Identifier
-
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00106: Standard tableaux —catabolism⟶ Standard tableaux
St000507: Standard tableaux ⟶ ℤ
Values
[1,0] => [1] => [[1]] => [[1]] => 1
[1,0,1,0] => [1,2] => [[1,2]] => [[1,2]] => 2
[1,1,0,0] => [2,1] => [[1],[2]] => [[1,2]] => 2
[1,0,1,0,1,0] => [1,2,3] => [[1,2,3]] => [[1,2,3]] => 3
[1,0,1,1,0,0] => [1,3,2] => [[1,2],[3]] => [[1,2,3]] => 3
[1,1,0,0,1,0] => [2,1,3] => [[1,3],[2]] => [[1,2],[3]] => 2
[1,1,0,1,0,0] => [2,3,1] => [[1,2],[3]] => [[1,2,3]] => 3
[1,1,1,0,0,0] => [3,2,1] => [[1],[2],[3]] => [[1,2],[3]] => 2
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [[1,2,3,4]] => [[1,2,3,4]] => 4
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [[1,2,3],[4]] => [[1,2,3,4]] => 4
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [[1,2,4],[3]] => [[1,2,3],[4]] => 3
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [[1,2,3],[4]] => [[1,2,3,4]] => 4
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [[1,2],[3],[4]] => [[1,2,3],[4]] => 3
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [[1,3,4],[2]] => [[1,2,4],[3]] => 3
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [[1,3],[2,4]] => [[1,2,4],[3]] => 3
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [[1,2,4],[3]] => [[1,2,3],[4]] => 3
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [[1,2,3],[4]] => [[1,2,3,4]] => 4
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [[1,2],[3],[4]] => [[1,2,3],[4]] => 3
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [[1,4],[2],[3]] => [[1,2],[3],[4]] => 2
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [[1,3],[2],[4]] => [[1,2,4],[3]] => 3
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [[1,3],[2],[4]] => [[1,2,4],[3]] => 3
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [[1],[2],[3],[4]] => [[1,2],[3],[4]] => 2
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [[1,2,3,4,5]] => [[1,2,3,4,5]] => 5
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [[1,2,3,4],[5]] => [[1,2,3,4,5]] => 5
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [[1,2,3,5],[4]] => [[1,2,3,4],[5]] => 4
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [[1,2,3,4],[5]] => [[1,2,3,4,5]] => 5
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [[1,2,3],[4],[5]] => [[1,2,3,4],[5]] => 4
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [[1,2,4,5],[3]] => [[1,2,3,5],[4]] => 4
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [[1,2,4],[3,5]] => [[1,2,3,5],[4]] => 4
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [[1,2,3,5],[4]] => [[1,2,3,4],[5]] => 4
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [[1,2,3,4],[5]] => [[1,2,3,4,5]] => 5
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [[1,2,3],[4],[5]] => [[1,2,3,4],[5]] => 4
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [[1,2,5],[3],[4]] => [[1,2,3],[4],[5]] => 3
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [[1,2,4],[3],[5]] => [[1,2,3,5],[4]] => 4
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [[1,2,4],[3],[5]] => [[1,2,3,5],[4]] => 4
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => [[1,2,3],[4],[5]] => 3
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [[1,3,4,5],[2]] => [[1,2,4,5],[3]] => 4
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [[1,3,4],[2,5]] => [[1,2,4,5],[3]] => 4
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [[1,3,5],[2,4]] => [[1,2,4],[3,5]] => 3
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [[1,3,4],[2,5]] => [[1,2,4,5],[3]] => 4
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [[1,3],[2,4],[5]] => [[1,2,4],[3,5]] => 3
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [[1,2,4,5],[3]] => [[1,2,3,5],[4]] => 4
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [[1,2,4],[3,5]] => [[1,2,3,5],[4]] => 4
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [[1,2,3,5],[4]] => [[1,2,3,4],[5]] => 4
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [[1,2,3,4],[5]] => [[1,2,3,4,5]] => 5
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [[1,2,3],[4],[5]] => [[1,2,3,4],[5]] => 4
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [[1,2,5],[3],[4]] => [[1,2,3],[4],[5]] => 3
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [[1,2,4],[3],[5]] => [[1,2,3,5],[4]] => 4
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [[1,2,4],[3],[5]] => [[1,2,3,5],[4]] => 4
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [[1,2],[3],[4],[5]] => [[1,2,3],[4],[5]] => 3
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [[1,4,5],[2],[3]] => [[1,2,5],[3],[4]] => 3
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [[1,4],[2,5],[3]] => [[1,2,5],[3],[4]] => 3
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [[1,3,5],[2],[4]] => [[1,2,4],[3],[5]] => 3
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [[1,3,4],[2],[5]] => [[1,2,4,5],[3]] => 4
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [[1,3],[2,4],[5]] => [[1,2,4],[3,5]] => 3
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [[1,3,5],[2],[4]] => [[1,2,4],[3],[5]] => 3
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [[1,3,4],[2],[5]] => [[1,2,4,5],[3]] => 4
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [[1,3,4],[2],[5]] => [[1,2,4,5],[3]] => 4
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [[1,3],[2],[4],[5]] => [[1,2,4],[3],[5]] => 3
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [[1,5],[2],[3],[4]] => [[1,2],[3],[4],[5]] => 2
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [[1,4],[2],[3],[5]] => [[1,2,5],[3],[4]] => 3
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [[1,4],[2],[3],[5]] => [[1,2,5],[3],[4]] => 3
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [[1,3],[2],[4],[5]] => [[1,2,4],[3],[5]] => 3
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]] => [[1,2],[3],[4],[5]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => [[1,2,3,4,5,6]] => 6
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => [[1,2,3,4,5],[6]] => 5
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [[1,2,3,4,5],[6]] => [[1,2,3,4,5,6]] => 6
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [[1,2,3,4],[5],[6]] => [[1,2,3,4,5],[6]] => 5
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => [[1,2,3,4,6],[5]] => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [[1,2,3,5],[4,6]] => [[1,2,3,4,6],[5]] => 5
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [[1,2,3,4,6],[5]] => [[1,2,3,4,5],[6]] => 5
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [[1,2,3,4,5],[6]] => [[1,2,3,4,5,6]] => 6
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [[1,2,3,4],[5],[6]] => [[1,2,3,4,5],[6]] => 5
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [[1,2,3,6],[4],[5]] => [[1,2,3,4],[5],[6]] => 4
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [[1,2,3,5],[4],[6]] => [[1,2,3,4,6],[5]] => 5
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [[1,2,3,5],[4],[6]] => [[1,2,3,4,6],[5]] => 5
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [[1,2,3],[4],[5],[6]] => [[1,2,3,4],[5],[6]] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => [[1,2,3,5,6],[4]] => 5
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [[1,2,4,5],[3,6]] => [[1,2,3,5,6],[4]] => 5
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [[1,2,4,6],[3,5]] => [[1,2,3,5],[4,6]] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [[1,2,4,5],[3,6]] => [[1,2,3,5,6],[4]] => 5
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [[1,2,4],[3,5],[6]] => [[1,2,3,5],[4,6]] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [[1,2,3,5,6],[4]] => [[1,2,3,4,6],[5]] => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [[1,2,3,5],[4,6]] => [[1,2,3,4,6],[5]] => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [[1,2,3,4,6],[5]] => [[1,2,3,4,5],[6]] => 5
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [[1,2,3,4,5],[6]] => [[1,2,3,4,5,6]] => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [[1,2,3,4],[5],[6]] => [[1,2,3,4,5],[6]] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [[1,2,3,6],[4],[5]] => [[1,2,3,4],[5],[6]] => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [[1,2,3,5],[4],[6]] => [[1,2,3,4,6],[5]] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [[1,2,3,5],[4],[6]] => [[1,2,3,4,6],[5]] => 5
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [[1,2,3],[4],[5],[6]] => [[1,2,3,4],[5],[6]] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [[1,2,5,6],[3],[4]] => [[1,2,3,6],[4],[5]] => 4
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [[1,2,5],[3,6],[4]] => [[1,2,3,6],[4],[5]] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [[1,2,4,6],[3],[5]] => [[1,2,3,5],[4],[6]] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [[1,2,4,5],[3],[6]] => [[1,2,3,5,6],[4]] => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [[1,2,4],[3,5],[6]] => [[1,2,3,5],[4,6]] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [[1,2,4,6],[3],[5]] => [[1,2,3,5],[4],[6]] => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [[1,2,4,5],[3],[6]] => [[1,2,3,5,6],[4]] => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [[1,2,4,5],[3],[6]] => [[1,2,3,5,6],[4]] => 5
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [[1,2,4],[3],[5],[6]] => [[1,2,3,5],[4],[6]] => 4
>>> Load all 1815 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [[1,2,6],[3],[4],[5]] => [[1,2,3],[4],[5],[6]] => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [[1,2,5],[3],[4],[6]] => [[1,2,3,6],[4],[5]] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [[1,2,5],[3],[4],[6]] => [[1,2,3,6],[4],[5]] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [[1,2,4],[3],[5],[6]] => [[1,2,3,5],[4],[6]] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => [[1,2,3],[4],[5],[6]] => 3
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => [[1,2,4,5,6],[3]] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [[1,3,4,5],[2,6]] => [[1,2,4,5,6],[3]] => 5
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => [[1,2,4,5],[3,6]] => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [[1,3,4,5],[2,6]] => [[1,2,4,5,6],[3]] => 5
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [[1,3,4],[2,5],[6]] => [[1,2,4,5],[3,6]] => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => [[1,2,4,6],[3,5]] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => [[1,2,4,6],[3,5]] => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[1,3,4,6],[2,5]] => [[1,2,4,5],[3,6]] => 4
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [[1,3,4,5],[2,6]] => [[1,2,4,5,6],[3]] => 5
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [[1,3,4],[2,5],[6]] => [[1,2,4,5],[3,6]] => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [[1,3,6],[2,4],[5]] => [[1,2,4],[3,5],[6]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [[1,3,5],[2,4],[6]] => [[1,2,4,6],[3,5]] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [[1,3,5],[2,4],[6]] => [[1,2,4,6],[3,5]] => 4
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => [[1,2,4],[3,5],[6]] => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [[1,2,4,5,6],[3]] => [[1,2,3,5,6],[4]] => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [[1,2,4,5],[3,6]] => [[1,2,3,5,6],[4]] => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [[1,2,4,6],[3,5]] => [[1,2,3,5],[4,6]] => 4
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [[1,2,4,5],[3,6]] => [[1,2,3,5,6],[4]] => 5
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [[1,2,4],[3,5],[6]] => [[1,2,3,5],[4,6]] => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [[1,2,3,5,6],[4]] => [[1,2,3,4,6],[5]] => 5
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [[1,2,3,5],[4,6]] => [[1,2,3,4,6],[5]] => 5
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [[1,2,3,4,6],[5]] => [[1,2,3,4,5],[6]] => 5
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [[1,2,3,4,5],[6]] => [[1,2,3,4,5,6]] => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [[1,2,3,4],[5],[6]] => [[1,2,3,4,5],[6]] => 5
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [[1,2,3,6],[4],[5]] => [[1,2,3,4],[5],[6]] => 4
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [[1,2,3,5],[4],[6]] => [[1,2,3,4,6],[5]] => 5
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [[1,2,3,5],[4],[6]] => [[1,2,3,4,6],[5]] => 5
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [[1,2,3],[4],[5],[6]] => [[1,2,3,4],[5],[6]] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [[1,2,5,6],[3],[4]] => [[1,2,3,6],[4],[5]] => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [[1,2,5],[3,6],[4]] => [[1,2,3,6],[4],[5]] => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [[1,2,4,6],[3],[5]] => [[1,2,3,5],[4],[6]] => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [[1,2,4,5],[3],[6]] => [[1,2,3,5,6],[4]] => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [[1,2,4],[3,5],[6]] => [[1,2,3,5],[4,6]] => 4
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [[1,2,4,6],[3],[5]] => [[1,2,3,5],[4],[6]] => 4
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [[1,2,4,5],[3],[6]] => [[1,2,3,5,6],[4]] => 5
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [[1,2,4,5],[3],[6]] => [[1,2,3,5,6],[4]] => 5
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [[1,2,4],[3],[5],[6]] => [[1,2,3,5],[4],[6]] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [[1,2,6],[3],[4],[5]] => [[1,2,3],[4],[5],[6]] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [[1,2,5],[3],[4],[6]] => [[1,2,3,6],[4],[5]] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [[1,2,5],[3],[4],[6]] => [[1,2,3,6],[4],[5]] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [[1,2,4],[3],[5],[6]] => [[1,2,3,5],[4],[6]] => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => [[1,2,5,6],[3],[4]] => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [[1,4,5],[2,6],[3]] => [[1,2,5,6],[3],[4]] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [[1,4,6],[2,5],[3]] => [[1,2,5],[3,6],[4]] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [[1,4,5],[2,6],[3]] => [[1,2,5,6],[3],[4]] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => [[1,2,5],[3,6],[4]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [[1,3,5,6],[2],[4]] => [[1,2,4,6],[3],[5]] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [[1,3,5],[2,6],[4]] => [[1,2,4,6],[3],[5]] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [[1,3,4,6],[2],[5]] => [[1,2,4,5],[3],[6]] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [[1,3,4,5],[2],[6]] => [[1,2,4,5,6],[3]] => 5
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [[1,3,4],[2,5],[6]] => [[1,2,4,5],[3,6]] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [[1,3,6],[2,4],[5]] => [[1,2,4],[3,5],[6]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [[1,3,5],[2,4],[6]] => [[1,2,4,6],[3,5]] => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [[1,3,5],[2,4],[6]] => [[1,2,4,6],[3,5]] => 4
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [[1,3],[2,4],[5],[6]] => [[1,2,4],[3,5],[6]] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [[1,3,5,6],[2],[4]] => [[1,2,4,6],[3],[5]] => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [[1,3,5],[2,6],[4]] => [[1,2,4,6],[3],[5]] => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [[1,3,4,6],[2],[5]] => [[1,2,4,5],[3],[6]] => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [[1,3,4,5],[2],[6]] => [[1,2,4,5,6],[3]] => 5
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [[1,3,4],[2,5],[6]] => [[1,2,4,5],[3,6]] => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [[1,3,4,6],[2],[5]] => [[1,2,4,5],[3],[6]] => 4
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [[1,3,4,5],[2],[6]] => [[1,2,4,5,6],[3]] => 5
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => [[1,2,4,5,6],[3]] => 5
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [[1,3,4],[2],[5],[6]] => [[1,2,4,5],[3],[6]] => 4
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [[1,3,6],[2],[4],[5]] => [[1,2,4],[3],[5],[6]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [[1,3,5],[2],[4],[6]] => [[1,2,4,6],[3],[5]] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [[1,3,5],[2],[4],[6]] => [[1,2,4,6],[3],[5]] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [[1,3,4],[2],[5],[6]] => [[1,2,4,5],[3],[6]] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [[1,3],[2],[4],[5],[6]] => [[1,2,4],[3],[5],[6]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]] => [[1,2,6],[3],[4],[5]] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]] => [[1,2,6],[3],[4],[5]] => 3
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [[1,4,6],[2],[3],[5]] => [[1,2,5],[3],[4],[6]] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [[1,4,5],[2],[3],[6]] => [[1,2,5,6],[3],[4]] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [[1,4],[2,5],[3],[6]] => [[1,2,5],[3,6],[4]] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [[1,4,6],[2],[3],[5]] => [[1,2,5],[3],[4],[6]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [[1,4,5],[2],[3],[6]] => [[1,2,5,6],[3],[4]] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [[1,4,5],[2],[3],[6]] => [[1,2,5,6],[3],[4]] => 4
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [[1,4],[2,5],[3],[6]] => [[1,2,5],[3,6],[4]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [[1,3,6],[2],[4],[5]] => [[1,2,4],[3],[5],[6]] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [[1,3,5],[2],[4],[6]] => [[1,2,4,6],[3],[5]] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [[1,3,5],[2],[4],[6]] => [[1,2,4,6],[3],[5]] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [[1,3,4],[2],[5],[6]] => [[1,2,4,5],[3],[6]] => 4
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [[1,3],[2],[4],[5],[6]] => [[1,2,4],[3],[5],[6]] => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [[1,5],[2],[3],[4],[6]] => [[1,2,6],[3],[4],[5]] => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [[1,5],[2],[3],[4],[6]] => [[1,2,6],[3],[4],[5]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [[1,4],[2],[3],[5],[6]] => [[1,2,5],[3],[4],[6]] => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [[1,4],[2],[3],[5],[6]] => [[1,2,5],[3],[4],[6]] => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,6,7]] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => [[1,2,3,4,5,6],[7]] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,6,7]] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,5,6],[7]] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => [[1,2,3,4,5,7],[6]] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [[1,2,3,4,6],[5,7]] => [[1,2,3,4,5,7],[6]] => 6
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [[1,2,3,4,5,7],[6]] => [[1,2,3,4,5,6],[7]] => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,6,7]] => 7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,5,6],[7]] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,4,5],[6],[7]] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,4,5,7],[6]] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,4,5,7],[6]] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,4,5],[6],[7]] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => [[1,2,3,4,6,7],[5]] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]] => [[1,2,3,4,6,7],[5]] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [[1,2,3,5,7],[4,6]] => [[1,2,3,4,6],[5,7]] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [[1,2,3,5,6],[4,7]] => [[1,2,3,4,6,7],[5]] => 6
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [[1,2,3,5],[4,6],[7]] => [[1,2,3,4,6],[5,7]] => 5
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [[1,2,3,4,6,7],[5]] => [[1,2,3,4,5,7],[6]] => 6
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [[1,2,3,4,6],[5,7]] => [[1,2,3,4,5,7],[6]] => 6
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [[1,2,3,4,5,7],[6]] => [[1,2,3,4,5,6],[7]] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,6,7]] => 7
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,5,6],[7]] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,4,5],[6],[7]] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,4,5,7],[6]] => 6
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,4,5,7],[6]] => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,4,5],[6],[7]] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [[1,2,3,6,7],[4],[5]] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [[1,2,3,6],[4,7],[5]] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [[1,2,3,5,7],[4],[6]] => [[1,2,3,4,6],[5],[7]] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [[1,2,3,5,6],[4],[7]] => [[1,2,3,4,6,7],[5]] => 6
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [[1,2,3,5],[4,6],[7]] => [[1,2,3,4,6],[5,7]] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [[1,2,3,5,7],[4],[6]] => [[1,2,3,4,6],[5],[7]] => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [[1,2,3,5,6],[4],[7]] => [[1,2,3,4,6,7],[5]] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [[1,2,3,5,6],[4],[7]] => [[1,2,3,4,6,7],[5]] => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [[1,2,3,5],[4],[6],[7]] => [[1,2,3,4,6],[5],[7]] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [[1,2,3,7],[4],[5],[6]] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [[1,2,3,6],[4],[5],[7]] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [[1,2,3,6],[4],[5],[7]] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [[1,2,3,5],[4],[6],[7]] => [[1,2,3,4,6],[5],[7]] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => [[1,2,3,5,6,7],[4]] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]] => [[1,2,3,5,6,7],[4]] => 6
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [[1,2,4,5,7],[3,6]] => [[1,2,3,5,6],[4,7]] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [[1,2,4,5,6],[3,7]] => [[1,2,3,5,6,7],[4]] => 6
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [[1,2,4,5],[3,6],[7]] => [[1,2,3,5,6],[4,7]] => 5
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [[1,2,4,6,7],[3,5]] => [[1,2,3,5,7],[4,6]] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [[1,2,4,6],[3,5,7]] => [[1,2,3,5,7],[4,6]] => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [[1,2,4,5,7],[3,6]] => [[1,2,3,5,6],[4,7]] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [[1,2,4,5,6],[3,7]] => [[1,2,3,5,6,7],[4]] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [[1,2,4,5],[3,6],[7]] => [[1,2,3,5,6],[4,7]] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [[1,2,4,7],[3,5],[6]] => [[1,2,3,5],[4,6],[7]] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [[1,2,4,6],[3,5],[7]] => [[1,2,3,5,7],[4,6]] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [[1,2,4,6],[3,5],[7]] => [[1,2,3,5,7],[4,6]] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [[1,2,4],[3,5],[6],[7]] => [[1,2,3,5],[4,6],[7]] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [[1,2,3,5,6,7],[4]] => [[1,2,3,4,6,7],[5]] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [[1,2,3,5,6],[4,7]] => [[1,2,3,4,6,7],[5]] => 6
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [[1,2,3,5,7],[4,6]] => [[1,2,3,4,6],[5,7]] => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [[1,2,3,5,6],[4,7]] => [[1,2,3,4,6,7],[5]] => 6
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [[1,2,3,5],[4,6],[7]] => [[1,2,3,4,6],[5,7]] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [[1,2,3,4,6,7],[5]] => [[1,2,3,4,5,7],[6]] => 6
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [[1,2,3,4,6],[5,7]] => [[1,2,3,4,5,7],[6]] => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [[1,2,3,4,5,7],[6]] => [[1,2,3,4,5,6],[7]] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,6,7]] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,5,6],[7]] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,4,5],[6],[7]] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,4,5,7],[6]] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,4,5,7],[6]] => 6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,4,5],[6],[7]] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [[1,2,3,6,7],[4],[5]] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [[1,2,3,6],[4,7],[5]] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [[1,2,3,5,7],[4],[6]] => [[1,2,3,4,6],[5],[7]] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [[1,2,3,5,6],[4],[7]] => [[1,2,3,4,6,7],[5]] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [[1,2,3,5],[4,6],[7]] => [[1,2,3,4,6],[5,7]] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [[1,2,3,5,7],[4],[6]] => [[1,2,3,4,6],[5],[7]] => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [[1,2,3,5,6],[4],[7]] => [[1,2,3,4,6,7],[5]] => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [[1,2,3,5,6],[4],[7]] => [[1,2,3,4,6,7],[5]] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [[1,2,3,5],[4],[6],[7]] => [[1,2,3,4,6],[5],[7]] => 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [[1,2,3,7],[4],[5],[6]] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [[1,2,3,6],[4],[5],[7]] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [[1,2,3,6],[4],[5],[7]] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [[1,2,3,5],[4],[6],[7]] => [[1,2,3,4,6],[5],[7]] => 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [[1,2,5,6,7],[3],[4]] => [[1,2,3,6,7],[4],[5]] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [[1,2,5,6],[3,7],[4]] => [[1,2,3,6,7],[4],[5]] => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [[1,2,5,7],[3,6],[4]] => [[1,2,3,6],[4,7],[5]] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [[1,2,5,6],[3,7],[4]] => [[1,2,3,6,7],[4],[5]] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [[1,2,5],[3,6],[4,7]] => [[1,2,3,6],[4,7],[5]] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [[1,2,4,6,7],[3],[5]] => [[1,2,3,5,7],[4],[6]] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [[1,2,4,6],[3,7],[5]] => [[1,2,3,5,7],[4],[6]] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [[1,2,4,5,7],[3],[6]] => [[1,2,3,5,6],[4],[7]] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [[1,2,4,5,6],[3],[7]] => [[1,2,3,5,6,7],[4]] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [[1,2,4,5],[3,6],[7]] => [[1,2,3,5,6],[4,7]] => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [[1,2,4,7],[3,5],[6]] => [[1,2,3,5],[4,6],[7]] => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [[1,2,4,6],[3,5],[7]] => [[1,2,3,5,7],[4,6]] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [[1,2,4,6],[3,5],[7]] => [[1,2,3,5,7],[4,6]] => 5
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [[1,2,4],[3,5],[6],[7]] => [[1,2,3,5],[4,6],[7]] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [[1,2,4,6,7],[3],[5]] => [[1,2,3,5,7],[4],[6]] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [[1,2,4,6],[3,7],[5]] => [[1,2,3,5,7],[4],[6]] => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [[1,2,4,5,7],[3],[6]] => [[1,2,3,5,6],[4],[7]] => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [[1,2,4,5,6],[3],[7]] => [[1,2,3,5,6,7],[4]] => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [[1,2,4,5],[3,6],[7]] => [[1,2,3,5,6],[4,7]] => 5
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [[1,2,4,5,7],[3],[6]] => [[1,2,3,5,6],[4],[7]] => 5
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [[1,2,4,5,6],[3],[7]] => [[1,2,3,5,6,7],[4]] => 6
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [[1,2,4,5,6],[3],[7]] => [[1,2,3,5,6,7],[4]] => 6
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [[1,2,4,5],[3],[6],[7]] => [[1,2,3,5,6],[4],[7]] => 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [[1,2,4,7],[3],[5],[6]] => [[1,2,3,5],[4],[6],[7]] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [[1,2,4,6],[3],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 5
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [[1,2,4,6],[3],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 5
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [[1,2,4,5],[3],[6],[7]] => [[1,2,3,5,6],[4],[7]] => 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [[1,2,4],[3],[5],[6],[7]] => [[1,2,3,5],[4],[6],[7]] => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [[1,2,6,7],[3],[4],[5]] => [[1,2,3,7],[4],[5],[6]] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [[1,2,6],[3,7],[4],[5]] => [[1,2,3,7],[4],[5],[6]] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [[1,2,5,7],[3],[4],[6]] => [[1,2,3,6],[4],[5],[7]] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [[1,2,5,6],[3],[4],[7]] => [[1,2,3,6,7],[4],[5]] => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [[1,2,5],[3,6],[4],[7]] => [[1,2,3,6],[4,7],[5]] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [[1,2,5,7],[3],[4],[6]] => [[1,2,3,6],[4],[5],[7]] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [[1,2,5,6],[3],[4],[7]] => [[1,2,3,6,7],[4],[5]] => 5
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [[1,2,5,6],[3],[4],[7]] => [[1,2,3,6,7],[4],[5]] => 5
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [[1,2,5],[3,6],[4],[7]] => [[1,2,3,6],[4,7],[5]] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [[1,2,4,7],[3],[5],[6]] => [[1,2,3,5],[4],[6],[7]] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [[1,2,4,6],[3],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 5
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [[1,2,4,6],[3],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 5
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [[1,2,4,5],[3],[6],[7]] => [[1,2,3,5,6],[4],[7]] => 5
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [[1,2,4],[3],[5],[6],[7]] => [[1,2,3,5],[4],[6],[7]] => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [[1,2,7],[3],[4],[5],[6]] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [[1,2,6],[3],[4],[5],[7]] => [[1,2,3,7],[4],[5],[6]] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [[1,2,6],[3],[4],[5],[7]] => [[1,2,3,7],[4],[5],[6]] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [[1,2,5],[3],[4],[6],[7]] => [[1,2,3,6],[4],[5],[7]] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [[1,2,5],[3],[4],[6],[7]] => [[1,2,3,6],[4],[5],[7]] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]] => [[1,2,4,5,6,7],[3]] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]] => [[1,2,4,5,6,7],[3]] => 6
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [[1,3,4,5,7],[2,6]] => [[1,2,4,5,6],[3,7]] => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [[1,3,4,5,6],[2,7]] => [[1,2,4,5,6,7],[3]] => 6
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [[1,3,4,5],[2,6],[7]] => [[1,2,4,5,6],[3,7]] => 5
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [[1,3,4,6,7],[2,5]] => [[1,2,4,5,7],[3,6]] => 5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [[1,3,4,6],[2,5,7]] => [[1,2,4,5,7],[3,6]] => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [[1,3,4,5,7],[2,6]] => [[1,2,4,5,6],[3,7]] => 5
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [[1,3,4,5,6],[2,7]] => [[1,2,4,5,6,7],[3]] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [[1,3,4,5],[2,6],[7]] => [[1,2,4,5,6],[3,7]] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [[1,3,4,7],[2,5],[6]] => [[1,2,4,5],[3,6],[7]] => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [[1,3,4,6],[2,5],[7]] => [[1,2,4,5,7],[3,6]] => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [[1,3,4,6],[2,5],[7]] => [[1,2,4,5,7],[3,6]] => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [[1,3,4],[2,5],[6],[7]] => [[1,2,4,5],[3,6],[7]] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[1,3,5,6,7],[2,4]] => [[1,2,4,6,7],[3,5]] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [[1,3,5,6],[2,4,7]] => [[1,2,4,6,7],[3,5]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [[1,3,5,7],[2,4,6]] => [[1,2,4,6],[3,5,7]] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [[1,3,5,6],[2,4,7]] => [[1,2,4,6,7],[3,5]] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [[1,3,5],[2,4,6],[7]] => [[1,2,4,6],[3,5,7]] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [[1,3,4,6,7],[2,5]] => [[1,2,4,5,7],[3,6]] => 5
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [[1,3,4,6],[2,5,7]] => [[1,2,4,5,7],[3,6]] => 5
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [[1,3,4,5,7],[2,6]] => [[1,2,4,5,6],[3,7]] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [[1,3,4,5,6],[2,7]] => [[1,2,4,5,6,7],[3]] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [[1,3,4,5],[2,6],[7]] => [[1,2,4,5,6],[3,7]] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [[1,3,4,7],[2,5],[6]] => [[1,2,4,5],[3,6],[7]] => 4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [[1,3,4,6],[2,5],[7]] => [[1,2,4,5,7],[3,6]] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [[1,3,4,6],[2,5],[7]] => [[1,2,4,5,7],[3,6]] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [[1,3,4],[2,5],[6],[7]] => [[1,2,4,5],[3,6],[7]] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [[1,3,6,7],[2,4],[5]] => [[1,2,4,7],[3,5],[6]] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [[1,3,6],[2,4,7],[5]] => [[1,2,4,7],[3,5],[6]] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [[1,3,5,7],[2,4],[6]] => [[1,2,4,6],[3,5],[7]] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [[1,3,5,6],[2,4],[7]] => [[1,2,4,6,7],[3,5]] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [[1,3,5],[2,4,6],[7]] => [[1,2,4,6],[3,5,7]] => 4
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [[1,3,5,7],[2,4],[6]] => [[1,2,4,6],[3,5],[7]] => 4
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [[1,3,5,6],[2,4],[7]] => [[1,2,4,6,7],[3,5]] => 5
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [[1,3,5,6],[2,4],[7]] => [[1,2,4,6,7],[3,5]] => 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [[1,3,5],[2,4],[6],[7]] => [[1,2,4,6],[3,5],[7]] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [[1,3,7],[2,4],[5],[6]] => [[1,2,4],[3,5],[6],[7]] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [[1,3,6],[2,4],[5],[7]] => [[1,2,4,7],[3,5],[6]] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [[1,3,6],[2,4],[5],[7]] => [[1,2,4,7],[3,5],[6]] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [[1,3,5],[2,4],[6],[7]] => [[1,2,4,6],[3,5],[7]] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => [[1,2,4],[3,5],[6],[7]] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [[1,2,4,5,6,7],[3]] => [[1,2,3,5,6,7],[4]] => 6
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [[1,2,4,5,6],[3,7]] => [[1,2,3,5,6,7],[4]] => 6
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [[1,2,4,5,7],[3,6]] => [[1,2,3,5,6],[4,7]] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [[1,2,4,5,6],[3,7]] => [[1,2,3,5,6,7],[4]] => 6
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [[1,2,4,5],[3,6],[7]] => [[1,2,3,5,6],[4,7]] => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [[1,2,4,6,7],[3,5]] => [[1,2,3,5,7],[4,6]] => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [[1,2,4,6],[3,5,7]] => [[1,2,3,5,7],[4,6]] => 5
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [[1,2,4,5,7],[3,6]] => [[1,2,3,5,6],[4,7]] => 5
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [[1,2,4,5,6],[3,7]] => [[1,2,3,5,6,7],[4]] => 6
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [[1,2,4,5],[3,6],[7]] => [[1,2,3,5,6],[4,7]] => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [[1,2,4,7],[3,5],[6]] => [[1,2,3,5],[4,6],[7]] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [[1,2,4,6],[3,5],[7]] => [[1,2,3,5,7],[4,6]] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [[1,2,4,6],[3,5],[7]] => [[1,2,3,5,7],[4,6]] => 5
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [[1,2,4],[3,5],[6],[7]] => [[1,2,3,5],[4,6],[7]] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [[1,2,3,5,6,7],[4]] => [[1,2,3,4,6,7],[5]] => 6
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [[1,2,3,5,6],[4,7]] => [[1,2,3,4,6,7],[5]] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [[1,2,3,5,7],[4,6]] => [[1,2,3,4,6],[5,7]] => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [[1,2,3,5,6],[4,7]] => [[1,2,3,4,6,7],[5]] => 6
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [[1,2,3,5],[4,6],[7]] => [[1,2,3,4,6],[5,7]] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [[1,2,3,4,6,7],[5]] => [[1,2,3,4,5,7],[6]] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [[1,2,3,4,6],[5,7]] => [[1,2,3,4,5,7],[6]] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [[1,2,3,4,5,7],[6]] => [[1,2,3,4,5,6],[7]] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,6,7]] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,5,6],[7]] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,4,5,7],[6]] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,4,5,7],[6]] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [[1,2,3,6,7],[4],[5]] => [[1,2,3,4,7],[5],[6]] => 5
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [[1,2,3,6],[4,7],[5]] => [[1,2,3,4,7],[5],[6]] => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [[1,2,3,5,7],[4],[6]] => [[1,2,3,4,6],[5],[7]] => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [[1,2,3,5,6],[4],[7]] => [[1,2,3,4,6,7],[5]] => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [[1,2,3,5],[4,6],[7]] => [[1,2,3,4,6],[5,7]] => 5
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [[1,2,3,5,7],[4],[6]] => [[1,2,3,4,6],[5],[7]] => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [[1,2,3,5,6],[4],[7]] => [[1,2,3,4,6,7],[5]] => 6
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [[1,2,3,5,6],[4],[7]] => [[1,2,3,4,6,7],[5]] => 6
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [[1,2,3,5],[4],[6],[7]] => [[1,2,3,4,6],[5],[7]] => 5
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [[1,2,3,7],[4],[5],[6]] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [[1,2,3,6],[4],[5],[7]] => [[1,2,3,4,7],[5],[6]] => 5
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [[1,2,3,6],[4],[5],[7]] => [[1,2,3,4,7],[5],[6]] => 5
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [[1,2,3,5],[4],[6],[7]] => [[1,2,3,4,6],[5],[7]] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [[1,2,5,6,7],[3],[4]] => [[1,2,3,6,7],[4],[5]] => 5
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [[1,2,5,6],[3,7],[4]] => [[1,2,3,6,7],[4],[5]] => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [[1,2,5,7],[3,6],[4]] => [[1,2,3,6],[4,7],[5]] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [[1,2,5,6],[3,7],[4]] => [[1,2,3,6,7],[4],[5]] => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [[1,2,5],[3,6],[4,7]] => [[1,2,3,6],[4,7],[5]] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [[1,2,4,6,7],[3],[5]] => [[1,2,3,5,7],[4],[6]] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [[1,2,4,6],[3,7],[5]] => [[1,2,3,5,7],[4],[6]] => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [[1,2,4,5,7],[3],[6]] => [[1,2,3,5,6],[4],[7]] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [[1,2,4,5,6],[3],[7]] => [[1,2,3,5,6,7],[4]] => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [[1,2,4,5],[3,6],[7]] => [[1,2,3,5,6],[4,7]] => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [[1,2,4,7],[3,5],[6]] => [[1,2,3,5],[4,6],[7]] => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [[1,2,4,6],[3,5],[7]] => [[1,2,3,5,7],[4,6]] => 5
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [[1,2,4,6],[3,5],[7]] => [[1,2,3,5,7],[4,6]] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [[1,2,4],[3,5],[6],[7]] => [[1,2,3,5],[4,6],[7]] => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [[1,2,4,6,7],[3],[5]] => [[1,2,3,5,7],[4],[6]] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [[1,2,4,6],[3,7],[5]] => [[1,2,3,5,7],[4],[6]] => 5
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [[1,2,4,5,7],[3],[6]] => [[1,2,3,5,6],[4],[7]] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [[1,2,4,5,6],[3],[7]] => [[1,2,3,5,6,7],[4]] => 6
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [[1,2,4,5],[3,6],[7]] => [[1,2,3,5,6],[4,7]] => 5
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [[1,2,4,5,7],[3],[6]] => [[1,2,3,5,6],[4],[7]] => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [[1,2,4,5,6],[3],[7]] => [[1,2,3,5,6,7],[4]] => 6
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [[1,2,4,5,6],[3],[7]] => [[1,2,3,5,6,7],[4]] => 6
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [[1,2,4,5],[3],[6],[7]] => [[1,2,3,5,6],[4],[7]] => 5
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [[1,2,4,7],[3],[5],[6]] => [[1,2,3,5],[4],[6],[7]] => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [[1,2,4,6],[3],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 5
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [[1,2,4,6],[3],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 5
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [[1,2,4,5],[3],[6],[7]] => [[1,2,3,5,6],[4],[7]] => 5
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [[1,2,4],[3],[5],[6],[7]] => [[1,2,3,5],[4],[6],[7]] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [[1,2,6,7],[3],[4],[5]] => [[1,2,3,7],[4],[5],[6]] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [[1,2,6],[3,7],[4],[5]] => [[1,2,3,7],[4],[5],[6]] => 4
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [[1,2,5,7],[3],[4],[6]] => [[1,2,3,6],[4],[5],[7]] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [[1,2,5,6],[3],[4],[7]] => [[1,2,3,6,7],[4],[5]] => 5
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [[1,2,5],[3,6],[4],[7]] => [[1,2,3,6],[4,7],[5]] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [[1,2,5,7],[3],[4],[6]] => [[1,2,3,6],[4],[5],[7]] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [[1,2,5,6],[3],[4],[7]] => [[1,2,3,6,7],[4],[5]] => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [[1,2,5,6],[3],[4],[7]] => [[1,2,3,6,7],[4],[5]] => 5
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [[1,2,5],[3,6],[4],[7]] => [[1,2,3,6],[4,7],[5]] => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [[1,2,4,7],[3],[5],[6]] => [[1,2,3,5],[4],[6],[7]] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [[1,2,4,6],[3],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 5
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [[1,2,4,6],[3],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 5
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [[1,2,4,5],[3],[6],[7]] => [[1,2,3,5,6],[4],[7]] => 5
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [[1,2,4],[3],[5],[6],[7]] => [[1,2,3,5],[4],[6],[7]] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [[1,2,7],[3],[4],[5],[6]] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [[1,2,6],[3],[4],[5],[7]] => [[1,2,3,7],[4],[5],[6]] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [[1,2,6],[3],[4],[5],[7]] => [[1,2,3,7],[4],[5],[6]] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [[1,2,5],[3],[4],[6],[7]] => [[1,2,3,6],[4],[5],[7]] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [[1,2,5],[3],[4],[6],[7]] => [[1,2,3,6],[4],[5],[7]] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]] => [[1,2,5,6,7],[3],[4]] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [[1,4,5,6],[2,7],[3]] => [[1,2,5,6,7],[3],[4]] => 5
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [[1,4,5,7],[2,6],[3]] => [[1,2,5,6],[3,7],[4]] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [[1,4,5,6],[2,7],[3]] => [[1,2,5,6,7],[3],[4]] => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [[1,4,5],[2,6],[3,7]] => [[1,2,5,6],[3,7],[4]] => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [[1,4,6,7],[2,5],[3]] => [[1,2,5,7],[3,6],[4]] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [[1,4,6],[2,5,7],[3]] => [[1,2,5,7],[3,6],[4]] => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [[1,4,5,7],[2,6],[3]] => [[1,2,5,6],[3,7],[4]] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [[1,4,5,6],[2,7],[3]] => [[1,2,5,6,7],[3],[4]] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [[1,4,5],[2,6],[3,7]] => [[1,2,5,6],[3,7],[4]] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [[1,4,7],[2,5],[3,6]] => [[1,2,5],[3,6],[4,7]] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [[1,4,6],[2,5],[3,7]] => [[1,2,5,7],[3,6],[4]] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [[1,4,6],[2,5],[3,7]] => [[1,2,5,7],[3,6],[4]] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => [[1,2,5],[3,6],[4,7]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => [[1,2,4,6,7],[3],[5]] => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [[1,3,5,6],[2,7],[4]] => [[1,2,4,6,7],[3],[5]] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [[1,3,5,7],[2,6],[4]] => [[1,2,4,6],[3,7],[5]] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [[1,3,5,6],[2,7],[4]] => [[1,2,4,6,7],[3],[5]] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => [[1,2,4,6],[3,7],[5]] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => [[1,2,4,5,7],[3],[6]] => 5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [[1,3,4,6],[2,7],[5]] => [[1,2,4,5,7],[3],[6]] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => [[1,2,4,5,6],[3],[7]] => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => [[1,2,4,5,6,7],[3]] => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [[1,3,4,5],[2,6],[7]] => [[1,2,4,5,6],[3,7]] => 5
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [[1,3,4,7],[2,5],[6]] => [[1,2,4,5],[3,6],[7]] => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [[1,3,4,6],[2,5],[7]] => [[1,2,4,5,7],[3,6]] => 5
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [[1,3,4,6],[2,5],[7]] => [[1,2,4,5,7],[3,6]] => 5
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [[1,3,4],[2,5],[6],[7]] => [[1,2,4,5],[3,6],[7]] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [[1,3,6,7],[2,4],[5]] => [[1,2,4,7],[3,5],[6]] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [[1,3,6],[2,4,7],[5]] => [[1,2,4,7],[3,5],[6]] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [[1,3,5,7],[2,4],[6]] => [[1,2,4,6],[3,5],[7]] => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [[1,3,5,6],[2,4],[7]] => [[1,2,4,6,7],[3,5]] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [[1,3,5],[2,4,6],[7]] => [[1,2,4,6],[3,5,7]] => 4
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [[1,3,5,7],[2,4],[6]] => [[1,2,4,6],[3,5],[7]] => 4
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [[1,3,5,6],[2,4],[7]] => [[1,2,4,6,7],[3,5]] => 5
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [[1,3,5,6],[2,4],[7]] => [[1,2,4,6,7],[3,5]] => 5
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [[1,3,5],[2,4],[6],[7]] => [[1,2,4,6],[3,5],[7]] => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [[1,3,7],[2,4],[5],[6]] => [[1,2,4],[3,5],[6],[7]] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [[1,3,6],[2,4],[5],[7]] => [[1,2,4,7],[3,5],[6]] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [[1,3,6],[2,4],[5],[7]] => [[1,2,4,7],[3,5],[6]] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [[1,3,5],[2,4],[6],[7]] => [[1,2,4,6],[3,5],[7]] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => [[1,2,4],[3,5],[6],[7]] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => [[1,2,4,6,7],[3],[5]] => 5
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [[1,3,5,6],[2,7],[4]] => [[1,2,4,6,7],[3],[5]] => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [[1,3,5,7],[2,6],[4]] => [[1,2,4,6],[3,7],[5]] => 4
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [[1,3,5,6],[2,7],[4]] => [[1,2,4,6,7],[3],[5]] => 5
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => [[1,2,4,6],[3,7],[5]] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => [[1,2,4,5,7],[3],[6]] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [[1,3,4,6],[2,7],[5]] => [[1,2,4,5,7],[3],[6]] => 5
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => [[1,2,4,5,6],[3],[7]] => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => [[1,2,4,5,6,7],[3]] => 6
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [[1,3,4,5],[2,6],[7]] => [[1,2,4,5,6],[3,7]] => 5
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [[1,3,4,7],[2,5],[6]] => [[1,2,4,5],[3,6],[7]] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [[1,3,4,6],[2,5],[7]] => [[1,2,4,5,7],[3,6]] => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [[1,3,4,6],[2,5],[7]] => [[1,2,4,5,7],[3,6]] => 5
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [[1,3,4],[2,5],[6],[7]] => [[1,2,4,5],[3,6],[7]] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [[1,3,4,6,7],[2],[5]] => [[1,2,4,5,7],[3],[6]] => 5
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [[1,3,4,6],[2,7],[5]] => [[1,2,4,5,7],[3],[6]] => 5
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [[1,3,4,5,7],[2],[6]] => [[1,2,4,5,6],[3],[7]] => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [[1,3,4,5,6],[2],[7]] => [[1,2,4,5,6,7],[3]] => 6
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [[1,3,4,5],[2,6],[7]] => [[1,2,4,5,6],[3,7]] => 5
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [[1,3,4,5,7],[2],[6]] => [[1,2,4,5,6],[3],[7]] => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [[1,3,4,5,6],[2],[7]] => [[1,2,4,5,6,7],[3]] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => [[1,2,4,5,6,7],[3]] => 6
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [[1,3,4,5],[2],[6],[7]] => [[1,2,4,5,6],[3],[7]] => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [[1,3,4,7],[2],[5],[6]] => [[1,2,4,5],[3],[6],[7]] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [[1,3,4,6],[2],[5],[7]] => [[1,2,4,5,7],[3],[6]] => 5
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [[1,3,4,6],[2],[5],[7]] => [[1,2,4,5,7],[3],[6]] => 5
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [[1,3,4,5],[2],[6],[7]] => [[1,2,4,5,6],[3],[7]] => 5
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [[1,3,4],[2],[5],[6],[7]] => [[1,2,4,5],[3],[6],[7]] => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [[1,3,6,7],[2],[4],[5]] => [[1,2,4,7],[3],[5],[6]] => 4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [[1,3,6],[2,7],[4],[5]] => [[1,2,4,7],[3],[5],[6]] => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [[1,3,5,7],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7]] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [[1,3,5,6],[2],[4],[7]] => [[1,2,4,6,7],[3],[5]] => 5
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [[1,3,5],[2,6],[4],[7]] => [[1,2,4,6],[3,7],[5]] => 4
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [[1,3,5,7],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7]] => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [[1,3,5,6],[2],[4],[7]] => [[1,2,4,6,7],[3],[5]] => 5
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [[1,3,5,6],[2],[4],[7]] => [[1,2,4,6,7],[3],[5]] => 5
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [[1,3,5],[2,6],[4],[7]] => [[1,2,4,6],[3,7],[5]] => 4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [[1,3,4,7],[2],[5],[6]] => [[1,2,4,5],[3],[6],[7]] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [[1,3,4,6],[2],[5],[7]] => [[1,2,4,5,7],[3],[6]] => 5
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [[1,3,4,6],[2],[5],[7]] => [[1,2,4,5,7],[3],[6]] => 5
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [[1,3,4,5],[2],[6],[7]] => [[1,2,4,5,6],[3],[7]] => 5
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [[1,3,4],[2],[5],[6],[7]] => [[1,2,4,5],[3],[6],[7]] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [[1,3,7],[2],[4],[5],[6]] => [[1,2,4],[3],[5],[6],[7]] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [[1,3,6],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6]] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [[1,3,6],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6]] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [[1,3,5],[2],[4],[6],[7]] => [[1,2,4,6],[3],[5],[7]] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [[1,3,5],[2],[4],[6],[7]] => [[1,2,4,6],[3],[5],[7]] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7]] => [[1,2,4],[3],[5],[6],[7]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [[1,5,6,7],[2],[3],[4]] => [[1,2,6,7],[3],[4],[5]] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [[1,5,6],[2,7],[3],[4]] => [[1,2,6,7],[3],[4],[5]] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [[1,5,7],[2,6],[3],[4]] => [[1,2,6],[3,7],[4],[5]] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [[1,5,6],[2,7],[3],[4]] => [[1,2,6,7],[3],[4],[5]] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]] => [[1,2,6],[3,7],[4],[5]] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [[1,4,6,7],[2],[3],[5]] => [[1,2,5,7],[3],[4],[6]] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [[1,4,6],[2,7],[3],[5]] => [[1,2,5,7],[3],[4],[6]] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [[1,4,5,7],[2],[3],[6]] => [[1,2,5,6],[3],[4],[7]] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [[1,4,5,6],[2],[3],[7]] => [[1,2,5,6,7],[3],[4]] => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [[1,4,5],[2,6],[3],[7]] => [[1,2,5,6],[3,7],[4]] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [[1,4,7],[2,5],[3],[6]] => [[1,2,5],[3,6],[4],[7]] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [[1,4,6],[2,5],[3],[7]] => [[1,2,5,7],[3,6],[4]] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [[1,4,6],[2,5],[3],[7]] => [[1,2,5,7],[3,6],[4]] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [[1,4],[2,5],[3,6],[7]] => [[1,2,5],[3,6],[4,7]] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [[1,4,6,7],[2],[3],[5]] => [[1,2,5,7],[3],[4],[6]] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [[1,4,6],[2,7],[3],[5]] => [[1,2,5,7],[3],[4],[6]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [[1,4,5,7],[2],[3],[6]] => [[1,2,5,6],[3],[4],[7]] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [[1,4,5,6],[2],[3],[7]] => [[1,2,5,6,7],[3],[4]] => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [[1,4,5],[2,6],[3],[7]] => [[1,2,5,6],[3,7],[4]] => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [[1,4,5,7],[2],[3],[6]] => [[1,2,5,6],[3],[4],[7]] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [[1,4,5,6],[2],[3],[7]] => [[1,2,5,6,7],[3],[4]] => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [[1,4,5,6],[2],[3],[7]] => [[1,2,5,6,7],[3],[4]] => 5
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [[1,4,5],[2,6],[3],[7]] => [[1,2,5,6],[3,7],[4]] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [[1,4,7],[2,5],[3],[6]] => [[1,2,5],[3,6],[4],[7]] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [[1,4,6],[2,5],[3],[7]] => [[1,2,5,7],[3,6],[4]] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [[1,4,6],[2,5],[3],[7]] => [[1,2,5,7],[3,6],[4]] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [[1,4,5],[2,6],[3],[7]] => [[1,2,5,6],[3,7],[4]] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [[1,4],[2,5],[3],[6],[7]] => [[1,2,5],[3,6],[4],[7]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [[1,3,6,7],[2],[4],[5]] => [[1,2,4,7],[3],[5],[6]] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [[1,3,6],[2,7],[4],[5]] => [[1,2,4,7],[3],[5],[6]] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [[1,3,5,7],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7]] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [[1,3,5,6],[2],[4],[7]] => [[1,2,4,6,7],[3],[5]] => 5
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [[1,3,5],[2,6],[4],[7]] => [[1,2,4,6],[3,7],[5]] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [[1,3,5,7],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7]] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [[1,3,5,6],[2],[4],[7]] => [[1,2,4,6,7],[3],[5]] => 5
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [[1,3,5,6],[2],[4],[7]] => [[1,2,4,6,7],[3],[5]] => 5
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [[1,3,5],[2,6],[4],[7]] => [[1,2,4,6],[3,7],[5]] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [[1,3,4,7],[2],[5],[6]] => [[1,2,4,5],[3],[6],[7]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [[1,3,4,6],[2],[5],[7]] => [[1,2,4,5,7],[3],[6]] => 5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [[1,3,4,6],[2],[5],[7]] => [[1,2,4,5,7],[3],[6]] => 5
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [[1,3,4,5],[2],[6],[7]] => [[1,2,4,5,6],[3],[7]] => 5
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [[1,3,4],[2],[5],[6],[7]] => [[1,2,4,5],[3],[6],[7]] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [[1,3,7],[2],[4],[5],[6]] => [[1,2,4],[3],[5],[6],[7]] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [[1,3,6],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6]] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [[1,3,6],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6]] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [[1,3,5],[2],[4],[6],[7]] => [[1,2,4,6],[3],[5],[7]] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [[1,3,5],[2],[4],[6],[7]] => [[1,2,4,6],[3],[5],[7]] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [[1,3],[2],[4],[5],[6],[7]] => [[1,2,4],[3],[5],[6],[7]] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5]] => [[1,2,7],[3],[4],[5],[6]] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [[1,6],[2,7],[3],[4],[5]] => [[1,2,7],[3],[4],[5],[6]] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [[1,5,7],[2],[3],[4],[6]] => [[1,2,6],[3],[4],[5],[7]] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [[1,5,6],[2],[3],[4],[7]] => [[1,2,6,7],[3],[4],[5]] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [[1,5],[2,6],[3],[4],[7]] => [[1,2,6],[3,7],[4],[5]] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [[1,5,7],[2],[3],[4],[6]] => [[1,2,6],[3],[4],[5],[7]] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [[1,5,6],[2],[3],[4],[7]] => [[1,2,6,7],[3],[4],[5]] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [[1,5,6],[2],[3],[4],[7]] => [[1,2,6,7],[3],[4],[5]] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [[1,5],[2,6],[3],[4],[7]] => [[1,2,6],[3,7],[4],[5]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => [[1,2,5],[3],[4],[6],[7]] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [[1,4,6],[2],[3],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [[1,4,5],[2],[3],[6],[7]] => [[1,2,5,6],[3],[4],[7]] => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [[1,4],[2,5],[3],[6],[7]] => [[1,2,5],[3,6],[4],[7]] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => [[1,2,5],[3],[4],[6],[7]] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [[1,4,6],[2],[3],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [[1,4,5],[2],[3],[6],[7]] => [[1,2,5,6],[3],[4],[7]] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [[1,4,5],[2],[3],[6],[7]] => [[1,2,5,6],[3],[4],[7]] => 4
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [[1,4],[2],[3],[5],[6],[7]] => [[1,2,5],[3],[4],[6],[7]] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6]] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [[1,6],[2],[3],[4],[5],[7]] => [[1,2,7],[3],[4],[5],[6]] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [[1,6],[2],[3],[4],[5],[7]] => [[1,2,7],[3],[4],[5],[6]] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [[1,5],[2],[3],[4],[6],[7]] => [[1,2,6],[3],[4],[5],[7]] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [[1,5],[2],[3],[4],[6],[7]] => [[1,2,6],[3],[4],[5],[7]] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => [[1,2,5],[3],[4],[6],[7]] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,7,8]] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,7,8]] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,6,7],[8]] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [[1,2,3,4,5,7],[6,8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,7,8]] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,6,7],[8]] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [[1,2,3,4,6,7],[5,8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [[1,2,3,4,6,8],[5,7]] => [[1,2,3,4,5,7],[6,8]] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [[1,2,3,4,6,7],[5,8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,4,5,7],[6,8]] => 6
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [[1,2,3,4,5,7,8],[6]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [[1,2,3,4,5,7],[6,8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,7,8]] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,6,7],[8]] => 7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [[1,2,3,4,7,8],[5],[6]] => [[1,2,3,4,5,8],[6],[7]] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [[1,2,3,4,7],[5,8],[6]] => [[1,2,3,4,5,8],[6],[7]] => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [[1,2,3,4,6,8],[5],[7]] => [[1,2,3,4,5,7],[6],[8]] => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,4,5,7],[6,8]] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => [[1,2,3,4,6,8],[5],[7]] => [[1,2,3,4,5,7],[6],[8]] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,4,5,7],[6],[8]] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,4,5,8],[6],[7]] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,4,5,8],[6],[7]] => 6
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,4,5,7],[6],[8]] => 6
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [[1,2,3,5,6,8],[4,7]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [[1,2,3,5,6,7],[4,8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,3,4,6],[5,7],[8]] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [[1,2,3,4,6,8],[5,7]] => [[1,2,3,4,5,7],[6,8]] => 6
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [[1,2,3,4,6,7],[5,8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,4,5,7],[6,8]] => 6
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [[1,2,3,4,5,7,8],[6]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [[1,2,3,4,5,7],[6,8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,7,8]] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,6,7],[8]] => 7
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [[1,2,3,4,7,8],[5],[6]] => [[1,2,3,4,5,8],[6],[7]] => 6
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,4,5,8],[6],[7]] => 6
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,4,5,8],[6],[7]] => 6
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => [[1,2,3,4,7],[5,8],[6]] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [[1,2,3,5,6,8],[4],[7]] => [[1,2,3,4,6,7],[5],[8]] => 6
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,3,4,6],[5,7],[8]] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => [[1,2,3,5,7,8],[4],[6]] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,8,4,6,7,5,3] => [[1,2,3,5,6],[4],[7],[8]] => [[1,2,3,4,6,7],[5],[8]] => 6
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => [[1,2,3,5],[4],[6],[7],[8]] => [[1,2,3,4,6],[5],[7],[8]] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [[1,2,3,7,8],[4],[5],[6]] => [[1,2,3,4,8],[5],[6],[7]] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [[1,2,3,6],[4,7],[5],[8]] => [[1,2,3,4,7],[5,8],[6]] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,7,5,4,6,3,8] => [[1,2,3,6,8],[4],[5],[7]] => [[1,2,3,4,7],[5],[6],[8]] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,7,5,4,6,8,3] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,8,5,4,7,6,3] => [[1,2,3,6],[4,7],[5],[8]] => [[1,2,3,4,7],[5,8],[6]] => 5
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => [[1,2,3,5,7],[4],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => [[1,2,3,5,6],[4],[7],[8]] => [[1,2,3,4,6,7],[5],[8]] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [[1,2,3,8],[4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [[1,2,3,7],[4],[5],[6],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => [[1,2,3,7],[4],[5],[6],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 5
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => [[1,2,3,6],[4],[5],[7],[8]] => [[1,2,3,4,7],[5],[6],[8]] => 5
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => [[1,2,3,6],[4],[5],[7],[8]] => [[1,2,3,4,7],[5],[6],[8]] => 5
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => [[1,2,3,5,6,7],[4,8]] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [[1,2,4,5,6,7],[3,8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [[1,2,4,5,6],[3,7],[8]] => [[1,2,3,5,6,7],[4,8]] => 6
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [[1,2,4,5,7,8],[3,6]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [[1,2,4,5,6,7],[3,8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [[1,2,4,5,6],[3,7],[8]] => [[1,2,3,5,6,7],[4,8]] => 6
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [[1,2,4,5,8],[3,6],[7]] => [[1,2,3,5,6],[4,7],[8]] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => [[1,2,4,5,7],[3,6],[8]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]] => [[1,2,3,5,6],[4,7],[8]] => 5
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => [[1,2,3,5,7,8],[4,6]] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => [[1,2,3,5,7],[4,6,8]] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [[1,2,4,6,7],[3,5,8]] => [[1,2,3,5,7,8],[4,6]] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [[1,2,4,6],[3,5,7],[8]] => [[1,2,3,5,7],[4,6,8]] => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [[1,2,4,5,7,8],[3,6]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [[1,2,4,5,7],[3,6,8]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [[1,2,4,5,6,8],[3,7]] => [[1,2,3,5,6,7],[4,8]] => 6
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [[1,2,4,5,6,7],[3,8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [[1,2,4,5,6],[3,7],[8]] => [[1,2,3,5,6,7],[4,8]] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [[1,2,4,5,8],[3,6],[7]] => [[1,2,3,5,6],[4,7],[8]] => 5
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [[1,2,4,5],[3,6],[7],[8]] => [[1,2,3,5,6],[4,7],[8]] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]] => [[1,2,3,5,8],[4,6],[7]] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]] => [[1,2,3,5,8],[4,6],[7]] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [[1,2,4,6,8],[3,5],[7]] => [[1,2,3,5,7],[4,6],[8]] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [[1,2,4,6,7],[3,5],[8]] => [[1,2,3,5,7,8],[4,6]] => 6
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [[1,2,4,6],[3,5,7],[8]] => [[1,2,3,5,7],[4,6,8]] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => [[1,2,4,6,7],[3,5],[8]] => [[1,2,3,5,7,8],[4,6]] => 6
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [[1,2,4,6],[3,5],[7],[8]] => [[1,2,3,5,7],[4,6],[8]] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [[1,2,4,8],[3,5],[6],[7]] => [[1,2,3,5],[4,6],[7],[8]] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [[1,2,4,7],[3,5],[6],[8]] => [[1,2,3,5,8],[4,6],[7]] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => [[1,2,4,7],[3,5],[6],[8]] => [[1,2,3,5,8],[4,6],[7]] => 5
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => [[1,2,4,6],[3,5],[7],[8]] => [[1,2,3,5,7],[4,6],[8]] => 5
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]] => [[1,2,3,5],[4,6],[7],[8]] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [[1,2,3,5,6,8],[4,7]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [[1,2,3,5,6,7],[4,8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,3,4,6],[5,7],[8]] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [[1,2,3,4,6,7,8],[5]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [[1,2,3,4,6,8],[5,7]] => [[1,2,3,4,5,7],[6,8]] => 6
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [[1,2,3,4,6,7],[5,8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,4,5,7],[6,8]] => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [[1,2,3,4,5,7,8],[6]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [[1,2,3,4,5,7],[6,8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,7,8]] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,6,7],[8]] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,4,5,8],[6],[7]] => 6
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => [[1,2,3,4,7],[5,8],[6]] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [[1,2,3,5,8],[4,6],[7]] => [[1,2,3,4,6],[5,7],[8]] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,3,4,6],[5,7],[8]] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,4,5,2,8,7] => [[1,2,3,5,7],[4,8],[6]] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => [[1,2,3,5,6,8],[4],[7]] => [[1,2,3,4,6,7],[5],[8]] => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => [[1,2,3,5,6,8],[4],[7]] => [[1,2,3,4,6,7],[5],[8]] => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,8,4,6,5,7,2] => [[1,2,3,5,7],[4],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [[1,2,3,7],[4,8],[5],[6]] => [[1,2,3,4,8],[5],[6],[7]] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [[1,2,3,6,8],[4],[5],[7]] => [[1,2,3,4,7],[5],[6],[8]] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [[1,2,3,6],[4,7],[5],[8]] => [[1,2,3,4,7],[5,8],[6]] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => [[1,2,3,6],[4,7],[5],[8]] => [[1,2,3,4,7],[5,8],[6]] => 5
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => [[1,2,3,5,6],[4],[7],[8]] => [[1,2,3,4,6,7],[5],[8]] => 6
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => [[1,2,3,5],[4],[6],[7],[8]] => [[1,2,3,4,6],[5],[7],[8]] => 5
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [[1,2,3,6],[4],[5],[7],[8]] => [[1,2,3,4,7],[5],[6],[8]] => 5
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => [[1,2,3,6],[4],[5],[7],[8]] => [[1,2,3,4,7],[5],[6],[8]] => 5
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [[1,2,5,6,7],[3,8],[4]] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [[1,2,5,6,8],[3,7],[4]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [[1,2,5,6,7],[3,8],[4]] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [[1,2,5,6,8],[3,7],[4]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [[1,2,5,8],[3,6],[4,7]] => [[1,2,3,6],[4,7],[5,8]] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [[1,2,5,7],[3,6],[4,8]] => [[1,2,3,6,8],[4,7],[5]] => 5
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => [[1,2,3,6],[4,7],[5,8]] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => [[1,2,3,5,7],[4,8],[6]] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [[1,2,4,5,7,8],[3],[6]] => [[1,2,3,5,6,8],[4],[7]] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [[1,2,4,5,6,7],[3],[8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [[1,2,4,5,8],[3,6],[7]] => [[1,2,3,5,6],[4,7],[8]] => 5
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [[1,2,4,5,7],[3,6],[8]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [[1,2,4,5],[3,6],[7],[8]] => [[1,2,3,5,6],[4,7],[8]] => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [[1,2,4,7,8],[3,5],[6]] => [[1,2,3,5,8],[4,6],[7]] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [[1,2,4,6,8],[3,5],[7]] => [[1,2,3,5,7],[4,6],[8]] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [[1,2,4,6,7],[3,5],[8]] => [[1,2,3,5,7,8],[4,6]] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [[1,2,4,6],[3,5,7],[8]] => [[1,2,3,5,7],[4,6,8]] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [[1,2,4,6,7],[3,5],[8]] => [[1,2,3,5,7,8],[4,6]] => 6
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => [[1,2,4,6],[3,5],[7],[8]] => [[1,2,3,5,7],[4,6],[8]] => 5
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => [[1,2,4,7],[3,5],[6],[8]] => [[1,2,3,5,8],[4,6],[7]] => 5
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => [[1,2,4,6],[3,5],[7],[8]] => [[1,2,3,5,7],[4,6],[8]] => 5
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [[1,2,4],[3,5],[6],[7],[8]] => [[1,2,3,5],[4,6],[7],[8]] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => [[1,2,3,5,7,8],[4],[6]] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => [[1,2,4,6,7],[3,8],[5]] => [[1,2,3,5,7,8],[4],[6]] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => [[1,2,3,5,7],[4,8],[6]] => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => [[1,2,4,5,7],[3,8],[6]] => [[1,2,3,5,6,8],[4],[7]] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => [[1,2,4,5,6,8],[3],[7]] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [[1,2,4,5,6,7],[3],[8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => [[1,2,4,5,7],[3,6],[8]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => [[1,2,4,5,7,8],[3],[6]] => [[1,2,3,5,6,8],[4],[7]] => 6
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => [[1,2,4,5,6],[3,7],[8]] => [[1,2,3,5,6,7],[4,8]] => 6
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => [[1,2,4,5,6,8],[3],[7]] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => [[1,2,4,5,6,7],[3],[8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3],[8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => [[1,2,4,5,6],[3],[7],[8]] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => [[1,2,4,7,8],[3],[5],[6]] => [[1,2,3,5,8],[4],[6],[7]] => 5
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => [[1,2,4,6],[3,7],[5],[8]] => [[1,2,3,5,7],[4,8],[6]] => 5
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => [[1,2,4,6,8],[3],[5],[7]] => [[1,2,3,5,7],[4],[6],[8]] => 5
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => [[1,2,4,6,7],[3],[5],[8]] => [[1,2,3,5,7,8],[4],[6]] => 6
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => [[1,2,4,5,7],[3],[6],[8]] => [[1,2,3,5,6,8],[4],[7]] => 6
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8,3,5,6,7,4,2] => [[1,2,4,5,6],[3],[7],[8]] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => [[1,2,4,5],[3],[6],[7],[8]] => [[1,2,3,5,6],[4],[7],[8]] => 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,7,3,6,5,4,2,8] => [[1,2,4,8],[3],[5],[6],[7]] => [[1,2,3,5],[4],[6],[7],[8]] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [[1,2,4,7],[3],[5],[6],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 5
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [[1,2,4,7],[3],[5],[6],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 5
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => [[1,2,4,6],[3],[5],[7],[8]] => [[1,2,3,5,7],[4],[6],[8]] => 5
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => [[1,2,4],[3],[5],[6],[7],[8]] => [[1,2,3,5],[4],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => [[1,2,3,7,8],[4],[5],[6]] => 5
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => [[1,2,3,7],[4,8],[5],[6]] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [[1,2,6,7],[3,8],[4],[5]] => [[1,2,3,7,8],[4],[5],[6]] => 5
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => [[1,2,3,7],[4,8],[5],[6]] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [[1,2,5,7,8],[3],[4],[6]] => [[1,2,3,6,8],[4],[5],[7]] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [[1,2,5,6,8],[3],[4],[7]] => [[1,2,3,6,7],[4],[5],[8]] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [[1,2,5,6,7],[3],[4],[8]] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [[1,2,5,6],[3,7],[4],[8]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [[1,2,5],[3,6],[4,7],[8]] => [[1,2,3,6],[4,7],[5,8]] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => [[1,2,5,7,8],[3],[4],[6]] => [[1,2,3,6,8],[4],[5],[7]] => 5
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [[1,2,5,6],[3,7],[4],[8]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [[1,2,5,6,7],[3],[4],[8]] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => [[1,2,5,6],[3,7],[4],[8]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => [[1,2,5,7],[3,6],[4],[8]] => [[1,2,3,6,8],[4,7],[5]] => 5
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => [[1,2,5,7],[3,6],[4],[8]] => [[1,2,3,6,8],[4,7],[5]] => 5
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => [[1,2,5,6],[3,7],[4],[8]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => [[1,2,4,7,8],[3],[5],[6]] => [[1,2,3,5,8],[4],[6],[7]] => 5
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => [[1,2,4,7],[3,8],[5],[6]] => [[1,2,3,5,8],[4],[6],[7]] => 5
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => [[1,2,4,6],[3,7],[5],[8]] => [[1,2,3,5,7],[4,8],[6]] => 5
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7,4,5,3,6,8,2] => [[1,2,4,6,7],[3],[5],[8]] => [[1,2,3,5,7,8],[4],[6]] => 6
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [[1,2,4,6,7],[3],[5],[8]] => [[1,2,3,5,7,8],[4],[6]] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => [[1,2,4,5,7],[3],[6],[8]] => [[1,2,3,5,6,8],[4],[7]] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,8,4,5,6,3,7,2] => [[1,2,4,5,7],[3],[6],[8]] => [[1,2,3,5,6,8],[4],[7]] => 6
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [[1,2,4,5,6],[3],[7],[8]] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => [[1,2,4,8],[3],[5],[6],[7]] => [[1,2,3,5],[4],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => [[1,2,4,7],[3],[5],[6],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 5
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => [[1,2,4,6],[3],[5],[7],[8]] => [[1,2,3,5,7],[4],[6],[8]] => 5
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => [[1,2,4],[3],[5],[6],[7],[8]] => [[1,2,3,5],[4],[6],[7],[8]] => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => [[1,2,3,8],[4],[5],[6],[7]] => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => [[1,2,3,8],[4],[5],[6],[7]] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [[1,2,6],[3,7],[4],[5],[8]] => [[1,2,3,7],[4,8],[5],[6]] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => [[1,2,6,8],[3],[4],[5],[7]] => [[1,2,3,7],[4],[5],[6],[8]] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7,5,4,3,6,8,2] => [[1,2,6,7],[3],[4],[5],[8]] => [[1,2,3,7,8],[4],[5],[6]] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [[1,2,6,7],[3],[4],[5],[8]] => [[1,2,3,7,8],[4],[5],[6]] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => [[1,2,5,7],[3],[4],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 5
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => [[1,2,3,6,7],[4],[5],[8]] => 5
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [[1,2,5],[3,6],[4],[7],[8]] => [[1,2,3,6],[4,7],[5],[8]] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => [[1,2,5,8],[3],[4],[6],[7]] => [[1,2,3,6],[4],[5],[7],[8]] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => [[1,2,5,7],[3],[4],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => [[1,2,3,6,7],[4],[5],[8]] => 5
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => [[1,2,3,6,7],[4],[5],[8]] => 5
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => [[1,2,5],[3],[4],[6],[7],[8]] => [[1,2,3,6],[4],[5],[7],[8]] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [[1,2,8],[3],[4],[5],[6],[7]] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [[1,2,7],[3],[4],[5],[6],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [[1,2,7],[3],[4],[5],[6],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 4
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [[1,2,6],[3],[4],[5],[7],[8]] => [[1,2,3,7],[4],[5],[6],[8]] => 4
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [[1,2,6],[3],[4],[5],[7],[8]] => [[1,2,3,7],[4],[5],[6],[8]] => 4
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [[1,2,5],[3],[4],[6],[7],[8]] => [[1,2,3,6],[4],[5],[7],[8]] => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [[1,2,4,5,6,7,8],[3]] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [[1,2,4,5,6,7,8],[3]] => 7
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => [[1,2,4,5,6,7],[3,8]] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [[1,3,4,5,6,7],[2,8]] => [[1,2,4,5,6,7,8],[3]] => 7
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,4,5,6,7],[3,8]] => 6
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => [[1,2,4,5,6,8],[3,7]] => 6
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => [[1,2,4,5,6,8],[3,7]] => 6
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [[1,3,4,5,6,7],[2,8]] => [[1,2,4,5,6,7,8],[3]] => 7
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [[1,3,4,5,7],[2,6],[8]] => [[1,2,4,5,6,8],[3,7]] => 6
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => [[1,3,4,5,7],[2,6],[8]] => [[1,2,4,5,6,8],[3,7]] => 6
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,4,5,6],[3,7],[8]] => 5
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [[1,3,4,6,7],[2,5,8]] => [[1,2,4,5,7,8],[3,6]] => 6
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [[1,3,4,6,7],[2,5,8]] => [[1,2,4,5,7,8],[3,6]] => 6
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [[1,3,4,6],[2,5,7],[8]] => [[1,2,4,5,7],[3,6,8]] => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [[1,3,4,5,7],[2,6,8]] => [[1,2,4,5,6,8],[3,7]] => 6
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [[1,3,4,5,6,7],[2,8]] => [[1,2,4,5,6,7,8],[3]] => 7
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [[1,3,4,5,7],[2,6],[8]] => [[1,2,4,5,6,8],[3,7]] => 6
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [[1,3,4,6],[2,5,7],[8]] => [[1,2,4,5,7],[3,6,8]] => 5
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => [[1,3,4,6,7],[2,5],[8]] => [[1,2,4,5,7,8],[3,6]] => 6
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [[1,3,4,6],[2,5],[7],[8]] => [[1,2,4,5,7],[3,6],[8]] => 5
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,8,6,5,7,4] => [[1,3,4,7],[2,5],[6],[8]] => [[1,2,4,5,8],[3,6],[7]] => 5
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => [[1,3,4,6],[2,5],[7],[8]] => [[1,2,4,5,7],[3,6],[8]] => 5
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,4,5],[3,6],[7],[8]] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4]] => [[1,2,4,6,7,8],[3,5]] => 6
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [[1,3,5,6,7],[2,4,8]] => [[1,2,4,6,7,8],[3,5]] => 6
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [[1,3,5,6,7],[2,4,8]] => [[1,2,4,6,7,8],[3,5]] => 6
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [[1,3,5,6],[2,4,7],[8]] => [[1,2,4,6,7],[3,5,8]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [[1,3,5,7,8],[2,4,6]] => [[1,2,4,6,8],[3,5,7]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => [[1,2,4,6,8],[3,5,7]] => 5
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [[1,3,5,6,7],[2,4,8]] => [[1,2,4,6,7,8],[3,5]] => 6
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [[1,3,5,6],[2,4,7],[8]] => [[1,2,4,6,7],[3,5,8]] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [[1,3,5,7],[2,4,6],[8]] => [[1,2,4,6,8],[3,5,7]] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [[1,3,5,7],[2,4,6],[8]] => [[1,2,4,6,8],[3,5,7]] => 5
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8]] => [[1,2,4,6],[3,5,7],[8]] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [[1,3,4,6,7,8],[2,5]] => [[1,2,4,5,7,8],[3,6]] => 6
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [[1,3,4,6,7],[2,5,8]] => [[1,2,4,5,7,8],[3,6]] => 6
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [[1,3,4,6],[2,5,7],[8]] => [[1,2,4,5,7],[3,6,8]] => 5
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [[1,3,4,5,7],[2,6,8]] => [[1,2,4,5,6,8],[3,7]] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [[1,3,4,5,6,8],[2,7]] => [[1,2,4,5,6,7],[3,8]] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [[1,3,4,5,6,7],[2,8]] => [[1,2,4,5,6,7,8],[3]] => 7
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,4,5,6,7],[3,8]] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [[1,3,4,5,7],[2,6],[8]] => [[1,2,4,5,6,8],[3,7]] => 6
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,4,5,6],[3,7],[8]] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [[1,3,4,7,8],[2,5],[6]] => [[1,2,4,5,8],[3,6],[7]] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [[1,3,4,7],[2,5,8],[6]] => [[1,2,4,5,8],[3,6],[7]] => 5
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [[1,3,4,6],[2,5,7],[8]] => [[1,2,4,5,7],[3,6,8]] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [[1,3,4,6,7],[2,5],[8]] => [[1,2,4,5,7,8],[3,6]] => 6
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [[1,3,4,6],[2,5],[7],[8]] => [[1,2,4,5,7],[3,6],[8]] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [[1,3,4,7],[2,5],[6],[8]] => [[1,2,4,5,8],[3,6],[7]] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [[1,3,4,7],[2,5],[6],[8]] => [[1,2,4,5,8],[3,6],[7]] => 5
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [[1,3,4,6],[2,5],[7],[8]] => [[1,2,4,5,7],[3,6],[8]] => 5
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,4,5],[3,6],[7],[8]] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [[1,3,6,7,8],[2,4],[5]] => [[1,2,4,7,8],[3,5],[6]] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [[1,3,6,8],[2,4,7],[5]] => [[1,2,4,7],[3,5,8],[6]] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [[1,3,6],[2,4,7],[5,8]] => [[1,2,4,7],[3,5,8],[6]] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [[1,3,5,7],[2,4,8],[6]] => [[1,2,4,6,8],[3,5],[7]] => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [[1,3,5,6,7],[2,4],[8]] => [[1,2,4,6,7,8],[3,5]] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [[1,3,5,6],[2,4,7],[8]] => [[1,2,4,6,7],[3,5,8]] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [[1,3,5,7],[2,4,6],[8]] => [[1,2,4,6,8],[3,5,7]] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [[1,3,5,7],[2,4,6],[8]] => [[1,2,4,6,8],[3,5,7]] => 5
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [[1,3,5],[2,4,6],[7],[8]] => [[1,2,4,6],[3,5,7],[8]] => 4
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [[1,3,5,7],[2,4,8],[6]] => [[1,2,4,6,8],[3,5],[7]] => 5
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [[1,3,5,6,7],[2,4],[8]] => [[1,2,4,6,7,8],[3,5]] => 6
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [[1,3,5,6],[2,4,7],[8]] => [[1,2,4,6,7],[3,5,8]] => 5
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [[1,3,5,6,7],[2,4],[8]] => [[1,2,4,6,7,8],[3,5]] => 6
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => [[1,3,5,6],[2,4],[7],[8]] => [[1,2,4,6,7],[3,5],[8]] => 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [[1,3,5,7],[2,4],[6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 5
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [[1,3,5,7],[2,4],[6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 5
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => [[1,3,5,6],[2,4],[7],[8]] => [[1,2,4,6,7],[3,5],[8]] => 5
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => [[1,3,5],[2,4],[6],[7],[8]] => [[1,2,4,6],[3,5],[7],[8]] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [[1,3,7],[2,4,8],[5],[6]] => [[1,2,4,8],[3,5],[6],[7]] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [[1,3,6],[2,4,7],[5],[8]] => [[1,2,4,7],[3,5,8],[6]] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => [[1,3,6,7],[2,4],[5],[8]] => [[1,2,4,7,8],[3,5],[6]] => 5
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [[1,3,6],[2,4,7],[5],[8]] => [[1,2,4,7],[3,5,8],[6]] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => [[1,3,5,7],[2,4],[6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 5
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [[1,3,5,7],[2,4],[6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 5
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [[1,3,5,6],[2,4],[7],[8]] => [[1,2,4,6,7],[3,5],[8]] => 5
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [[1,3,5],[2,4],[6],[7],[8]] => [[1,2,4,6],[3,5],[7],[8]] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [[1,3,8],[2,4],[5],[6],[7]] => [[1,2,4],[3,5],[6],[7],[8]] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [[1,3,7],[2,4],[5],[6],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [[1,3,7],[2,4],[5],[6],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 4
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => [[1,2,4,7],[3,5],[6],[8]] => 4
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => [[1,2,4,7],[3,5],[6],[8]] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => [[1,2,4],[3,5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => [[1,2,3,5,6,7],[4,8]] => 6
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [[1,2,4,5,6,7],[3,8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [[1,2,4,5,6,8],[3,7]] => [[1,2,3,5,6,7],[4,8]] => 6
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [[1,2,4,5,6,7],[3,8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]] => [[1,2,3,5,6],[4,7],[8]] => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => [[1,2,3,5,7,8],[4,6]] => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => [[1,2,3,5,7],[4,6,8]] => 5
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [[1,2,4,5,7,8],[3,6]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [[1,2,4,5,6,8],[3,7]] => [[1,2,3,5,6,7],[4,8]] => 6
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [[1,2,4,5,6,7],[3,8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [[1,2,4,5,7],[3,6],[8]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]] => [[1,2,3,5,8],[4,6],[7]] => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]] => [[1,2,3,5,8],[4,6],[7]] => 5
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [[1,2,4,6,8],[3,5],[7]] => [[1,2,3,5,7],[4,6],[8]] => 5
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [[1,2,4,6],[3,5,7],[8]] => [[1,2,3,5,7],[4,6,8]] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,7,5,6,4,8] => [[1,2,4,6,8],[3,5],[7]] => [[1,2,3,5,7],[4,6],[8]] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [[1,2,4,6,7],[3,5],[8]] => [[1,2,3,5,7,8],[4,6]] => 6
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [[1,2,4,7],[3,5],[6],[8]] => [[1,2,3,5,8],[4,6],[7]] => 5
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [[1,2,4,6],[3,5],[7],[8]] => [[1,2,3,5,7],[4,6],[8]] => 5
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]] => [[1,2,3,5],[4,6],[7],[8]] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [[1,2,3,5,6,8],[4,7]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [[1,2,3,5,6,7],[4,8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [[1,2,3,5,8],[4,6],[7]] => [[1,2,3,4,6],[5,7],[8]] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,3,4,6],[5,7],[8]] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [[1,2,3,4,6,7,8],[5]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [[1,2,3,4,6,7],[5,8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [[1,2,3,4,6,8],[5,7]] => [[1,2,3,4,5,7],[6,8]] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [[1,2,3,4,6,7],[5,8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,4,5,7],[6,8]] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [[1,2,3,4,5,7,8],[6]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [[1,2,3,4,5,7],[6,8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,6,7],[8]] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,7,8]] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,6,7],[8]] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => 7
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => [[1,2,3,4,5,8],[6],[7]] => 6
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => [[1,2,3,4,5,7],[6],[8]] => 6
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,4,5,7],[6,8]] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => [[1,2,3,4,6,8],[5],[7]] => [[1,2,3,4,5,7],[6],[8]] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,7,5,6,8,1] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,4,5,7,8],[6]] => 7
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,4,5,7],[6],[8]] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,4,5,8],[6],[7]] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,4,5,8],[6],[7]] => 6
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,4,5,7],[6],[8]] => 6
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => [[1,2,3,4,7],[5,8],[6]] => 5
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => [[1,2,3,4,7],[5,8],[6]] => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [[1,2,3,5,7,8],[4],[6]] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [[1,2,3,5,6,8],[4],[7]] => [[1,2,3,4,6,7],[5],[8]] => 6
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,3,4,6,8],[5,7]] => 6
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,3,4,6],[5,7],[8]] => 5
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => [[1,2,3,5,7,8],[4],[6]] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [[1,2,3,5,7],[4,8],[6]] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,4,5,8,7,1] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,3,4,6,7],[5,8]] => 6
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,3,4,6,7,8],[5]] => 7
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => [[1,2,3,5,7],[4],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [[1,2,3,5,6],[4],[7],[8]] => [[1,2,3,4,6,7],[5],[8]] => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [[1,2,3,7,8],[4],[5],[6]] => [[1,2,3,4,8],[5],[6],[7]] => 5
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => [[1,2,3,4,8],[5],[6],[7]] => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => [[1,2,3,6,8],[4],[5],[7]] => [[1,2,3,4,7],[5],[6],[8]] => 5
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,7,5,4,6,8,1] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,3,4,7,8],[5],[6]] => 6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => [[1,2,3,5,8],[4],[6],[7]] => [[1,2,3,4,6],[5],[7],[8]] => 5
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => [[1,2,3,5,7],[4],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => [[1,2,3,5,7],[4],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => [[1,2,3,5,6],[4],[7],[8]] => [[1,2,3,4,6,7],[5],[8]] => 6
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => [[1,2,3,5],[4],[6],[7],[8]] => [[1,2,3,4,6],[5],[7],[8]] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => [[1,2,3,7],[4],[5],[6],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 5
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [[1,2,5,7,8],[3,6],[4]] => [[1,2,3,6,8],[4,7],[5]] => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [[1,2,5,7],[3,6,8],[4]] => [[1,2,3,6,8],[4,7],[5]] => 5
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [[1,2,5,7],[3,6],[4,8]] => [[1,2,3,6,8],[4,7],[5]] => 5
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => [[1,2,3,6],[4,7],[5,8]] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => [[1,2,3,5,7,8],[4],[6]] => 6
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [[1,2,4,6,7],[3,8],[5]] => [[1,2,3,5,7,8],[4],[6]] => 6
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => [[1,2,3,5,7],[4,8],[6]] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [[1,2,4,6,7],[3,8],[5]] => [[1,2,3,5,7,8],[4],[6]] => 6
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => [[1,2,3,5,7],[4,8],[6]] => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [[1,2,4,5,7],[3,8],[6]] => [[1,2,3,5,6,8],[4],[7]] => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [[1,2,4,5,6],[3,7],[8]] => [[1,2,3,5,6,7],[4,8]] => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [[1,2,4,5,7],[3,6],[8]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => [[1,2,4,5,7],[3,6],[8]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [[1,2,4,7,8],[3,5],[6]] => [[1,2,3,5,8],[4,6],[7]] => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [[1,2,4,7],[3,5,8],[6]] => [[1,2,3,5,8],[4,6],[7]] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [[1,2,4,6,8],[3,5],[7]] => [[1,2,3,5,7],[4,6],[8]] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [[1,2,4,6,7],[3,5],[8]] => [[1,2,3,5,7,8],[4,6]] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [[1,2,4,6],[3,5,7],[8]] => [[1,2,3,5,7],[4,6,8]] => 5
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [[1,2,4,6,7],[3,5],[8]] => [[1,2,3,5,7,8],[4,6]] => 6
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => [[1,2,4,6,7],[3,5],[8]] => [[1,2,3,5,7,8],[4,6]] => 6
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,8,5,7,6,1] => [[1,2,4,6],[3,5],[7],[8]] => [[1,2,3,5,7],[4,6],[8]] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [[1,2,4,7],[3,5],[6],[8]] => [[1,2,3,5,8],[4,6],[7]] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,8,6,5,7,1] => [[1,2,4,7],[3,5],[6],[8]] => [[1,2,3,5,8],[4,6],[7]] => 5
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [[1,2,4],[3,5],[6],[7],[8]] => [[1,2,3,5],[4,6],[7],[8]] => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => [[1,2,3,5,7,8],[4],[6]] => 6
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => [[1,2,3,5,7],[4,8],[6]] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => [[1,2,4,5,6,8],[3],[7]] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => [[1,2,4,5,6],[3,7],[8]] => [[1,2,3,5,6,7],[4,8]] => 6
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => [[1,2,4,5,7],[3,6],[8]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => [[1,2,4,5,7],[3,6],[8]] => [[1,2,3,5,6,8],[4,7]] => 6
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,3,4,8,7,6,1] => [[1,2,4,5],[3,6],[7],[8]] => [[1,2,3,5,6],[4,7],[8]] => 5
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => [[1,2,4,5,7,8],[3],[6]] => [[1,2,3,5,6,8],[4],[7]] => 6
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => [[1,2,4,5,6],[3,7],[8]] => [[1,2,3,5,6,7],[4,8]] => 6
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => [[1,2,4,5,6,8],[3],[7]] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [[1,2,4,5,6,7],[3],[8]] => [[1,2,3,5,6,7,8],[4]] => 7
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => [[1,2,4,5,6],[3],[7],[8]] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => [[1,2,4,7],[3,8],[5],[6]] => [[1,2,3,5,8],[4],[6],[7]] => 5
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,6,3,5,4,7,8,1] => [[1,2,4,6,7],[3],[5],[8]] => [[1,2,3,5,7,8],[4],[6]] => 6
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,6,3,5,4,8,7,1] => [[1,2,4,6],[3,7],[5],[8]] => [[1,2,3,5,7],[4,8],[6]] => 5
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => [[1,2,4,6,7],[3],[5],[8]] => [[1,2,3,5,7,8],[4],[6]] => 6
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => [[1,2,4,6],[3,7],[5],[8]] => [[1,2,3,5,7],[4,8],[6]] => 5
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => [[1,2,4,5,7],[3],[6],[8]] => [[1,2,3,5,6,8],[4],[7]] => 6
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => [[1,2,4,5,6],[3],[7],[8]] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => [[1,2,4,5],[3],[6],[7],[8]] => [[1,2,3,5,6],[4],[7],[8]] => 5
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => [[1,2,3,5],[4],[6],[7],[8]] => 4
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,8,3,7,5,6,4,1] => [[1,2,4,6],[3],[5],[7],[8]] => [[1,2,3,5,7],[4],[6],[8]] => 5
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => [[1,2,4],[3],[5],[6],[7],[8]] => [[1,2,3,5],[4],[6],[7],[8]] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => [[1,2,3,7,8],[4],[5],[6]] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [[1,2,6,7],[3,8],[4],[5]] => [[1,2,3,7,8],[4],[5],[6]] => 5
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => [[1,2,3,7],[4,8],[5],[6]] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [[1,2,6,7],[3,8],[4],[5]] => [[1,2,3,7,8],[4],[5],[6]] => 5
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => [[1,2,3,7],[4,8],[5],[6]] => 4
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => [[1,2,3,6,8],[4],[5],[7]] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [[1,2,5,6,8],[3],[4],[7]] => [[1,2,3,6,7],[4],[5],[8]] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [[1,2,5,6],[3,7],[4],[8]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [[1,2,5,7],[3,6],[4],[8]] => [[1,2,3,6,8],[4,7],[5]] => 5
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => [[1,2,5,7],[3,6],[4],[8]] => [[1,2,3,6,8],[4,7],[5]] => 5
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [[1,2,5],[3,6],[4,7],[8]] => [[1,2,3,6],[4,7],[5,8]] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => [[1,2,3,6,8],[4],[5],[7]] => 5
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,6,4,3,5,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => [[1,2,5,6],[3,7],[4],[8]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => [[1,2,5,6,7],[3],[4],[8]] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => [[1,2,5,6,7],[3],[4],[8]] => [[1,2,3,6,7,8],[4],[5]] => 6
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => [[1,2,5,6],[3,7],[4],[8]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => [[1,2,5,7],[3,6],[4],[8]] => [[1,2,3,6,8],[4,7],[5]] => 5
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => [[1,2,5,7],[3,6],[4],[8]] => [[1,2,3,6,8],[4,7],[5]] => 5
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => [[1,2,5,6],[3,7],[4],[8]] => [[1,2,3,6,7],[4,8],[5]] => 5
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => [[1,2,5],[3,6],[4],[7],[8]] => [[1,2,3,6],[4,7],[5],[8]] => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,4,5,3,1,7,8] => [[1,2,4,7,8],[3],[5],[6]] => [[1,2,3,5,8],[4],[6],[7]] => 5
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,4,5,3,7,8,1] => [[1,2,4,6,7],[3],[5],[8]] => [[1,2,3,5,7,8],[4],[6]] => 6
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => [[1,2,4,6,7],[3],[5],[8]] => [[1,2,3,5,7,8],[4],[6]] => 6
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => [[1,2,4,5,8],[3],[6],[7]] => [[1,2,3,5,6],[4],[7],[8]] => 5
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => [[1,2,4,5,7],[3],[6],[8]] => [[1,2,3,5,6,8],[4],[7]] => 6
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => [[1,2,4,5,7],[3],[6],[8]] => [[1,2,3,5,6,8],[4],[7]] => 6
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => [[1,2,4,5,6],[3],[7],[8]] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => [[1,2,3,5],[4],[6],[7],[8]] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => [[1,2,4,7],[3],[5],[6],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 5
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => [[1,2,4,7],[3],[5],[6],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 5
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => [[1,2,4],[3],[5],[6],[7],[8]] => [[1,2,3,5],[4],[6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => [[1,2,3,8],[4],[5],[6],[7]] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [[1,2,6,7],[3],[4],[5],[8]] => [[1,2,3,7,8],[4],[5],[6]] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [[1,2,6],[3,7],[4],[5],[8]] => [[1,2,3,7],[4,8],[5],[6]] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => [[1,2,6,7],[3],[4],[5],[8]] => [[1,2,3,7,8],[4],[5],[6]] => 5
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => [[1,2,6,7],[3],[4],[5],[8]] => [[1,2,3,7,8],[4],[5],[6]] => 5
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,8,5,4,3,7,6,1] => [[1,2,6],[3,7],[4],[5],[8]] => [[1,2,3,7],[4,8],[5],[6]] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => [[1,2,5,7],[3],[4],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 5
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,5,4,6,7,3,1] => [[1,2,5,6],[3],[4],[7],[8]] => [[1,2,3,6,7],[4],[5],[8]] => 5
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => [[1,2,5],[3,6],[4],[7],[8]] => [[1,2,3,6],[4,7],[5],[8]] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => [[1,2,5,7],[3],[4],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 5
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,8,7,4,5,6,3,1] => [[1,2,5,6],[3],[4],[7],[8]] => [[1,2,3,6,7],[4],[5],[8]] => 5
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => [[1,2,5],[3],[4],[6],[7],[8]] => [[1,2,3,6],[4],[5],[7],[8]] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 4
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [[1,2,6],[3],[4],[5],[7],[8]] => [[1,2,3,7],[4],[5],[6],[8]] => 4
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => [[1,2,5],[3],[4],[6],[7],[8]] => [[1,2,3,6],[4],[5],[7],[8]] => 4
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [[1,2,5,6,7,8],[3],[4]] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => [[1,2,5,6,7,8],[3],[4]] => 6
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [[1,4,5,6,7],[2,8],[3]] => [[1,2,5,6,7,8],[3],[4]] => 6
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => [[1,2,5,6,7],[3,8],[4]] => 5
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [[1,4,5,6,7],[2,8],[3]] => [[1,2,5,6,7,8],[3],[4]] => 6
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [[1,4,5,6],[2,7],[3,8]] => [[1,2,5,6,7],[3,8],[4]] => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]] => [[1,2,5,6],[3,7],[4,8]] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [[1,4,5,7],[2,6],[3,8]] => [[1,2,5,6,8],[3,7],[4]] => 5
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [[1,4,5,7],[2,6],[3,8]] => [[1,2,5,6,8],[3,7],[4]] => 5
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [[1,4,5],[2,6],[3,7],[8]] => [[1,2,5,6],[3,7],[4,8]] => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [[1,4,6,7,8],[2,5],[3]] => [[1,2,5,7,8],[3,6],[4]] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [[1,4,6,8],[2,5,7],[3]] => [[1,2,5,7],[3,6,8],[4]] => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [[1,4,5,7,8],[2,6],[3]] => [[1,2,5,6,8],[3,7],[4]] => 5
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [[1,4,5,6,7],[2,8],[3]] => [[1,2,5,6,7,8],[3],[4]] => 6
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [[1,4,5,6],[2,7],[3,8]] => [[1,2,5,6,7],[3,8],[4]] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [[1,4,5,8],[2,6],[3,7]] => [[1,2,5,6],[3,7],[4,8]] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [[1,4,5,7],[2,6],[3,8]] => [[1,2,5,6,8],[3,7],[4]] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => [[1,4,5,7],[2,6],[3,8]] => [[1,2,5,6,8],[3,7],[4]] => 5
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [[1,4,5],[2,6],[3,7],[8]] => [[1,2,5,6],[3,7],[4,8]] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [[1,4,7,8],[2,5],[3,6]] => [[1,2,5,8],[3,6],[4,7]] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [[1,4,7],[2,5,8],[3,6]] => [[1,2,5,8],[3,6],[4,7]] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [[1,4,6,7],[2,5],[3,8]] => [[1,2,5,7,8],[3,6],[4]] => 5
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [[1,4,6],[2,5,7],[3,8]] => [[1,2,5,7],[3,6,8],[4]] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => [[1,4,6,7],[2,5],[3,8]] => [[1,2,5,7,8],[3,6],[4]] => 5
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => [[1,4,6,7],[2,5],[3,8]] => [[1,2,5,7,8],[3,6],[4]] => 5
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [[1,4,6],[2,5],[3,7],[8]] => [[1,2,5,7],[3,6],[4,8]] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [[1,4,8],[2,5],[3,6],[7]] => [[1,2,5],[3,6],[4,7],[8]] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [[1,4,7],[2,5],[3,6],[8]] => [[1,2,5,8],[3,6],[4,7]] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => [[1,4,7],[2,5],[3,6],[8]] => [[1,2,5,8],[3,6],[4,7]] => 4
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [[1,4,6],[2,5],[3,7],[8]] => [[1,2,5,7],[3,6],[4,8]] => 4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => [[1,2,5],[3,6],[4,7],[8]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => [[1,2,4,6,7,8],[3],[5]] => 6
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [[1,3,5,6,7],[2,8],[4]] => [[1,2,4,6,7,8],[3],[5]] => 6
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [[1,3,5,6,8],[2,7],[4]] => [[1,2,4,6,7],[3,8],[5]] => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [[1,3,5,6,7],[2,8],[4]] => [[1,2,4,6,7,8],[3],[5]] => 6
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [[1,3,5,6],[2,7],[4,8]] => [[1,2,4,6,7],[3,8],[5]] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [[1,3,5,7,8],[2,6],[4]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [[1,3,5,6,8],[2,7],[4]] => [[1,2,4,6,7],[3,8],[5]] => 5
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [[1,3,5,6,7],[2,8],[4]] => [[1,2,4,6,7,8],[3],[5]] => 6
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [[1,3,5,6],[2,7],[4,8]] => [[1,2,4,6,7],[3,8],[5]] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [[1,3,5,8],[2,6],[4,7]] => [[1,2,4,6],[3,7],[5,8]] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [[1,3,5,7],[2,6],[4,8]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [[1,3,5],[2,6],[4,7],[8]] => [[1,2,4,6],[3,7],[5,8]] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => [[1,2,4,5,7,8],[3],[6]] => 6
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => [[1,2,4,5,7],[3,8],[6]] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => [[1,2,4,5,6,8],[3],[7]] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => [[1,2,4,5,6,7],[3],[8]] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => [[1,2,4,5,6,7,8],[3]] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,4,5,6,7],[3,8]] => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [[1,3,4,5,7],[2,6],[8]] => [[1,2,4,5,6,8],[3,7]] => 6
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => [[1,3,4,5,7],[2,6],[8]] => [[1,2,4,5,6,8],[3,7]] => 6
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [[1,3,4,6],[2,5,7],[8]] => [[1,2,4,5,7],[3,6,8]] => 5
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,7,5,6,8,1] => [[1,3,4,6,7],[2,5],[8]] => [[1,2,4,5,7,8],[3,6]] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => [[1,3,4,6,7],[2,5],[8]] => [[1,2,4,5,7,8],[3,6]] => 6
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [[1,3,4,7],[2,5],[6],[8]] => [[1,2,4,5,8],[3,6],[7]] => 5
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => [[1,3,4,6],[2,5],[7],[8]] => [[1,2,4,5,7],[3,6],[8]] => 5
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,4,5],[3,6],[7],[8]] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [[1,3,6,7,8],[2,4],[5]] => [[1,2,4,7,8],[3,5],[6]] => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [[1,3,6,7],[2,4,8],[5]] => [[1,2,4,7,8],[3,5],[6]] => 5
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [[1,3,6,8],[2,4,7],[5]] => [[1,2,4,7],[3,5,8],[6]] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [[1,3,6,7],[2,4,8],[5]] => [[1,2,4,7,8],[3,5],[6]] => 5
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [[1,3,6],[2,4,7],[5,8]] => [[1,2,4,7],[3,5,8],[6]] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [[1,3,5,7],[2,4,8],[6]] => [[1,2,4,6,8],[3,5],[7]] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [[1,3,5,6,7],[2,4],[8]] => [[1,2,4,6,7,8],[3,5]] => 6
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [[1,3,5,6],[2,4,7],[8]] => [[1,2,4,6,7],[3,5,8]] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [[1,3,5,8],[2,4,6],[7]] => [[1,2,4,6],[3,5,7],[8]] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [[1,3,5,7],[2,4,6],[8]] => [[1,2,4,6,8],[3,5,7]] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => [[1,3,5,7],[2,4,6],[8]] => [[1,2,4,6,8],[3,5,7]] => 5
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [[1,3,5,7],[2,4,8],[6]] => [[1,2,4,6,8],[3,5],[7]] => 5
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [[1,3,5,6,8],[2,4],[7]] => [[1,2,4,6,7],[3,5],[8]] => 5
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => [[1,3,5,6,7],[2,4],[8]] => [[1,2,4,6,7,8],[3,5]] => 6
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => [[1,3,5,8],[2,4],[6],[7]] => [[1,2,4,6],[3,5],[7],[8]] => 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => [[1,3,5,7],[2,4],[6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 5
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => [[1,3,5,7],[2,4],[6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [[1,3,7],[2,4,8],[5],[6]] => [[1,2,4,8],[3,5],[6],[7]] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [[1,3,6,8],[2,4],[5],[7]] => [[1,2,4,7],[3,5],[6],[8]] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [[1,3,6],[2,4,7],[5],[8]] => [[1,2,4,7],[3,5,8],[6]] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [[1,3,6,8],[2,4],[5],[7]] => [[1,2,4,7],[3,5],[6],[8]] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => [[1,3,6,7],[2,4],[5],[8]] => [[1,2,4,7,8],[3,5],[6]] => 5
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => [[1,3,6],[2,4,7],[5],[8]] => [[1,2,4,7],[3,5,8],[6]] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [[1,3,5,8],[2,4],[6],[7]] => [[1,2,4,6],[3,5],[7],[8]] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => [[1,3,5,7],[2,4],[6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 5
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => [[1,3,5,7],[2,4],[6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 5
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => [[1,3,5],[2,4],[6],[7],[8]] => [[1,2,4,6],[3,5],[7],[8]] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => [[1,2,4],[3,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [[1,3,7],[2,4],[5],[6],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 4
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,8,6,5,7,4,1] => [[1,3,6],[2,4],[5],[7],[8]] => [[1,2,4,7],[3,5],[6],[8]] => 4
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => [[1,3,6],[2,4],[5],[7],[8]] => [[1,2,4,7],[3,5],[6],[8]] => 4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => [[1,2,4],[3,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => [[1,2,4,6,7,8],[3],[5]] => 6
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,2,3,1,5,7,6,8] => [[1,3,5,6,8],[2,7],[4]] => [[1,2,4,6,7],[3,8],[5]] => 5
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => [[1,3,5,6,7],[2,8],[4]] => [[1,2,4,6,7,8],[3],[5]] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [[1,3,5,6,7],[2,8],[4]] => [[1,2,4,6,7,8],[3],[5]] => 6
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [[1,3,5,6],[2,7],[4,8]] => [[1,2,4,6,7],[3,8],[5]] => 5
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [[1,3,5,7],[2,6],[4,8]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [[1,3,5],[2,6],[4,7],[8]] => [[1,2,4,6],[3,7],[5,8]] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => [[1,2,4,5,7,8],[3],[6]] => 6
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,2,3,5,1,6,8,7] => [[1,3,4,6,7],[2,8],[5]] => [[1,2,4,5,7,8],[3],[6]] => 6
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => [[1,3,4,6,7],[2,8],[5]] => [[1,2,4,5,7,8],[3],[6]] => 6
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => [[1,2,4,5,7],[3,8],[6]] => 5
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => [[1,2,4,5,6,8],[3],[7]] => 6
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => [[1,3,4,5,7],[2,8],[6]] => [[1,2,4,5,6,8],[3],[7]] => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => [[1,2,4,5,6,7],[3],[8]] => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => [[1,2,4,5,6,7,8],[3]] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,4,5,6,7],[3,8]] => 6
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,2,3,5,8,7,6,1] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,4,5,6],[3,7],[8]] => 5
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => [[1,3,4,6],[2,5,7],[8]] => [[1,2,4,5,7],[3,6,8]] => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,2,3,7,5,6,1,8] => [[1,3,4,6,8],[2,5],[7]] => [[1,2,4,5,7],[3,6],[8]] => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [[1,3,4,6,7],[2,5],[8]] => [[1,2,4,5,7,8],[3,6]] => 6
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => [[1,3,4,6,7],[2,5],[8]] => [[1,2,4,5,7,8],[3,6]] => 6
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => [[1,3,4,6],[2,5],[7],[8]] => [[1,2,4,5,7],[3,6],[8]] => 5
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => [[1,3,4,7],[2,5],[6],[8]] => [[1,2,4,5,8],[3,6],[7]] => 5
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,2,3,8,7,6,5,1] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,4,5],[3,6],[7],[8]] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => [[1,2,4,5,7,8],[3],[6]] => 6
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => [[1,3,4,6,7],[2,8],[5]] => [[1,2,4,5,7,8],[3],[6]] => 6
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [[1,3,4,6,7],[2,8],[5]] => [[1,2,4,5,7,8],[3],[6]] => 6
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => [[1,2,4,5,7],[3,8],[6]] => 5
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => [[1,2,4,5,6,8],[3],[7]] => 6
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => [[1,3,4,5,7],[2,8],[6]] => [[1,2,4,5,6,8],[3],[7]] => 6
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => [[1,2,4,5,6,7],[3],[8]] => 6
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => [[1,2,4,5,6,7,8],[3]] => 7
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => [[1,3,4,5,8],[2,6],[7]] => [[1,2,4,5,6],[3,7],[8]] => 5
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => [[1,3,4,5,7],[2,6],[8]] => [[1,2,4,5,6,8],[3,7]] => 6
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,4,5,6],[3,7],[8]] => 5
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => [[1,2,4,5,6,8],[3],[7]] => 6
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => [[1,3,4,5,7],[2,8],[6]] => [[1,2,4,5,6,8],[3],[7]] => 6
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => [[1,2,4,5,6,7],[3],[8]] => 6
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => [[1,2,4,5,6,7,8],[3]] => 7
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,4,5,6,7],[3,8]] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]] => [[1,2,4,5,6,7],[3],[8]] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [[1,3,4,5,6,7],[2],[8]] => [[1,2,4,5,6,7,8],[3]] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => [[1,2,4,5,6,7,8],[3]] => 7
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [[1,3,4,5,6],[2],[7],[8]] => [[1,2,4,5,6,7],[3],[8]] => 6
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => [[1,3,4,5,8],[2],[6],[7]] => [[1,2,4,5,6],[3],[7],[8]] => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => [[1,3,4,7,8],[2],[5],[6]] => [[1,2,4,5,8],[3],[6],[7]] => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => [[1,3,4,7],[2,8],[5],[6]] => [[1,2,4,5,8],[3],[6],[7]] => 5
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [6,2,3,5,4,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => [[1,2,4,5,7],[3],[6],[8]] => 5
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,2,3,5,4,7,8,1] => [[1,3,4,6,7],[2],[5],[8]] => [[1,2,4,5,7,8],[3],[6]] => 6
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => [[1,3,4,6,8],[2],[5],[7]] => [[1,2,4,5,7],[3],[6],[8]] => 5
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => [[1,3,4,6,7],[2],[5],[8]] => [[1,2,4,5,7,8],[3],[6]] => 6
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => [[1,3,4,5,8],[2],[6],[7]] => [[1,2,4,5,6],[3],[7],[8]] => 5
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8,2,3,5,6,7,4,1] => [[1,3,4,5,6],[2],[7],[8]] => [[1,2,4,5,6,7],[3],[8]] => 6
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8,2,3,5,7,6,4,1] => [[1,3,4,5],[2],[6],[7],[8]] => [[1,2,4,5,6],[3],[7],[8]] => 5
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => [[1,2,4,5],[3],[6],[7],[8]] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8,2,3,6,5,4,7,1] => [[1,3,4,7],[2],[5],[6],[8]] => [[1,2,4,5,8],[3],[6],[7]] => 5
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => [[1,3,4,6],[2],[5],[7],[8]] => [[1,2,4,5,7],[3],[6],[8]] => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => [[1,2,4,7,8],[3],[5],[6]] => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => [[1,3,6,7],[2,8],[4],[5]] => [[1,2,4,7,8],[3],[5],[6]] => 5
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => [[1,3,6,8],[2,7],[4],[5]] => [[1,2,4,7],[3,8],[5],[6]] => 4
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => [[1,3,6],[2,7],[4,8],[5]] => [[1,2,4,7],[3,8],[5],[6]] => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => [[1,3,5,7,8],[2],[4],[6]] => [[1,2,4,6,8],[3],[5],[7]] => 5
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => [[1,2,4,6,8],[3],[5],[7]] => 5
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [5,2,4,3,6,7,1,8] => [[1,3,5,6,8],[2],[4],[7]] => [[1,2,4,6,7],[3],[5],[8]] => 5
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [5,2,4,3,7,6,1,8] => [[1,3,5,8],[2,6],[4],[7]] => [[1,2,4,6],[3,7],[5],[8]] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => [[1,3,5,7],[2,6],[4],[8]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,2,4,3,8,7,6,1] => [[1,3,5],[2,6],[4,7],[8]] => [[1,2,4,6],[3,7],[5,8]] => 4
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => [[1,2,4,6,8],[3],[5],[7]] => 5
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => [[1,3,5,8],[2,6],[4],[7]] => [[1,2,4,6],[3,7],[5],[8]] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [[1,3,5,7],[2,6],[4],[8]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [[1,3,5,7],[2,6],[4],[8]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => [[1,3,5,6],[2,7],[4],[8]] => [[1,2,4,6,7],[3,8],[5]] => 5
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,2,4,5,3,1,7,8] => [[1,3,4,7,8],[2],[5],[6]] => [[1,2,4,5,8],[3],[6],[7]] => 5
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => [[1,3,4,6,8],[2],[5],[7]] => [[1,2,4,5,7],[3],[6],[8]] => 5
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => [[1,3,4,6,7],[2],[5],[8]] => [[1,2,4,5,7,8],[3],[6]] => 6
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [[1,3,4,6],[2,7],[5],[8]] => [[1,2,4,5,7],[3,8],[6]] => 5
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8,2,4,5,6,7,3,1] => [[1,3,4,5,6],[2],[7],[8]] => [[1,2,4,5,6,7],[3],[8]] => 6
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => [[1,3,4,5],[2],[6],[7],[8]] => [[1,2,4,5,6],[3],[7],[8]] => 5
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => [[1,2,4,5],[3],[6],[7],[8]] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => [[1,3,4,7],[2],[5],[6],[8]] => [[1,2,4,5,8],[3],[6],[7]] => 5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8,2,4,7,5,6,3,1] => [[1,3,4,6],[2],[5],[7],[8]] => [[1,2,4,5,7],[3],[6],[8]] => 5
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => [[1,3,4],[2],[5],[6],[7],[8]] => [[1,2,4,5],[3],[6],[7],[8]] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => [[1,3,7,8],[2],[4],[5],[6]] => [[1,2,4,8],[3],[5],[6],[7]] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [[1,3,7],[2,8],[4],[5],[6]] => [[1,2,4,8],[3],[5],[6],[7]] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6],[8]] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,2,5,4,3,7,8,1] => [[1,3,6,7],[2],[4],[5],[8]] => [[1,2,4,7,8],[3],[5],[6]] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6],[8]] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => [[1,3,6,7],[2],[4],[5],[8]] => [[1,2,4,7,8],[3],[5],[6]] => 5
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [[1,3,6],[2,7],[4],[5],[8]] => [[1,2,4,7],[3,8],[5],[6]] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,2,5,4,6,3,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 5
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8,2,5,4,7,6,3,1] => [[1,3,5],[2,6],[4],[7],[8]] => [[1,2,4,6],[3,7],[5],[8]] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,6,4,5,3,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => [[1,2,4,6],[3],[5],[7],[8]] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => [[1,3,5,7],[2],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 5
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => [[1,3,5,6],[2],[4],[7],[8]] => [[1,2,4,6,7],[3],[5],[8]] => 5
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => [[1,3,5,6],[2],[4],[7],[8]] => [[1,2,4,6,7],[3],[5],[8]] => 5
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [[1,3,5],[2],[4],[6],[7],[8]] => [[1,2,4,6],[3],[5],[7],[8]] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,6,5,4,3,8,1] => [[1,3,7],[2],[4],[5],[6],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => [[1,3,7],[2],[4],[5],[6],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => 4
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => [[1,3,6],[2],[4],[5],[7],[8]] => [[1,2,4,7],[3],[5],[6],[8]] => 4
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [[1,3,6],[2],[4],[5],[7],[8]] => [[1,2,4,7],[3],[5],[6],[8]] => 4
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => [[1,3,5],[2],[4],[6],[7],[8]] => [[1,2,4,6],[3],[5],[7],[8]] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => [[1,2,4],[3],[5],[6],[7],[8]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [[1,2,6,7,8],[3],[4],[5]] => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [[1,2,6,7,8],[3],[4],[5]] => 5
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [[1,5,6,8],[2,7],[3],[4]] => [[1,2,6,7],[3,8],[4],[5]] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [[1,5,6,7],[2,8],[3],[4]] => [[1,2,6,7,8],[3],[4],[5]] => 5
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [[1,5,6],[2,7],[3,8],[4]] => [[1,2,6,7],[3,8],[4],[5]] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [[1,5,7,8],[2,6],[3],[4]] => [[1,2,6,8],[3,7],[4],[5]] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [[1,5,7],[2,6,8],[3],[4]] => [[1,2,6,8],[3,7],[4],[5]] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [[1,5,6,8],[2,7],[3],[4]] => [[1,2,6,7],[3,8],[4],[5]] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [[1,5,6,7],[2,8],[3],[4]] => [[1,2,6,7,8],[3],[4],[5]] => 5
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [[1,5,6],[2,7],[3,8],[4]] => [[1,2,6,7],[3,8],[4],[5]] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [[1,5,8],[2,6],[3,7],[4]] => [[1,2,6],[3,7],[4,8],[5]] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [[1,5,7],[2,6],[3,8],[4]] => [[1,2,6,8],[3,7],[4],[5]] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [[1,5,7],[2,6],[3,8],[4]] => [[1,2,6,8],[3,7],[4],[5]] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => [[1,2,6],[3,7],[4,8],[5]] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => [[1,2,5,7,8],[3],[4],[6]] => 5
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [[1,4,6,7],[2,8],[3],[5]] => [[1,2,5,7,8],[3],[4],[6]] => 5
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [[1,4,6],[2,7],[3,8],[5]] => [[1,2,5,7],[3,8],[4],[6]] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [[1,4,5,7,8],[2],[3],[6]] => [[1,2,5,6,8],[3],[4],[7]] => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [[1,4,5,7],[2,8],[3],[6]] => [[1,2,5,6,8],[3],[4],[7]] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => [[1,2,5,6,7],[3],[4],[8]] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => [[1,2,5,6,7,8],[3],[4]] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [[1,4,5,6],[2,7],[3],[8]] => [[1,2,5,6,7],[3,8],[4]] => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [[1,4,5,8],[2,6],[3],[7]] => [[1,2,5,6],[3,7],[4],[8]] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [[1,4,5,7],[2,6],[3],[8]] => [[1,2,5,6,8],[3,7],[4]] => 5
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [[1,4,5],[2,6],[3,7],[8]] => [[1,2,5,6],[3,7],[4,8]] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [[1,4,7,8],[2,5],[3],[6]] => [[1,2,5,8],[3,6],[4],[7]] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [[1,4,7],[2,5,8],[3],[6]] => [[1,2,5,8],[3,6],[4],[7]] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [[1,4,6,8],[2,5],[3],[7]] => [[1,2,5,7],[3,6],[4],[8]] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [[1,4,6,7],[2,5],[3],[8]] => [[1,2,5,7,8],[3,6],[4]] => 5
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [[1,4,6],[2,5,7],[3],[8]] => [[1,2,5,7],[3,6,8],[4]] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => [[1,4,6,7],[2,5],[3],[8]] => [[1,2,5,7,8],[3,6],[4]] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => [[1,4,6,7],[2,5],[3],[8]] => [[1,2,5,7,8],[3,6],[4]] => 5
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => [[1,4,6],[2,5],[3,7],[8]] => [[1,2,5,7],[3,6],[4,8]] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [[1,4,7],[2,5],[3,6],[8]] => [[1,2,5,8],[3,6],[4,7]] => 4
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => [[1,4,6],[2,5],[3,7],[8]] => [[1,2,5,7],[3,6],[4,8]] => 4
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => [[1,2,5],[3,6],[4,7],[8]] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => [[1,2,5,7,8],[3],[4],[6]] => 5
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => [[1,4,6,7],[2,8],[3],[5]] => [[1,2,5,7,8],[3],[4],[6]] => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => [[1,4,6,8],[2,7],[3],[5]] => [[1,2,5,7],[3,8],[4],[6]] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => [[1,4,6],[2,7],[3,8],[5]] => [[1,2,5,7],[3,8],[4],[6]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => [[1,4,5,7,8],[2],[3],[6]] => [[1,2,5,6,8],[3],[4],[7]] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => [[1,4,5,7],[2,8],[3],[6]] => [[1,2,5,6,8],[3],[4],[7]] => 5
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => [[1,2,5,6,7,8],[3],[4]] => 6
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => [[1,4,5,8],[2,6],[3],[7]] => [[1,2,5,6],[3,7],[4],[8]] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [6,3,2,4,5,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => [[1,2,5,6,7],[3],[4],[8]] => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [[1,4,5,6,7],[2],[3],[8]] => [[1,2,5,6,7,8],[3],[4]] => 6
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => [[1,2,5,6,7,8],[3],[4]] => 6
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => [[1,4,5,6],[2,7],[3],[8]] => [[1,2,5,6,7],[3,8],[4]] => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,3,2,5,4,1,7,8] => [[1,4,7,8],[2,5],[3],[6]] => [[1,2,5,8],[3,6],[4],[7]] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [[1,4,7],[2,5,8],[3],[6]] => [[1,2,5,8],[3,6],[4],[7]] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => [[1,4,6,8],[2,5],[3],[7]] => [[1,2,5,7],[3,6],[4],[8]] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => [[1,4,6,7],[2,5],[3],[8]] => [[1,2,5,7,8],[3,6],[4]] => 5
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,3,2,5,4,8,7,1] => [[1,4,6],[2,5,7],[3],[8]] => [[1,2,5,7],[3,6,8],[4]] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [[1,4,6,8],[2,5],[3],[7]] => [[1,2,5,7],[3,6],[4],[8]] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [[1,4,6],[2,5,7],[3],[8]] => [[1,2,5,7],[3,6,8],[4]] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => [[1,4,5,7],[2,6],[3],[8]] => [[1,2,5,6,8],[3,7],[4]] => 5
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8,3,2,5,6,4,7,1] => [[1,4,5,7],[2,6],[3],[8]] => [[1,2,5,6,8],[3,7],[4]] => 5
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => [[1,4,5,6],[2,7],[3],[8]] => [[1,2,5,6,7],[3,8],[4]] => 5
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [[1,4,5],[2,6],[3],[7],[8]] => [[1,2,5,6],[3,7],[4],[8]] => 4
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => [[1,4,6],[2,5],[3],[7],[8]] => [[1,2,5,7],[3,6],[4],[8]] => 4
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => [[1,4,6],[2,5],[3],[7],[8]] => [[1,2,5,7],[3,6],[4],[8]] => 4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [[1,4],[2,5],[3],[6],[7],[8]] => [[1,2,5],[3,6],[4],[7],[8]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => [[1,2,4,7,8],[3],[5],[6]] => 5
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => [[1,3,6,7],[2,8],[4],[5]] => [[1,2,4,7,8],[3],[5],[6]] => 5
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [[1,3,6,7],[2,8],[4],[5]] => [[1,2,4,7,8],[3],[5],[6]] => 5
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => [[1,3,6],[2,7],[4,8],[5]] => [[1,2,4,7],[3,8],[5],[6]] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => [[1,2,4,6,8],[3],[5],[7]] => 5
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => [[1,3,5,6,7],[2],[4],[8]] => [[1,2,4,6,7,8],[3],[5]] => 6
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => [[1,3,5,8],[2,6],[4],[7]] => [[1,2,4,6],[3,7],[5],[8]] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,3,4,2,7,6,8,1] => [[1,3,5,7],[2,6],[4],[8]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => [[1,3,5,7],[2,6],[4],[8]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => [[1,2,4,6,8],[3],[5],[7]] => 5
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [[1,3,5,6,7],[2],[4],[8]] => [[1,2,4,6,7,8],[3],[5]] => 6
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,2,6,5,1,8] => [[1,3,5,8],[2,6],[4],[7]] => [[1,2,4,6],[3,7],[5],[8]] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => [[1,3,5,7],[2,6],[4],[8]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => [[1,3,5,7],[2,6],[4],[8]] => [[1,2,4,6,8],[3,7],[5]] => 5
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [[1,3,4,7],[2,8],[5],[6]] => [[1,2,4,5,8],[3],[6],[7]] => 5
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => [[1,2,4,5,7],[3],[6],[8]] => 5
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => [[1,3,4,6,7],[2],[5],[8]] => [[1,2,4,5,7,8],[3],[6]] => 6
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => [[1,3,4,6],[2,7],[5],[8]] => [[1,2,4,5,7],[3,8],[6]] => 5
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [[1,3,4,6,7],[2],[5],[8]] => [[1,2,4,5,7,8],[3],[6]] => 6
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [[1,3,4,6],[2,7],[5],[8]] => [[1,2,4,5,7],[3,8],[6]] => 5
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => [[1,3,4,5,8],[2],[6],[7]] => [[1,2,4,5,6],[3],[7],[8]] => 5
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [[1,3,4,5,7],[2],[6],[8]] => [[1,2,4,5,6,8],[3],[7]] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [[1,3,4,5,7],[2],[6],[8]] => [[1,2,4,5,6,8],[3],[7]] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [[1,3,4,5,6],[2],[7],[8]] => [[1,2,4,5,6,7],[3],[8]] => 6
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => [[1,2,4,5,6],[3],[7],[8]] => 5
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,3,4,6,5,2,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => [[1,2,4,5],[3],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => [[1,2,4,5],[3],[6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => [[1,3,7],[2,8],[4],[5],[6]] => [[1,2,4,8],[3],[5],[6],[7]] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6],[8]] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => [[1,3,6,7],[2],[4],[5],[8]] => [[1,2,4,7,8],[3],[5],[6]] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,3,5,4,2,8,7,1] => [[1,3,6],[2,7],[4],[5],[8]] => [[1,2,4,7],[3,8],[5],[6]] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6],[8]] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => [[1,3,6,7],[2],[4],[5],[8]] => [[1,2,4,7,8],[3],[5],[6]] => 5
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8,3,5,4,2,7,6,1] => [[1,3,6],[2,7],[4],[5],[8]] => [[1,2,4,7],[3,8],[5],[6]] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => [[1,2,4,6],[3],[5],[7],[8]] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 5
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => [[1,3,5,6],[2],[4],[7],[8]] => [[1,2,4,6,7],[3],[5],[8]] => 5
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [[1,3,5],[2,6],[4],[7],[8]] => [[1,2,4,6],[3,7],[5],[8]] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => [[1,2,4,6],[3],[5],[7],[8]] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [[1,3,5,7],[2],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 5
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8,3,7,4,5,6,2,1] => [[1,3,5,6],[2],[4],[7],[8]] => [[1,2,4,6,7],[3],[5],[8]] => 5
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => [[1,2,4,6],[3],[5],[7],[8]] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [[1,3,8],[2],[4],[5],[6],[7]] => [[1,2,4],[3],[5],[6],[7],[8]] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => [[1,3,7],[2],[4],[5],[6],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => [[1,3,7],[2],[4],[5],[6],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => 4
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => [[1,3,6],[2],[4],[5],[7],[8]] => [[1,2,4,7],[3],[5],[6],[8]] => 4
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => [[1,3,6],[2],[4],[5],[7],[8]] => [[1,2,4,7],[3],[5],[6],[8]] => 4
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => [[1,2,4,6],[3],[5],[7],[8]] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => [[1,2,4],[3],[5],[6],[7],[8]] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => [[1,2,7,8],[3],[4],[5],[6]] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => [[1,2,7,8],[3],[4],[5],[6]] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [[1,6,8],[2,7],[3],[4],[5]] => [[1,2,7],[3,8],[4],[5],[6]] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [[1,6,7],[2,8],[3],[4],[5]] => [[1,2,7,8],[3],[4],[5],[6]] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]] => [[1,2,7],[3,8],[4],[5],[6]] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [[1,5,7,8],[2],[3],[4],[6]] => [[1,2,6,8],[3],[4],[5],[7]] => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [[1,5,7],[2,8],[3],[4],[6]] => [[1,2,6,8],[3],[4],[5],[7]] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => [[1,2,6,7],[3],[4],[5],[8]] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => [[1,2,6,7,8],[3],[4],[5]] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [[1,5,6],[2,7],[3],[4],[8]] => [[1,2,6,7],[3,8],[4],[5]] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [[1,5,8],[2,6],[3],[4],[7]] => [[1,2,6],[3,7],[4],[5],[8]] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [[1,5,7],[2,6],[3],[4],[8]] => [[1,2,6,8],[3,7],[4],[5]] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => [[1,5,7],[2,6],[3],[4],[8]] => [[1,2,6,8],[3,7],[4],[5]] => 4
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [[1,5],[2,6],[3,7],[4],[8]] => [[1,2,6],[3,7],[4,8],[5]] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => [[1,5,7,8],[2],[3],[4],[6]] => [[1,2,6,8],[3],[4],[5],[7]] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => [[1,5,7],[2,8],[3],[4],[6]] => [[1,2,6,8],[3],[4],[5],[7]] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [6,4,3,2,5,8,7,1] => [[1,5,6],[2,7],[3],[4],[8]] => [[1,2,6,7],[3,8],[4],[5]] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => [[1,2,6,7,8],[3],[4],[5]] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => [[1,2,6,7,8],[3],[4],[5]] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => [[1,5,7],[2,6],[3],[4],[8]] => [[1,2,6,8],[3,7],[4],[5]] => 4
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8,4,3,2,6,7,5,1] => [[1,5,6],[2,7],[3],[4],[8]] => [[1,2,6,7],[3,8],[4],[5]] => 4
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [[1,5],[2,6],[3,7],[4],[8]] => [[1,2,6],[3,7],[4,8],[5]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => [[1,4,7],[2,8],[3],[5],[6]] => [[1,2,5,8],[3],[4],[6],[7]] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => [[1,2,5,7],[3],[4],[6],[8]] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => [[1,2,5,7,8],[3],[4],[6]] => 5
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8,4,3,5,2,7,6,1] => [[1,4,6],[2,7],[3],[5],[8]] => [[1,2,5,7],[3,8],[4],[6]] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]] => [[1,2,5,6,8],[3],[4],[7]] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => [[1,2,5,6,7],[3],[4],[8]] => 5
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => [[1,2,5,6],[3,7],[4],[8]] => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => [[1,4,8],[2,5],[3],[6],[7]] => [[1,2,5],[3,6],[4],[7],[8]] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => [[1,4,7],[2,5],[3],[6],[8]] => [[1,2,5,8],[3,6],[4],[7]] => 4
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => [[1,4,6],[2,5],[3],[7],[8]] => [[1,2,5,7],[3,6],[4],[8]] => 4
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8,4,3,7,6,5,2,1] => [[1,4],[2,5],[3],[6],[7],[8]] => [[1,2,5],[3,6],[4],[7],[8]] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => [[1,2,5,8],[3],[4],[6],[7]] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => [[1,4,7],[2,8],[3],[5],[6]] => [[1,2,5,8],[3],[4],[6],[7]] => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,3,4,2,7,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => [[1,2,5,7,8],[3],[4],[6]] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => [[1,2,5,7],[3],[4],[6],[8]] => 4
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => [[1,4,6,7],[2],[3],[5],[8]] => [[1,2,5,7,8],[3],[4],[6]] => 5
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => [[1,4,6],[2,7],[3],[5],[8]] => [[1,2,5,7],[3,8],[4],[6]] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => [[1,2,5,6,8],[3],[4],[7]] => 5
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => [[1,2,5,6,7],[3],[4],[8]] => 5
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => [[1,2,5,6],[3,7],[4],[8]] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => [[1,2,5,6],[3],[4],[7],[8]] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => [[1,2,5,6,8],[3],[4],[7]] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]] => [[1,2,5,6,8],[3],[4],[7]] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => [[1,2,5,6,7],[3],[4],[8]] => 5
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => [[1,2,5,6],[3],[4],[7],[8]] => 4
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => [[1,2,5],[3],[4],[6],[7],[8]] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => [[1,4,7],[2],[3],[5],[6],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => 4
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8,6,3,5,4,7,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => [[1,2,5,7],[3],[4],[6],[8]] => 4
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => [[1,2,5,7],[3],[4],[6],[8]] => 4
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => [[1,2,5,6],[3],[4],[7],[8]] => 4
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => [[1,2,5],[3],[4],[6],[7],[8]] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [[1,2,8],[3],[4],[5],[6],[7]] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [[1,7],[2,8],[3],[4],[5],[6]] => [[1,2,8],[3],[4],[5],[6],[7]] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => [[1,2,7],[3],[4],[5],[6],[8]] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [[1,2,7,8],[3],[4],[5],[6]] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [[1,6],[2,7],[3],[4],[5],[8]] => [[1,2,7],[3,8],[4],[5],[6]] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => [[1,2,7],[3],[4],[5],[6],[8]] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [[1,2,7,8],[3],[4],[5],[6]] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [[1,2,7,8],[3],[4],[5],[6]] => 4
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [[1,6],[2,7],[3],[4],[5],[8]] => [[1,2,7],[3,8],[4],[5],[6]] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => [[1,2,6],[3],[4],[5],[7],[8]] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => 4
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [[1,2,6,7],[3],[4],[5],[8]] => 4
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => [[1,2,6],[3,7],[4],[5],[8]] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => [[1,2,6],[3],[4],[5],[7],[8]] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [[1,2,6,7],[3],[4],[5],[8]] => 4
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [[1,2,6,7],[3],[4],[5],[8]] => 4
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => [[1,2,6],[3,7],[4],[5],[8]] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => [[1,2,5],[3],[4],[6],[7],[8]] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [[1,4,7],[2],[3],[5],[6],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => [[1,4,7],[2],[3],[5],[6],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => 4
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => [[1,2,5,7],[3],[4],[6],[8]] => 4
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => [[1,2,5,6],[3],[4],[7],[8]] => 4
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => [[1,2,5],[3],[4],[6],[7],[8]] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => [[1,2,7],[3],[4],[5],[6],[8]] => 3
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => [[1,2,7],[3],[4],[5],[6],[8]] => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => [[1,2,6],[3],[4],[5],[7],[8]] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => [[1,2,6],[3],[4],[5],[7],[8]] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 3
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => [[1,2,4],[3,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,10,9,8,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[] => [] => [] => [] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8],[2],[9]] => [[1,2,4,5,6,7,8,9],[3]] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,9,8,1] => [[1,3,5,7],[2,4,6,8],[9]] => [[1,2,4,6,8],[3,5,7,9]] => 5
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,1] => [[1,3,4,5,6,7,8],[2],[9]] => [[1,2,4,5,6,7,8,9],[3]] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [[1,3,4,5,6,7,8],[2],[9]] => [[1,2,4,5,6,7,8,9],[3]] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2],[9]] => [[1,2,4,5,6,7,8,9],[3]] => 8
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [[1,4,5,6,7,8],[2],[3],[9]] => [[1,2,5,6,7,8,9],[3],[4]] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,3,2,4,5,6,7,8,1] => [[1,4,5,6,7,8],[2],[3],[9]] => [[1,2,5,6,7,8,9],[3],[4]] => 7
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => [[1,5,6,7,8],[2],[3],[4],[9]] => [[1,2,6,7,8,9],[3],[4],[5]] => 6
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,4,3,2,9,8,7,6,1] => [[1,5],[2,6],[3,7],[4,8],[9]] => [[1,2,6],[3,7],[4,8],[5,9]] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [9,4,3,2,5,6,7,8,1] => [[1,5,6,7,8],[2],[3],[4],[9]] => [[1,2,6,7,8,9],[3],[4],[5]] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,1] => [[1,6,7,8],[2],[3],[4],[5],[9]] => [[1,2,7,8,9],[3],[4],[5],[6]] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => [[1,7,8],[2],[3],[4],[5],[6],[9]] => [[1,2,8,9],[3],[4],[5],[6],[7]] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => [[1,7,8],[2],[3],[4],[5],[6],[9]] => [[1,2,8,9],[3],[4],[5],[6],[7]] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [[1,8],[2],[3],[4],[5],[6],[7],[9]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9,7,6,5,4,3,2,8,1] => [[1,8],[2],[3],[4],[5],[6],[7],[9]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [[1,2,3,4,5,6,7,8],[9]] => [[1,2,3,4,5,6,7,8,9]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [[1,2,3,4,5,6],[7],[8],[9]] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => [[1,2,4,5,6,7,8,9,10],[3]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,6,10,8,9,7] => [[1,2,3,4,5,6,7,9],[8],[10]] => [[1,2,3,4,5,6,7,8,10],[9]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => [[1,2,4,5,6,7,8,9,10],[3]] => 9
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,10,1] => [[1,4,5,6,7,8,9],[2],[3],[10]] => [[1,2,5,6,7,8,9,10],[3],[4]] => 8
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,2,3,4,5,7,8,9,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => [[1,2,4,5,6,7,8,9,10],[3]] => 9
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,10,1] => [[1,5,6,7,8,9],[2],[3],[4],[10]] => [[1,2,6,7,8,9,10],[3],[4],[5]] => 7
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,10,1] => [[1,6,7,8,9],[2],[3],[4],[5],[10]] => [[1,2,7,8,9,10],[3],[4],[5],[6]] => 6
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,10,3,4,5,6,7,8,9,2] => [[1,2,4,5,6,7,8,9],[3],[10]] => [[1,2,3,5,6,7,8,9,10],[4]] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => [[1,2,4,5,6,7,8,9,10],[3]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [[1,2,3,4,5,6,7,9],[8]] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => [[1,2,3,4,5,7,9],[6,8]] => [[1,2,3,4,5,6,8],[7,9]] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,9,8,7] => [[1,2,3,4,5,7],[6,8],[9]] => [[1,2,3,4,5,6,8],[7,9]] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,9,8,7,6] => [[1,2,3,4,6],[5,7],[8],[9]] => [[1,2,3,4,5,7],[6,8],[9]] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [[1,2,3,5,7,9],[4,6,8]] => [[1,2,3,4,6,8],[5,7,9]] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,9,8,7] => [[1,2,3,5,7],[4,6,8],[9]] => [[1,2,3,4,6,8],[5,7,9]] => 6
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,9,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8],[9]] => [[1,2,3,4,6],[5,7],[8],[9]] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,9,8,7,6] => [[1,2,4,6],[3,5,7],[8],[9]] => [[1,2,3,5,7],[4,6,8],[9]] => 5
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,9,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8],[9]] => [[1,2,3,5],[4,6],[7],[8],[9]] => 4
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,4,3,2,9,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8],[9]] => [[1,2,3,6],[4,7],[5,8],[9]] => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [[1,2,4,5,6,7,8,9],[3]] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [[1,3,4,5,6,7,8],[2,9]] => [[1,2,4,5,6,7,8,9],[3]] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [[1,3,5,7,9],[2,4,6,8]] => [[1,2,4,6,8],[3,5,7,9]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,9,8,7] => [[1,3,5,7],[2,4,6,8],[9]] => [[1,2,4,6,8],[3,5,7,9]] => 5
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,9,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8],[9]] => [[1,2,4,6],[3,5,7],[8],[9]] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,5,4,3,9,8,7,6] => [[1,3,6],[2,4,7],[5,8],[9]] => [[1,2,4,7],[3,5,8],[6,9]] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => [[1,3,9],[2,4],[5],[6],[7],[8]] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]] => [[1,2,5,6,7,8,9],[3],[4]] => 7
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9]] => [[1,2,5],[3,6],[4,7],[8],[9]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [[1,5,6,7,8,9],[2],[3],[4]] => [[1,2,6,7,8,9],[3],[4],[5]] => 6
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,8,7,6,5,9] => [[1,5,9],[2,6],[3,7],[4,8]] => [[1,2,6],[3,7],[4,8],[5,9]] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9]] => [[1,2,6],[3,7],[4,8],[5,9]] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [[1,6,7,8,9],[2],[3],[4],[5]] => [[1,2,7,8,9],[3],[4],[5],[6]] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [[1,7,8,9],[2],[3],[4],[5],[6]] => [[1,2,8,9],[3],[4],[5],[6],[7]] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [[1,2,3,4,5,6,7,8,10],[9]] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => [[1,2,3,4,5,6,7,8,10],[9]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [[1,2,3,4,5,6,7,9],[8,10]] => [[1,2,3,4,5,6,7,8,10],[9]] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]] => [[1,2,3,4,5,6,7,9,10],[8]] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => [[1,2,3,4,5,6,8,9,10],[7]] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7,10,9] => [[1,2,3,4,5,7,9],[6,8,10]] => [[1,2,3,4,5,6,8,10],[7,9]] => 8
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]] => [[1,2,3,4,5,7,8,9,10],[6]] => 9
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]] => [[1,2,3,4,5,7,9],[6,8,10]] => 7
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => [[1,2,3,4,6,7,8,9,10],[5]] => 9
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [[1,2,3,5,7,9],[4,6,8,10]] => [[1,2,3,4,6,8,10],[5,7,9]] => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]] => [[1,2,3,5,6,7,8,9,10],[4]] => 9
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => [[1,2,3,5,7,9],[4,6,8,10]] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => [[1,2,4,6,8],[3,5,7,9],[10]] => [[1,2,3,5,7,9],[4,6,8,10]] => 6
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,2,6,5,4,10,9,8,7] => [[1,2,4,7],[3,5,8],[6,9],[10]] => [[1,2,3,5,8],[4,6,9],[7,10]] => 5
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,10,9,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8],[9],[10]] => [[1,2,3,5],[4,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,4,3,2,10,9,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8],[9],[10]] => [[1,2,3,6],[4,7],[5,8],[9],[10]] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,5,4,3,2,10,9,8,7,6] => [[1,2,6],[3,7],[4,8],[5,9],[10]] => [[1,2,3,7],[4,8],[5,9],[6,10]] => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [[1,2,4,5,6,7,8,9,10],[3]] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [[1,2,4,5,6,7,8,9,10],[3]] => 9
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => [[1,3,5,6,7,8,9,10],[2,4]] => [[1,2,4,6,7,8,9,10],[3,5]] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9,10] => [[1,3,5,7,8,9,10],[2,4,6]] => [[1,2,4,6,8,9,10],[3,5,7]] => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => [[1,3,5,7,9,10],[2,4,6,8]] => [[1,2,4,6,8,10],[3,5,7,9]] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => [[1,2,4,6,8,10],[3,5,7,9]] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => [[1,3,5,7],[2,4,6,8],[9],[10]] => [[1,2,4,6,8],[3,5,7,9],[10]] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [[1,4,5,6,7,8,9,10],[2],[3]] => [[1,2,5,6,7,8,9,10],[3],[4]] => 8
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,6,5,4,10,9,8,7] => [[1,4,7],[2,5,8],[3,6,9],[10]] => [[1,2,5,8],[3,6,9],[4,7,10]] => 4
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => [[1,2,5],[3,6],[4,7],[8],[9],[10]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [[1,5,6,7,8,9,10],[2],[3],[4]] => [[1,2,6,7,8,9,10],[3],[4],[5]] => 7
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => [[1,2,6],[3,7],[4,8],[5,9],[10]] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => [[1,2,7,8,9,10],[3],[4],[5],[6]] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => [[1,2,8,9,10],[3],[4],[5],[6],[7]] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [[1,2,9,10],[3],[4],[5],[6],[7],[8]] => 4
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [[1,2,3,4,5,6,7,9],[8]] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]] => [[1,2,3,5,6,7,8,9,10],[4]] => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => [[1,2,3,4,6,7,8,9,10],[5]] => 9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]] => [[1,2,3,4,5,7,8,9,10],[6]] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => [[1,2,3,4,5,6,8,9,10],[7]] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]] => [[1,2,3,4,5,6,7,9,10],[8]] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [[1,2,3,4,5,6,9],[7],[8]] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => [[1,2,3,4,5,6,7,8,10],[9]] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [[1,2,3,4,5,6,7,8,10],[9]] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [[1,3,4,5,6,7,8],[2,9]] => [[1,2,4,5,6,7,8,9],[3]] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,7,9,10,8] => [[1,3,4,5,6,7,8,9],[2,10]] => [[1,2,4,5,6,7,8,9,10],[3]] => 9
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,10,3,4,5,6,7,8,9,1] => [[1,2,4,5,6,7,8,9],[3],[10]] => [[1,2,3,5,6,7,8,9,10],[4]] => 9
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8],[9]] => [[1,2,3,5],[4,6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => [[1,2,3,4,5,6,7,8,10],[9]] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,9,6,10] => [[1,2,3,4,5,6,7,8,10],[9]] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,6,3,4,5,7,8,9,10,1] => [[1,2,4,5,6,7,8,9],[3],[10]] => [[1,2,3,5,6,7,8,9,10],[4]] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [[1,3,4,5,6,7,8],[2,9]] => [[1,2,4,5,6,7,8,9],[3]] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => [[1,2,3,4,5,7],[6,8],[9]] => [[1,2,3,4,5,6,8],[7,9]] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,9,8,7,6] => [[1,2,3,4,6],[5,7],[8],[9]] => [[1,2,3,4,5,7],[6,8],[9]] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10,3,4,5,6,7,8,9,2,1] => [[1,3,4,5,6,7,8],[2],[9],[10]] => [[1,2,4,5,6,7,8,9],[3],[10]] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => [[1,7,8],[2,9],[3],[4],[5],[6]] => [[1,2,8,9],[3],[4],[5],[6],[7]] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [10,8,7,6,5,4,3,2,9,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => [[1,2,3,4,5,7,9],[6,8]] => [[1,2,3,4,5,6,8],[7,9]] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,8,7,1,9] => [[1,2,4,6,9],[3,5,7],[8]] => [[1,2,3,5,7],[4,6,8],[9]] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => [[1,2,4,6,8],[3,5,7,9],[10]] => [[1,2,3,5,7,9],[4,6,8,10]] => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => [[1,2,3,5,7,9],[4,6,8,10]] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,10,8,9,1] => [[1,2,3,4,5,6,7,9],[8],[10]] => [[1,2,3,4,5,6,7,8,10],[9]] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,2,3,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => [[1,2,4,5,6,7,8,9,10],[3]] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,3,2,4,5,6,7,8,9,1] => [[1,4,5,6,7,8,9],[2],[3],[10]] => [[1,2,5,6,7,8,9,10],[3],[4]] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1,10] => [[1,3,4,5,6,7,8,10],[2],[9]] => [[1,2,4,5,6,7,8,9],[3],[10]] => 8
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [[1,2,3,4,5,6],[7],[8],[9]] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,9,4] => [[1,4,5,6,7,8],[2,9],[3]] => [[1,2,5,6,7,8,9],[3],[4]] => 7
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,9,5] => [[1,5,6,7,8],[2,9],[3],[4]] => [[1,2,6,7,8,9],[3],[4],[5]] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => [[1,3,4,5,6,7,8,9],[2,10]] => [[1,2,4,5,6,7,8,9,10],[3]] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [[1,2,3,4,5,6,7,9],[8]] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,7,9,8,4] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,6,8,9,7,10] => [[1,2,3,4,5,6,7,8,10],[9]] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [[1,2,3,4,5,6,7,9],[8]] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,2,10,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => [[1,2,4],[3,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,9,4] => [[1,3,4,5,6,7,8],[2,9]] => [[1,2,4,5,6,7,8,9],[3]] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [[1,2,3,4,5,6,7,9],[8,10]] => [[1,2,3,4,5,6,7,8,10],[9]] => 9
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => [[1,2,3,4,6,7,8,9,10],[5]] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [[1,2,3,4,5,6,7,8,10],[9]] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,3,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => [[1,2,3,4,5,6,8,9,10],[7]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,6,8,10,9,7] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,7,8,4,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => [[1,2,3,4,5,6,7,8,10],[9]] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,7,10,9,8,5] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,10,1] => [[1,3,5,7,9],[2,4,6,8],[10]] => [[1,2,4,6,8,10],[3,5,7,9]] => 6
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,9,8,1,10] => [[1,3,5,7,10],[2,4,6,8],[9]] => [[1,2,4,6,8],[3,5,7,9],[10]] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,2,1,7,8,9,6] => [[1,6,7,8],[2,9],[3],[4],[5]] => [[1,2,7,8,9],[3],[4],[5],[6]] => 5
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,2,8,7,6,5,4,1,9] => [[1,3,9],[2,4],[5],[6],[7],[8]] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,10,1] => [[1,8,9],[2],[3],[4],[5],[6],[7],[10]] => [[1,2,9,10],[3],[4],[5],[6],[7],[8]] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,10,1] => [[1,7,8,9],[2],[3],[4],[5],[6],[10]] => [[1,2,8,9,10],[3],[4],[5],[6],[7]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,8,10,7] => [[1,3,5,7,9],[2,4,6,8],[10]] => [[1,2,4,6,8,10],[3,5,7,9]] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,7,6,9,8,10,5] => [[1,3,5,7,9],[2,4,6,8],[10]] => [[1,2,4,6,8,10],[3,5,7,9]] => 6
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,9,8,10,3] => [[1,3,5,7,9],[2,4,6,8],[10]] => [[1,2,4,6,8,10],[3,5,7,9]] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [[1,2,4,6,8,9],[3,5,7,10]] => [[1,2,3,5,7,9,10],[4,6,8]] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => [[1,2,3,4,5,6,7,10],[8],[9]] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,9,8,5] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,9,8,3] => [[1,2,3,5,7],[4,6,8],[9]] => [[1,2,3,4,6,8],[5,7,9]] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,10,9,2] => [[1,2,4,6,8],[3,5,7,9],[10]] => [[1,2,3,5,7,9],[4,6,8,10]] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,4,5,7,8,9,10,6] => [[1,3,4,5,6,7,8,9],[2,10]] => [[1,2,4,5,6,7,8,9,10],[3]] => 9
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,10,4,5,6,7,8,9,1] => [[1,3,5,6,7,8,9],[2,4],[10]] => [[1,2,4,6,7,8,9,10],[3,5]] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => [[1,2,4,6,8,10,12],[3,5,7,9,11]] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8,10] => [[1,2,3,4,5,6,8,10],[7,9]] => [[1,2,3,4,5,6,7,9],[8,10]] => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,10,9] => [[1,2,3,5,7,9],[4,6,8,10]] => [[1,2,3,4,6,8,10],[5,7,9]] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,5,4,3,2,1,9,10,8] => [[1,8,9],[2,10],[3],[4],[5],[6],[7]] => [[1,2,9,10],[3],[4],[5],[6],[7],[8]] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7,9] => [[1,2,3,5,7,9],[4,6,8]] => [[1,2,3,4,6,8],[5,7,9]] => 6
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,10,9,8,1] => [[1,4,7],[2,5,8],[3,6,9],[10]] => [[1,2,5,8],[3,6,9],[4,7,10]] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,7,1,9,10,8] => [[1,2,3,4,5,6,8,9],[7,10]] => [[1,2,3,4,5,6,7,9,10],[8]] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,8,10,9,5] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,5,7,8,10,9,6] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7,9] => [[1,2,3,5,7,9],[4,6,8]] => [[1,2,3,4,6,8],[5,7,9]] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]] => [[1,2,3,4,5,7,9],[6,8,10]] => 7
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]] => [[1,2,3,4,5,7,9],[6,8,10]] => 7
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,10,9,8,7,6,5,3] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,10,9] => [[1,2,3,4,5,7,9],[6,8,10]] => [[1,2,3,4,5,6,8,10],[7,9]] => 8
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,10,9] => [[1,2,3,5,7,9],[4,6,8,10]] => [[1,2,3,4,6,8,10],[5,7,9]] => 7
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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:
2,3 2,8,4 2,15,20,5 2,24,60,40,6 2,35,140,175,70,7
$F_{1} = q$
$F_{2} = 2\ q^{2}$
$F_{3} = 2\ q^{2} + 3\ q^{3}$
$F_{4} = 2\ q^{2} + 8\ q^{3} + 4\ q^{4}$
$F_{5} = 2\ q^{2} + 15\ q^{3} + 20\ q^{4} + 5\ q^{5}$
$F_{6} = 2\ q^{2} + 24\ q^{3} + 60\ q^{4} + 40\ q^{5} + 6\ q^{6}$
$F_{7} = 2\ q^{2} + 35\ q^{3} + 140\ q^{4} + 175\ q^{5} + 70\ q^{6} + 7\ q^{7}$
Description
The number of ascents of a standard tableau.
Entry $i$ of a standard Young tableau is an ascent if $i+1$ appears to the right or above $i$ in the tableau (with respect to the English notation for tableaux).
Entry $i$ of a standard Young tableau is an ascent if $i+1$ appears to the right or above $i$ in the tableau (with respect to the English notation for tableaux).
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
catabolism
Description
Remove the first row of the standard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording 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 recording 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 recording tableau.
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