6],[4,5],[7,8]] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,6,7,2,8,3,5] => [1,7,8,5,4,6,2,3] => [[1,2,3],[4,6],[5,8],[7]] => 2
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,6,7,8,2,3,5] => [1,7,8,6,5,4,2,3] => [[1,2,3],[4,8],[5],[6],[7]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,8,3,5,7] => [6,2,7,4,8,1,3,5] => [[1,3,5],[2,4,8],[6,7]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,8,3,5,7] => [6,7,3,4,8,1,2,5] => [[1,2,5],[3,4,8],[6,7]] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,8,2,3,5,7] => [6,2,7,8,5,1,3,4] => [[1,3,4],[2,5,8],[6,7]] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,8,2,3,5,7] => [6,7,3,8,5,1,2,4] => [[1,2,4],[3,5,8],[6,7]] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,8,1,2,3,5,7] => [6,7,8,4,5,1,2,3] => [[1,2,3],[4,5,8],[6,7]] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,8,5,7] => [5,2,7,4,1,8,3,6] => [[1,3,6],[2,4,8],[5,7]] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [5,2,3,7,1,8,4,6] => [[1,3,4,6],[2,7,8],[5]] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,8,5,7] => [1,5,3,7,2,8,4,6] => [[1,2,4,6],[3,7,8],[5]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,8,5,7] => [1,5,7,4,2,8,3,6] => [[1,2,3,6],[4,7,8],[5]] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,8,3,5,7] => [1,6,3,7,8,2,4,5] => [[1,2,4,5],[3,7,8],[6]] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,8,3,5,7] => [1,6,7,4,8,2,3,5] => [[1,2,3,5],[4,7,8],[6]] => 2
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [1,6,7,8,5,2,3,4] => [[1,2,3,4],[5,7,8],[6]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,8,7] => [5,2,6,4,1,3,8,7] => [[1,3,7],[2,4,8],[5,6]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,8,7] => [5,6,3,4,1,2,8,7] => [[1,2,7],[3,4,8],[5,6]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,8,7] => [5,2,3,6,1,4,8,7] => [[1,3,4,7],[2,6,8],[5]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7] => [4,2,3,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => 5
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,8,7] => [1,2,5,6,3,4,8,7] => [[1,2,3,4,7],[5,6,8]] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,8,5,7] => [4,2,3,1,7,8,5,6] => [[1,3,5,6],[2,7,8],[4]] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,8,5,7] => [1,2,4,3,7,8,5,6] => [[1,2,3,5,6],[4,7,8]] => 4
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,8,5,7] => [1,2,5,7,3,8,4,6] => [[1,2,3,4,6],[5,7,8]] => 3
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,8,3,5,7] => [1,2,6,7,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => [5,2,6,4,1,3,7,8] => [[1,3,7,8],[2,4],[5,6]] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7,8] => [1,5,3,6,2,4,7,8] => [[1,2,4,7,8],[3,6],[5]] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7,8] => [1,5,6,4,2,3,7,8] => [[1,2,3,7,8],[4,6],[5]] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => 6
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => [1,2,5,6,3,4,7,8] => [[1,2,3,4,7,8],[5,6]] => 5
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5,8] => [1,4,3,2,7,6,5,8] => [[1,2,5,8],[3,6],[4,7]] => 4
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5,8] => [1,2,5,7,3,6,4,8] => [[1,2,3,4,8],[5,6],[7]] => 4
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5,8] => [1,2,6,7,5,3,4,8] => [[1,2,3,4,8],[5,7],[6]] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,6,7,8,5] => [4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => 2
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,6,3,7,8,5] => [1,2,5,8,3,6,7,4] => [[1,2,3,4,7],[5,6],[8]] => 3
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,6,7,3,8,5] => [1,2,6,8,5,3,7,4] => [[1,2,3,4],[5,7],[6,8]] => 3
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,6,7,8,3,5] => [1,2,7,8,5,6,3,4] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,7,2,8,3,5,6] => [6,2,8,4,7,1,5,3] => [[1,3,5],[2,4],[6,7],[8]] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,7,1,2,8,3,5,6] => [6,8,3,4,7,1,5,2] => [[1,2,5],[3,4],[6,7],[8]] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,7,8,2,3,5,6] => [6,2,8,7,5,1,4,3] => [[1,3],[2,4],[5,7],[6],[8]] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,7,1,8,2,3,5,6] => [6,8,3,7,5,1,4,2] => [[1,2],[3,4],[5,7],[6],[8]] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,7,8,1,2,3,5,6] => [6,8,7,4,5,1,3,2] => [[1,2],[3,5],[4,7],[6],[8]] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,7,2,3,8,5,6] => [5,2,8,4,1,7,6,3] => [[1,3,6],[2,4],[5,7],[8]] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [4,7,1,2,3,8,5,6] => [5,8,3,4,1,7,6,2] => [[1,2,6],[3,4],[5,7],[8]] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,7,2,3,8,5,6] => [1,5,8,4,2,7,6,3] => [[1,2,3],[4,6],[5,7],[8]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,7,8,3,5,6] => [6,2,3,8,7,1,5,4] => [[1,3,4],[2,5],[6,7],[8]] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,7,8,3,5,6] => [1,6,3,8,7,2,5,4] => [[1,2,4],[3,5],[6,7],[8]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,7,2,8,3,5,6] => [1,6,8,4,7,2,5,3] => [[1,2,3],[4,5],[6,7],[8]] => 2
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,7,8,2,3,5,6] => [1,6,8,7,5,2,4,3] => [[1,2,3],[4,7],[5],[6],[8]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,7,2,3,5,8,6] => [5,2,8,4,1,6,7,3] => [[1,3,6,7],[2,4],[5,8]] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [4,7,1,2,3,5,8,6] => [5,8,3,4,1,6,7,2] => [[1,2,6,7],[3,4],[5,8]] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,2,7,3,5,8,6] => [5,2,3,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,2,7,3,5,8,6] => [1,5,3,8,2,6,7,4] => [[1,2,4,7],[3,6],[5,8]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,7,2,3,5,8,6] => [1,5,8,4,2,6,7,3] => [[1,2,3,7],[4,6],[5,8]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,2,3,7,5,8,6] => [4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => 2
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,8,6] => [1,2,5,8,3,6,7,4] => [[1,2,3,4,7],[5,6],[8]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,3,7,8,5,6] => [4,2,3,1,8,7,6,5] => [[1,3,5],[2,6],[4,7],[8]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,3,7,8,5,6] => [1,4,3,2,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,4,3,7,8,5,6] => [1,2,4,3,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => 4
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,4,7,3,8,5,6] => [1,2,5,8,3,7,6,4] => [[1,2,3,4],[5,6],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6,8] => [5,2,7,4,1,6,3,8] => [[1,3,6,8],[2,4],[5,7]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6,8] => [5,7,3,4,1,6,2,8] => [[1,2,6,8],[3,4],[5,7]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6,8] => [1,5,3,7,2,6,4,8] => [[1,2,4,8],[3,6],[5,7]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6,8] => [1,5,7,4,2,6,3,8] => [[1,2,3,8],[4,6],[5,7]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6,8] => [1,4,3,2,7,6,5,8] => [[1,2,5,8],[3,6],[4,7]] => 4
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [1,2,5,7,3,6,4,8] => [[1,2,3,4,8],[5,6],[7]] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6,8] => [4,2,3,1,5,7,6,8] => [[1,3,5,6,8],[2,7],[4]] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6,8] => [1,4,3,2,5,7,6,8] => [[1,2,5,6,8],[3,7],[4]] => 5
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => 6
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6,8] => [1,2,6,4,7,3,5,8] => [[1,2,3,5,8],[4,7],[6]] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,7,8,6] => [1,4,3,2,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]] => 5
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,7,8,6] => [1,2,5,4,3,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,4,5,7,3,8,6] => [1,2,6,4,8,3,7,5] => [[1,2,3,5],[4,7],[6,8]] => 3
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,4,5,7,8,3,6] => [1,2,7,4,8,6,3,5] => [[1,2,3,5],[4,6],[7,8]] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,8,2,3,5,6,7] => [5,2,8,4,1,6,7,3] => [[1,3,6,7],[2,4],[5,8]] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,8,1,2,3,5,6,7] => [5,8,3,4,1,6,7,2] => [[1,2,6,7],[3,4],[5,8]] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,8,3,5,6,7] => [5,2,3,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,4,2,8,3,5,6,7] => [1,5,3,8,2,6,7,4] => [[1,2,4,7],[3,6],[5,8]] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,4,8,2,3,5,6,7] => [1,5,8,4,2,6,7,3] => [[1,2,3,7],[4,6],[5,8]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,3,8,5,6,7] => [4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [1,2,5,8,3,6,7,4] => [[1,2,3,4,7],[5,6],[8]] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [1,4,3,2,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,4,3,5,8,6,7] => [1,2,4,3,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]] => 5
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,4,5,3,8,6,7] => [1,2,5,4,3,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 4
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,4,5,8,3,6,7] => [1,2,6,4,8,3,7,5] => [[1,2,3,5],[4,7],[6,8]] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,8,7] => [1,4,3,2,5,6,8,7] => [[1,2,5,6,7],[3,8],[4]] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => 6
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,4,5,6,8,3,7] => [1,2,7,4,5,8,3,6] => [[1,2,3,5,6],[4,8],[7]] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8] => [1,4,3,2,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 7
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [1,2,5,4,3,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,3] => [1,2,8,4,5,6,7,3] => [[1,2,3,5,6,7],[4],[8]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4] => [8,2,6,4,5,3,7,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [5,6,1,2,7,3,8,4] => [8,6,3,4,5,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,6,7,2,3,8,4] => [8,2,6,5,4,3,7,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [5,6,1,7,2,3,8,4] => [8,6,3,5,4,2,7,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,1,2,3,8,4] => [8,6,5,4,3,2,7,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [5,1,6,2,7,8,3,4] => [8,2,7,4,5,6,3,1] => [[1,3,5,6],[2],[4],[7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,6,1,2,7,8,3,4] => [8,7,3,4,5,6,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [5,1,6,7,2,8,3,4] => [8,2,7,5,4,6,3,1] => [[1,3,6],[2],[4],[5],[7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [5,6,1,7,2,8,3,4] => [8,7,3,5,4,6,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,6,7,1,2,8,3,4] => [8,7,5,4,3,6,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,1,6,7,8,2,3,4] => [8,2,7,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [5,6,1,7,8,2,3,4] => [8,7,3,6,5,4,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [8,7,6,4,5,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4,8] => [7,2,6,4,5,3,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [5,6,1,2,7,3,4,8] => [7,6,3,4,5,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4,8] => [7,6,3,5,4,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4,8] => [7,6,5,4,3,2,1,8] => [[1,8],[2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4,8] => [7,2,5,4,3,6,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4,8] => [7,2,3,5,4,6,1,8] => [[1,3,4,6,8],[2],[5],[7]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4,8] => [1,7,3,5,4,6,2,8] => [[1,2,4,6,8],[3],[5],[7]] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4,8] => [7,2,3,6,5,4,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4,8] => [1,7,3,6,5,4,2,8] => [[1,2,4,8],[3],[5],[6],[7]] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4,8] => [1,7,6,4,5,3,2,8] => [[1,2,5,8],[3],[4],[6],[7]] => 3
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4,8] => [1,7,6,5,4,3,2,8] => [[1,2,8],[3],[4],[5],[6],[7]] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => [8,2,5,4,3,6,7,1] => [[1,3,6,7],[2],[4],[5],[8]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [5,6,1,2,3,7,8,4] => [8,5,3,4,2,6,7,1] => [[1,4,6,7],[2],[3],[5],[8]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [5,1,2,6,3,7,8,4] => [8,2,3,5,4,6,7,1] => [[1,3,4,6,7],[2],[5],[8]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,5,2,6,3,7,8,4] => [1,8,3,5,4,6,7,2] => [[1,2,4,6,7],[3],[5],[8]] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,5,6,2,3,7,8,4] => [1,8,5,4,3,6,7,2] => [[1,2,6,7],[3],[4],[5],[8]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [5,1,2,6,7,3,8,4] => [8,2,3,6,5,4,7,1] => [[1,3,4,7],[2],[5],[6],[8]] => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,8,4] => [1,8,6,5,4,3,7,2] => [[1,2,7],[3],[4],[5],[6],[8]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [5,1,2,6,7,8,3,4] => [8,2,3,7,5,6,4,1] => [[1,3,4,6],[2],[5],[7],[8]] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,5,2,6,7,8,3,4] => [1,8,3,7,5,6,4,2] => [[1,2,4,6],[3],[5],[7],[8]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,5,6,2,7,8,3,4] => [1,8,7,4,5,6,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,5,6,7,2,8,3,4] => [1,8,7,5,4,6,3,2] => [[1,2,6],[3],[4],[5],[7],[8]] => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,5,6,7,8,2,3,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,6,2,8,3,4,7] => [7,2,6,4,8,3,1,5] => [[1,3,5],[2,8],[4],[6],[7]] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,6,1,2,8,3,4,7] => [7,6,3,4,8,2,1,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,6,1,8,2,3,4,7] => [7,6,3,8,5,2,1,4] => [[1,4],[2,5],[3,8],[6],[7]] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,6,8,1,2,3,4,7] => [7,6,8,4,5,2,1,3] => [[1,3],[2,5],[4,8],[6],[7]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,8,4,7] => [7,2,5,4,3,8,1,6] => [[1,3,6],[2,8],[4],[5],[7]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,8,4,7] => [7,5,3,4,2,8,1,6] => [[1,4,6],[2,8],[3],[5],[7]] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,8,4,7] => [7,2,3,5,4,8,1,6] => [[1,3,4,6],[2,8],[5],[7]] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,8,4,7] => [1,7,3,5,4,8,2,6] => [[1,2,4,6],[3,8],[5],[7]] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => [1,7,5,4,3,8,2,6] => [[1,2,6],[3,8],[4],[5],[7]] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,1,2,6,8,3,4,7] => [7,2,3,6,8,4,1,5] => [[1,3,4,5],[2,8],[6],[7]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,8,3,4,7] => [1,7,3,6,8,4,2,5] => [[1,2,4,5],[3,8],[6],[7]] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,6,2,8,3,4,7] => [1,7,6,4,8,3,2,5] => [[1,2,5],[3,8],[4],[6],[7]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,8,7] => [6,2,5,4,3,1,8,7] => [[1,3,7],[2,8],[4],[5],[6]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,8,7] => [6,5,3,4,2,1,8,7] => [[1,4,7],[2,8],[3],[5],[6]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,8,7] => [6,2,3,5,4,1,8,7] => [[1,3,4,7],[2,8],[5],[6]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,8,7] => [1,6,5,4,3,2,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [7,2,3,4,5,8,1,6] => [[1,3,4,5,6],[2,8],[7]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,8,4,7] => [1,7,3,4,5,8,2,6] => [[1,2,4,5,6],[3,8],[7]] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,8,4,7] => [1,2,7,5,4,8,3,6] => [[1,2,3,6],[4,8],[5],[7]] => 3
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,2,5,6,8,3,4,7] => [1,2,7,6,8,4,3,5] => [[1,2,3,5],[4,8],[6],[7]] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7,8] => [6,5,3,4,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7,8] => [6,2,3,5,4,1,7,8] => [[1,3,4,7,8],[2],[5],[6]] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7,8] => [1,6,3,5,4,2,7,8] => [[1,2,4,7,8],[3],[5],[6]] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7,8] => [1,6,5,4,3,2,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7,8] => [6,2,3,4,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7,8] => [1,6,3,4,5,2,7,8] => [[1,2,4,5,7,8],[3],[6]] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [1,2,6,5,4,3,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 5
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4,8] => [7,2,3,4,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4,8] => [1,7,3,4,5,6,2,8] => [[1,2,4,5,6,8],[3],[7]] => 3
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4,8] => [1,2,7,5,4,6,3,8] => [[1,2,3,6,8],[4],[5],[7]] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,6,7,8,4] => [8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,6,7,8,4] => [1,8,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3],[8]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,2,5,3,6,7,8,4] => [1,2,8,4,5,6,7,3] => [[1,2,3,5,6,7],[4],[8]] => 3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,2,5,6,3,7,8,4] => [1,2,8,5,4,6,7,3] => [[1,2,3,6,7],[4],[5],[8]] => 3
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,2,5,6,7,3,8,4] => [1,2,8,6,5,4,7,3] => [[1,2,3,7],[4],[5],[6],[8]] => 3
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,5,6,7,8,3,4] => [1,2,8,7,5,6,4,3] => [[1,2,3,6],[4],[5],[7],[8]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,7,2,8,3,4,6] => [7,2,8,4,6,5,1,3] => [[1,3,5],[2,4],[6,8],[7]] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,7,1,2,8,3,4,6] => [7,8,3,4,6,5,1,2] => [[1,2,5],[3,4],[6,8],[7]] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,1,7,8,2,3,4,6] => [7,2,8,6,5,4,1,3] => [[1,3],[2,4],[5,8],[6],[7]] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,7,1,8,2,3,4,6] => [7,8,3,6,5,4,1,2] => [[1,2],[3,4],[5,8],[6],[7]] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,7,8,1,2,3,4,6] => [7,8,6,4,5,3,1,2] => [[1,2],[3,5],[4,8],[6],[7]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,7,2,3,8,4,6] => [7,2,8,4,5,6,1,3] => [[1,3,5,6],[2,4],[7,8]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,7,1,2,3,8,4,6] => [7,8,3,4,5,6,1,2] => [[1,2,5,6],[3,4],[7,8]] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,7,3,8,4,6] => [7,2,3,8,5,6,1,4] => [[1,3,4,6],[2,5],[7,8]] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,7,3,8,4,6] => [1,7,3,8,5,6,2,4] => [[1,2,4,6],[3,5],[7,8]] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,5,7,2,3,8,4,6] => [1,7,8,4,5,6,2,3] => [[1,2,3,6],[4,5],[7,8]] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [1,7,8,4,6,5,2,3] => [[1,2,3],[4,5],[6,8],[7]] => 2
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,5,7,8,2,3,4,6] => [1,7,8,6,5,4,2,3] => [[1,2,3],[4,8],[5],[6],[7]] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,7,2,3,4,8,6] => [6,2,8,4,5,1,7,3] => [[1,3,5,7],[2,4],[6,8]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [6,8,3,4,5,1,7,2] => [[1,2,5,7],[3,4],[6,8]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,7,3,4,8,6] => [6,2,3,8,5,1,7,4] => [[1,3,4,7],[2,5],[6,8]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,7,3,4,8,6] => [1,6,3,8,5,2,7,4] => [[1,2,4,7],[3,5],[6,8]] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,5,7,2,3,4,8,6] => [1,6,8,4,5,2,7,3] => [[1,2,3,7],[4,5],[6,8]] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,7,4,8,6] => [1,6,3,4,8,2,7,5] => [[1,2,4,5],[3,7],[6,8]] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,7,4,8,6] => [1,2,6,4,8,3,7,5] => [[1,2,3,5],[4,7],[6,8]] => 3
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,8,6] => [1,2,6,8,5,3,7,4] => [[1,2,3,4],[5,7],[6,8]] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,7,8,4,6] => [7,2,3,4,8,6,1,5] => [[1,3,4,5],[2,6],[7,8]] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,8,4,6] => [1,7,3,4,8,6,2,5] => [[1,2,4,5],[3,6],[7,8]] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,7,8,4,6] => [1,2,7,4,8,6,3,5] => [[1,2,3,5],[4,6],[7,8]] => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,7,3,8,4,6] => [1,2,7,8,5,6,3,4] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,7,8,3,4,6] => [1,2,7,8,6,5,3,4] => [[1,2,3,4],[5,8],[6],[7]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6,8] => [6,2,7,4,5,1,3,8] => [[1,3,5,8],[2,4],[6,7]] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6,8] => [6,7,3,4,5,1,2,8] => [[1,2,5,8],[3,4],[6,7]] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6,8] => [6,2,3,7,5,1,4,8] => [[1,3,4,8],[2,5],[6,7]] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6,8] => [1,6,3,7,5,2,4,8] => [[1,2,4,8],[3,5],[6,7]] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6,8] => [1,6,7,4,5,2,3,8] => [[1,2,3,8],[4,5],[6,7]] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6,8] => [1,2,6,4,7,3,5,8] => [[1,2,3,5,8],[4,7],[6]] => 4
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [1,2,6,7,5,3,4,8] => [[1,2,3,4,8],[5,7],[6]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [[1,2,3,4,6,8],[5,7]] => 6
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6,8] => [1,2,3,6,7,4,5,8] => [[1,2,3,4,5,8],[6,7]] => 5
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,8,6] => [5,2,3,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,7,8,6] => [1,5,3,4,2,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,7,8,6] => [1,2,5,4,3,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 4
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => 5
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,7,4,8,6] => [1,2,3,6,8,4,7,5] => [[1,2,3,4,5],[6,7],[8]] => 4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,7,8,4,6] => [1,2,3,7,8,6,4,5] => [[1,2,3,4,5],[6,8],[7]] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,8,2,3,4,6,7] => [6,2,8,4,5,1,7,3] => [[1,3,5,7],[2,4],[6,8]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [5,8,1,2,3,4,6,7] => [6,8,3,4,5,1,7,2] => [[1,2,5,7],[3,4],[6,8]] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,8,3,4,6,7] => [6,2,3,8,5,1,7,4] => [[1,3,4,7],[2,5],[6,8]] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,5,2,8,3,4,6,7] => [1,6,3,8,5,2,7,4] => [[1,2,4,7],[3,5],[6,8]] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,5,8,2,3,4,6,7] => [1,6,8,4,5,2,7,3] => [[1,2,3,7],[4,5],[6,8]] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,5,2,3,8,4,6,7] => [1,6,3,4,8,2,7,5] => [[1,2,4,5],[3,7],[6,8]] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [1,2,6,4,8,3,7,5] => [[1,2,3,5],[4,7],[6,8]] => 3
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => [1,2,6,8,5,3,7,4] => [[1,2,3,4],[5,7],[6,8]] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [5,1,2,3,4,8,6,7] => [5,2,3,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [1,5,3,4,2,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,2,5,3,4,8,6,7] => [1,2,5,4,3,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 4
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => 5
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,5,8,4,6,7] => [1,2,3,6,8,4,7,5] => [[1,2,3,4,5],[6,7],[8]] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [5,2,3,4,1,6,8,7] => [[1,3,4,6,7],[2,8],[5]] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,8,7] => [1,2,5,4,3,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [[1,2,3,4,6,7],[5,8]] => 6
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,8,7] => [1,2,3,6,5,4,8,7] => [[1,2,3,4,7],[5,8],[6]] => 5
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,5,6,8,4,7] => [1,2,3,7,5,8,4,6] => [[1,2,3,4,6],[5,8],[7]] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8] => [5,2,3,4,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7,8] => [1,5,3,4,2,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7,8] => [1,2,5,4,3,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 7
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7,8] => [1,2,3,6,5,4,7,8] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4,8] => [1,2,3,7,5,6,4,8] => [[1,2,3,4,6,8],[5],[7]] => 5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => [[1,2,3,4,6,7],[5],[8]] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,7,2,8,3,4,5] => [8,2,7,4,6,5,3,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,7,1,2,8,3,4,5] => [8,7,3,4,6,5,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [6,1,7,8,2,3,4,5] => [8,2,7,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,7,1,8,2,3,4,5] => [8,7,3,6,5,4,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [8,7,6,4,5,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,7,2,3,8,4,5] => [8,2,7,4,5,6,3,1] => [[1,3,5,6],[2],[4],[7],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,7,1,2,3,8,4,5] => [8,7,3,4,5,6,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [6,1,2,7,3,8,4,5] => [8,2,3,7,5,6,4,1] => [[1,3,4,6],[2],[5],[7],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,6,2,7,3,8,4,5] => [1,8,3,7,5,6,4,2] => [[1,2,4,6],[3],[5],[7],[8]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,6,7,2,3,8,4,5] => [1,8,7,4,5,6,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [6,1,2,7,8,3,4,5] => [8,2,3,7,6,5,4,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,6,2,7,8,3,4,5] => [1,8,3,7,6,5,4,2] => [[1,2,4],[3],[5],[6],[7],[8]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,6,7,2,8,3,4,5] => [1,8,7,4,6,5,3,2] => [[1,2,5],[3],[4],[6],[7],[8]] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,7,2,3,4,8,5] => [8,2,6,4,5,3,7,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,7,1,2,3,4,8,5] => [8,6,3,4,5,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [6,1,2,7,3,4,8,5] => [8,2,3,6,5,4,7,1] => [[1,3,4,7],[2],[5],[6],[8]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,6,2,7,3,4,8,5] => [1,8,3,6,5,4,7,2] => [[1,2,4,7],[3],[5],[6],[8]] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,6,7,2,3,4,8,5] => [1,8,6,4,5,3,7,2] => [[1,2,5,7],[3],[4],[6],[8]] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,8,5] => [1,2,8,6,5,4,7,3] => [[1,2,3,7],[4],[5],[6],[8]] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [6,1,2,3,7,8,4,5] => [8,2,3,4,7,6,5,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,7,8,4,5] => [1,2,8,4,7,6,5,3] => [[1,2,3,5],[4],[6],[7],[8]] => 3
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,7,3,8,4,5] => [1,2,8,7,5,6,4,3] => [[1,2,3,6],[4],[5],[7],[8]] => 3
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,7,8,3,4,5] => [1,2,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5,8] => [7,2,6,4,5,3,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5,8] => [7,6,3,4,5,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5,8] => [7,2,3,6,5,4,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5,8] => [1,7,3,6,5,4,2,8] => [[1,2,4,8],[3],[5],[6],[7]] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5,8] => [1,7,6,4,5,3,2,8] => [[1,2,5,8],[3],[4],[6],[7]] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5,8] => [7,2,3,4,6,5,1,8] => [[1,3,4,5,8],[2],[6],[7]] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5,8] => [1,2,7,6,5,4,3,8] => [[1,2,3,8],[4],[5],[6],[7]] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5,8] => [7,2,3,4,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5,8] => [1,7,3,4,5,6,2,8] => [[1,2,4,5,6,8],[3],[7]] => 3
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5,8] => [1,2,3,7,5,6,4,8] => [[1,2,3,4,6,8],[5],[7]] => 5
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5,8] => [1,2,3,7,6,5,4,8] => [[1,2,3,4,8],[5],[6],[7]] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,8,5] => [8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,8,5] => [1,8,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3],[8]] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,7,8,5] => [1,2,8,4,5,6,7,3] => [[1,2,3,5,6,7],[4],[8]] => 3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,7,8,5] => [1,2,3,8,5,6,7,4] => [[1,2,3,4,6,7],[5],[8]] => 4
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,2,3,6,7,4,8,5] => [1,2,3,8,6,5,7,4] => [[1,2,3,4,7],[5],[6],[8]] => 4
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,2,3,6,7,8,4,5] => [1,2,3,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,8,2,3,4,5,7] => [7,2,8,4,5,6,1,3] => [[1,3,5,6],[2,4],[7,8]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,8,1,2,3,4,5,7] => [7,8,3,4,5,6,1,2] => [[1,2,5,6],[3,4],[7,8]] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,8,3,4,5,7] => [7,2,3,8,5,6,1,4] => [[1,3,4,6],[2,5],[7,8]] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,6,2,8,3,4,5,7] => [1,7,3,8,5,6,2,4] => [[1,2,4,6],[3,5],[7,8]] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,6,8,2,3,4,5,7] => [1,7,8,4,5,6,2,3] => [[1,2,3,6],[4,5],[7,8]] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,8,4,5,7] => [7,2,3,4,8,6,1,5] => [[1,3,4,5],[2,6],[7,8]] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,8,4,5,7] => [1,7,3,4,8,6,2,5] => [[1,2,4,5],[3,6],[7,8]] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => [1,2,7,4,8,6,3,5] => [[1,2,3,5],[4,6],[7,8]] => 3
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => [1,2,7,8,5,6,3,4] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,8,5,7] => [7,2,3,4,5,8,1,6] => [[1,3,4,5,6],[2,8],[7]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [1,7,3,4,5,8,2,6] => [[1,2,4,5,6],[3,8],[7]] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,8,5,7] => [1,2,7,4,5,8,3,6] => [[1,2,3,5,6],[4,8],[7]] => 3
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,8,5,7] => [1,2,3,7,5,8,4,6] => [[1,2,3,4,6],[5,8],[7]] => 4
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,8,4,5,7] => [1,2,3,7,8,6,4,5] => [[1,2,3,4,5],[6,8],[7]] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [6,2,3,4,5,1,8,7] => [[1,3,4,5,7],[2,8],[6]] => 2
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,8,7] => [1,2,3,6,5,4,8,7] => [[1,2,3,4,7],[5,8],[6]] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [[1,2,3,4,5,7],[6,8]] => 6
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7] => [1,2,3,4,7,8,5,6] => [[1,2,3,4,5,6],[7,8]] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8] => [6,2,3,4,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7,8] => [1,6,3,4,5,2,7,8] => [[1,2,4,5,7,8],[3],[6]] => 4
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [1,2,3,6,5,4,7,8] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]] => 7
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,6,5,8] => [[1,2,3,4,5,8],[6],[7]] => 6
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => [[1,2,3,4,5,7],[6],[8]] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,6] => [8,2,7,4,5,6,3,1] => [[1,3,5,6],[2],[4],[7],[8]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [8,7,3,4,5,6,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1,2,8,3,4,5,6] => [8,2,3,7,5,6,4,1] => [[1,3,4,6],[2],[5],[7],[8]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,7,2,8,3,4,5,6] => [1,8,3,7,5,6,4,2] => [[1,2,4,6],[3],[5],[7],[8]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,8,2,3,4,5,6] => [1,8,7,4,5,6,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1,2,3,8,4,5,6] => [8,2,3,4,7,6,5,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [1,2,8,4,7,6,5,3] => [[1,2,3,5],[4],[6],[7],[8]] => 3
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [1,2,8,7,5,6,4,3] => [[1,2,3,6],[4],[5],[7],[8]] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1,2,3,4,8,5,6] => [8,2,3,4,5,7,6,1] => [[1,3,4,5,6],[2],[7],[8]] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,3,7,4,8,5,6] => [1,2,3,8,5,7,6,4] => [[1,2,3,4,6],[5],[7],[8]] => 4
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,3,7,8,4,5,6] => [1,2,3,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => [1,8,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3],[8]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,2,7,3,4,5,8,6] => [1,2,8,4,5,6,7,3] => [[1,2,3,5,6,7],[4],[8]] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,2,3,7,4,5,8,6] => [1,2,3,8,5,6,7,4] => [[1,2,3,4,6,7],[5],[8]] => 4
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6] => [1,2,3,4,8,6,7,5] => [[1,2,3,4,5,7],[6],[8]] => 5
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,6] => [1,2,3,4,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => [7,2,3,4,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,8] => [1,7,3,4,5,6,2,8] => [[1,2,4,5,6,8],[3],[7]] => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [1,2,3,7,5,6,4,8] => [[1,2,3,4,6,8],[5],[7]] => 5
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6,8] => [1,2,3,4,7,6,5,8] => [[1,2,3,4,5,8],[6],[7]] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [[1,2,3,4,5,6,8],[7]] => 7
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,7] => [1,8,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3],[8]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,8,3,4,5,6,7] => [1,2,8,4,5,6,7,3] => [[1,2,3,5,6,7],[4],[8]] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [1,2,3,8,5,6,7,4] => [[1,2,3,4,6,7],[5],[8]] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,3,4,8,5,6,7] => [1,2,3,4,8,6,7,5] => [[1,2,3,4,5,7],[6],[8]] => 5
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,7,6] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 8
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,2,1 5,5,3,1 14,14,9,4,1 42,42,28,14,5,1 132,132,90,48,20,6,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 2\ q + 2\ q^{2} + q^{3}$
$F_{4} = 5\ q + 5\ q^{2} + 3\ q^{3} + q^{4}$
$F_{5} = 14\ q + 14\ q^{2} + 9\ q^{3} + 4\ q^{4} + q^{5}$
$F_{6} = 42\ q + 42\ q^{2} + 28\ q^{3} + 14\ q^{4} + 5\ q^{5} + q^{6}$
$F_{7} = 132\ q + 132\ q^{2} + 90\ q^{3} + 48\ q^{4} + 20\ q^{5} + 6\ q^{6} + q^{7}$
Description
The number of factors of a standard tableaux under concatenation.
The concatenation of two standard Young tableaux $T_1$ and $T_2$ is obtained by adding the largest entry of $T_1$ to each entry of $T_2$, and then appending the rows of the result to $T_1$, see [1, dfn 2.10].
This statistic returns the maximal number of standard tableaux such that their concatenation is the given tableau.
The concatenation of two standard Young tableaux $T_1$ and $T_2$ is obtained by adding the largest entry of $T_1$ to each entry of $T_2$, and then appending the rows of the result to $T_1$, see [1, dfn 2.10].
This statistic returns the maximal number of standard tableaux such that their concatenation is the given tableau.
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
Map
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
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