Identifier
-
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
St000744: Standard tableaux ⟶ ℤ
Values
[1,0,1,0] => [1,2] => [1,1] => [[1],[2]] => 1
[1,1,0,0] => [2,1] => [2] => [[1,2]] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,1,1] => [[1],[2],[3]] => 2
[1,0,1,1,0,0] => [1,3,2] => [2,1] => [[1,3],[2]] => 1
[1,1,0,0,1,0] => [2,1,3] => [2,1] => [[1,3],[2]] => 1
[1,1,0,1,0,0] => [2,3,1] => [3] => [[1,2,3]] => 2
[1,1,1,0,0,0] => [3,2,1] => [2,1] => [[1,3],[2]] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,1,1,1] => [[1],[2],[3],[4]] => 3
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [2,1,1] => [[1,4],[2],[3]] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [2,1,1] => [[1,4],[2],[3]] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,1] => [[1,3,4],[2]] => 2
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [2,1,1] => [[1,4],[2],[3]] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,1] => [[1,4],[2],[3]] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,2] => [[1,2],[3,4]] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1] => [[1,3,4],[2]] => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4] => [[1,2,3,4]] => 3
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [3,1] => [[1,3,4],[2]] => 2
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,1,1] => [[1,4],[2],[3]] => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,1] => [[1,3,4],[2]] => 2
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,1,1] => [[1,4],[2],[3]] => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [2,2] => [[1,2],[3,4]] => 2
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 4
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [3,1,1] => [[1,4,5],[2],[3]] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [2,2,1] => [[1,3],[2,5],[4]] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,1,1] => [[1,4,5],[2],[3]] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [4,1] => [[1,3,4,5],[2]] => 3
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [3,1,1] => [[1,4,5],[2],[3]] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [3,1,1] => [[1,4,5],[2],[3]] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [2,2,1] => [[1,3],[2,5],[4]] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,2,1] => [[1,3],[2,5],[4]] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,2,1] => [[1,3],[2,5],[4]] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,2] => [[1,2,5],[3,4]] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,2,1] => [[1,3],[2,5],[4]] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,1,1] => [[1,4,5],[2],[3]] => 2
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2] => [[1,2,5],[3,4]] => 2
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1] => [[1,3,4,5],[2]] => 3
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5] => [[1,2,3,4,5]] => 4
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [4,1] => [[1,3,4,5],[2]] => 3
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,1,1] => [[1,4,5],[2],[3]] => 2
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [4,1] => [[1,3,4,5],[2]] => 3
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [3,1,1] => [[1,4,5],[2],[3]] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [3,2] => [[1,2,5],[3,4]] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,2,1] => [[1,3],[2,5],[4]] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,1,1] => [[1,4,5],[2],[3]] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [4,1] => [[1,3,4,5],[2]] => 3
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [3,1,1] => [[1,4,5],[2],[3]] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [3,1,1] => [[1,4,5],[2],[3]] => 2
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [2,2,1] => [[1,3],[2,5],[4]] => 2
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [2,2,1] => [[1,3],[2,5],[4]] => 2
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [3,2] => [[1,2,5],[3,4]] => 2
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [2,2,1] => [[1,3],[2,5],[4]] => 2
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [3,2] => [[1,2,5],[3,4]] => 2
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [5,1] => [[1,3,4,5,6],[2]] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
>>> Load all 1564 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,2,2] => [[1,2],[3,4],[5,6]] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [4,2] => [[1,2,5,6],[3,4]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,2,2] => [[1,2],[3,4],[5,6]] => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,3] => [[1,2,3],[4,5,6]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,2] => [[1,2,5,6],[3,4]] => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1] => [[1,3,4,5,6],[2]] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6] => [[1,2,3,4,5,6]] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [5,1] => [[1,3,4,5,6],[2]] => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [5,1] => [[1,3,4,5,6],[2]] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [4,2] => [[1,2,5,6],[3,4]] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [5,1] => [[1,3,4,5,6],[2]] => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [4,2] => [[1,2,5,6],[3,4]] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [3,3] => [[1,2,3],[4,5,6]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [5,1] => [[1,3,4,5,6],[2]] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [2,2,2] => [[1,2],[3,4],[5,6]] => 3
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,2] => [[1,2,5,6],[3,4]] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [2,2,2] => [[1,2],[3,4],[5,6]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [3,3] => [[1,2,3],[4,5,6]] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [4,2] => [[1,2,5,6],[3,4]] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [2,2,2] => [[1,2],[3,4],[5,6]] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [6,1] => [[1,3,4,5,6,7],[2]] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [5,2] => [[1,2,5,6,7],[3,4]] => 4
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [4,3] => [[1,2,3,7],[4,5,6]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,3] => [[1,2,3,7],[4,5,6]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,2] => [[1,2,5,6,7],[3,4]] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,1] => [[1,3,4,5,6,7],[2]] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7] => [[1,2,3,4,5,6,7]] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [6,1] => [[1,3,4,5,6,7],[2]] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [5,2] => [[1,2,5,6,7],[3,4]] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [6,1] => [[1,3,4,5,6,7],[2]] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [5,2] => [[1,2,5,6,7],[3,4]] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [4,3] => [[1,2,3,7],[4,5,6]] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [6,1] => [[1,3,4,5,6,7],[2]] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [5,2] => [[1,2,5,6,7],[3,4]] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [4,3] => [[1,2,3,7],[4,5,6]] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [4,3] => [[1,2,3,7],[4,5,6]] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [6,1] => [[1,3,4,5,6,7],[2]] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [5,2] => [[1,2,5,6,7],[3,4]] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [4,3] => [[1,2,3,7],[4,5,6]] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [4,3] => [[1,2,3,7],[4,5,6]] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [5,2] => [[1,2,5,6,7],[3,4]] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,8,4,6,7,5,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,8,5,4,7,6,3] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,4,5,2,8,7] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,8,4,6,5,7,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,8,6,7,5] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,8,3,5,4,7,6,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8,3,5,6,7,4,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7,4,5,3,6,8,2] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8,5,4,3,7,6,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [2,2,2,2] => [[1,2],[3,4],[5,6],[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] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 4
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 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] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,7,5,6,4,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [8] => [[1,2,3,4,5,6,7,8]] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,7,5,6,8,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 5
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,4,5,8,7,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 5
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,7,5,4,6,8,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 4
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,8,6,5,7,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,3,4,8,7,6,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,6,3,5,4,7,8,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,8,3,7,5,6,4,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,6,4,3,5,7,8,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,4,5,3,7,8,1] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 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] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,8,5,4,3,7,6,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,5,4,6,7,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,8,7,4,5,6,3,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,7,5,6,8,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,2,3,1,5,8,7,6] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,3,1,6,5,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,2,3,1,7,6,5,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,2,3,5,1,6,8,7] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,2,3,7,5,6,1,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8,2,3,4,7,6,5,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [6,2,3,5,4,7,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8,2,3,5,4,7,6,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8,2,3,5,6,7,4,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8,2,3,5,7,6,4,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8,2,3,7,6,5,4,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [5,2,4,3,7,6,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8,2,4,3,7,6,5,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8,2,4,5,6,7,3,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8,2,4,7,5,6,3,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,6,4,5,3,1,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,2,6,5,4,3,1,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 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] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [6,3,2,4,5,7,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8,3,2,4,6,5,7,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8,3,2,4,7,6,5,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 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] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 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] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,3,4,2,7,6,8,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 5
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 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] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8,3,7,4,5,6,2,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [6,4,3,2,5,8,7,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8,4,3,2,5,7,6,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,4,3,2,6,5,1,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8,4,3,2,6,5,7,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8,4,3,2,6,7,5,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 4
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8,6,3,5,4,2,7,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[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] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[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] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 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] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 4
[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] => [9] => [[1,2,3,4,5,6,7,8,9]] => 8
[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] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,9,7,8,1] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6
[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] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,1] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,5,8,6,7,9,1] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,5,8,7,6,9,1] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 6
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,9,7,8,6,1] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,1] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,4,7,5,6,8,9,1] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,9,4,5,6,7,8,3,1] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 5
[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] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7
[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] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6
[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] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,3,4,5,6,7,8,2,1] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 6
[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] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6
[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] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6
[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] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6
[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] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 6
[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] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 6
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 5
[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] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 5
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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:
3,2 6,6,2 10,25,5,2 15,80,29,6,2 21,231,140,28,7,2
$F_{2} = 2\ q$
$F_{3} = 3\ q + 2\ q^{2}$
$F_{4} = 6\ q + 6\ q^{2} + 2\ q^{3}$
$F_{5} = 10\ q + 25\ q^{2} + 5\ q^{3} + 2\ q^{4}$
$F_{6} = 15\ q + 80\ q^{2} + 29\ q^{3} + 6\ q^{4} + 2\ q^{5}$
$F_{7} = 21\ q + 231\ q^{2} + 140\ q^{3} + 28\ q^{4} + 7\ q^{5} + 2\ q^{6}$
Description
The length of the path to the largest entry in a standard Young tableau.
Map
reading tableau
Description
Return the RSK recording tableau of the reading word of the (standard) tableau $T$ labeled down (in English convention) each column to the shape of a partition.
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
cycle type
Description
The cycle type of a permutation as a partition.
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