Identifier
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00294: Standard tableaux —peak composition⟶ Integer compositions
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00294: Standard tableaux —peak composition⟶ Integer compositions
Images
[1,0] => [1] => [[1]] => [1]
[1,0,1,0] => [2,1] => [[1],[2]] => [2]
[1,1,0,0] => [1,2] => [[1,2]] => [2]
[1,0,1,0,1,0] => [2,3,1] => [[1,3],[2]] => [3]
[1,0,1,1,0,0] => [2,1,3] => [[1,3],[2]] => [3]
[1,1,0,0,1,0] => [1,3,2] => [[1,2],[3]] => [2,1]
[1,1,0,1,0,0] => [3,1,2] => [[1,2],[3]] => [2,1]
[1,1,1,0,0,0] => [1,2,3] => [[1,2,3]] => [3]
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [[1,3,4],[2]] => [4]
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [[1,3,4],[2]] => [4]
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [[1,3],[2,4]] => [3,1]
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [[1,3],[2,4]] => [3,1]
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [[1,3,4],[2]] => [4]
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [[1,2,4],[3]] => [2,2]
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [[1,2,4],[3]] => [2,2]
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [[1,2],[3,4]] => [2,2]
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [[1,2],[3,4]] => [2,2]
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [[1,2,4],[3]] => [2,2]
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [[1,2,3],[4]] => [3,1]
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [[1,2,3],[4]] => [3,1]
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [[1,2,3],[4]] => [3,1]
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [[1,2,3,4]] => [4]
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => [[1,3,4,5],[2]] => [5]
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [[1,3,4,5],[2]] => [5]
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [[1,3,4],[2,5]] => [4,1]
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [[1,3,4],[2,5]] => [4,1]
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [[1,3,4,5],[2]] => [5]
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [[1,3,5],[2,4]] => [3,2]
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [[1,3,5],[2,4]] => [3,2]
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [[1,3,5],[2,4]] => [3,2]
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [[1,3,5],[2,4]] => [3,2]
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [[1,3,5],[2,4]] => [3,2]
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [[1,3,4],[2,5]] => [4,1]
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [[1,3,4],[2,5]] => [4,1]
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [[1,3,4],[2,5]] => [4,1]
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [[1,3,4,5],[2]] => [5]
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [[1,2,4,5],[3]] => [2,3]
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [[1,2,4,5],[3]] => [2,3]
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [[1,2,4],[3,5]] => [2,2,1]
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [[1,2,4],[3,5]] => [2,2,1]
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [[1,2,4,5],[3]] => [2,3]
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [[1,2,5],[3,4]] => [2,3]
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [[1,2,5],[3,4]] => [2,3]
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [[1,2,5],[3,4]] => [2,3]
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [[1,2,5],[3,4]] => [2,3]
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [[1,2,5],[3,4]] => [2,3]
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [[1,2,4],[3,5]] => [2,2,1]
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [[1,2,4],[3,5]] => [2,2,1]
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [[1,2,4],[3,5]] => [2,2,1]
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [[1,2,4,5],[3]] => [2,3]
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [[1,2,3,5],[4]] => [3,2]
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [[1,2,3,5],[4]] => [3,2]
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [[1,2,3],[4,5]] => [3,2]
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [[1,2,3],[4,5]] => [3,2]
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [[1,2,3,5],[4]] => [3,2]
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [[1,2,3],[4,5]] => [3,2]
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [[1,2,3],[4,5]] => [3,2]
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [[1,2,3],[4,5]] => [3,2]
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [[1,2,3,5],[4]] => [3,2]
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [[1,2,3,4],[5]] => [4,1]
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [[1,2,3,4],[5]] => [4,1]
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [[1,2,3,4],[5]] => [4,1]
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [[1,2,3,4],[5]] => [4,1]
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [[1,2,3,4,5]] => [5]
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => [[1,3,4,5,6],[2]] => [6]
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [[1,3,4,5,6],[2]] => [6]
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [[1,3,4,5],[2,6]] => [5,1]
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [[1,3,4,5],[2,6]] => [5,1]
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [[1,3,4,5,6],[2]] => [6]
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [[1,3,4,6],[2,5]] => [4,2]
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [[1,3,4,6],[2,5]] => [4,2]
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [[1,3,4,6],[2,5]] => [4,2]
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [[1,3,4,6],[2,5]] => [4,2]
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [[1,3,4,6],[2,5]] => [4,2]
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [[1,3,4,5],[2,6]] => [5,1]
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [[1,3,4,5],[2,6]] => [5,1]
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [[1,3,4,5],[2,6]] => [5,1]
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [[1,3,4,5,6],[2]] => [6]
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [[1,3,5,6],[2,4]] => [3,3]
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [[1,3,5,6],[2,4]] => [3,3]
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => [3,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [[1,3,5],[2,4,6]] => [3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => [3,3]
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [[1,3,5,6],[2,4]] => [3,3]
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [[1,3,5,6],[2,4]] => [3,3]
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [[1,3,5,6],[2,4]] => [3,3]
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [[1,3,5,6],[2,4]] => [3,3]
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [[1,3,5,6],[2,4]] => [3,3]
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [[1,3,5],[2,4,6]] => [3,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [[1,3,5],[2,4,6]] => [3,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [[1,3,5],[2,4,6]] => [3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [[1,3,5,6],[2,4]] => [3,3]
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [[1,3,4,6],[2,5]] => [4,2]
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => [4,2]
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [[1,3,4],[2,5,6]] => [4,2]
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [[1,3,4],[2,5,6]] => [4,2]
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [[1,3,4,6],[2,5]] => [4,2]
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [[1,3,4],[2,5,6]] => [4,2]
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [[1,3,4],[2,5,6]] => [4,2]
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [[1,3,4],[2,5,6]] => [4,2]
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [[1,3,4,6],[2,5]] => [4,2]
>>> Load all 2076 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [[1,3,4,5],[2,6]] => [5,1]
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [[1,3,4,5],[2,6]] => [5,1]
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [[1,3,4,5],[2,6]] => [5,1]
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [[1,3,4,5],[2,6]] => [5,1]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => [6]
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [[1,2,4,5,6],[3]] => [2,4]
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [[1,2,4,5,6],[3]] => [2,4]
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [[1,2,4,5],[3,6]] => [2,3,1]
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [[1,2,4,5],[3,6]] => [2,3,1]
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [[1,2,4,5,6],[3]] => [2,4]
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [[1,2,4,6],[3,5]] => [2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [[1,2,4,6],[3,5]] => [2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [[1,2,4,6],[3,5]] => [2,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [[1,2,4,6],[3,5]] => [2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [[1,2,4,6],[3,5]] => [2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [[1,2,4,5],[3,6]] => [2,3,1]
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [[1,2,4,5],[3,6]] => [2,3,1]
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [[1,2,4,5],[3,6]] => [2,3,1]
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => [2,4]
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [[1,2,5,6],[3,4]] => [2,4]
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [[1,2,5,6],[3,4]] => [2,4]
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [[1,2,5],[3,4,6]] => [2,3,1]
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [[1,2,5],[3,4,6]] => [2,3,1]
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [[1,2,5,6],[3,4]] => [2,4]
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [[1,2,5,6],[3,4]] => [2,4]
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [[1,2,5,6],[3,4]] => [2,4]
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [[1,2,5,6],[3,4]] => [2,4]
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [[1,2,5,6],[3,4]] => [2,4]
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [[1,2,5,6],[3,4]] => [2,4]
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [[1,2,5],[3,4,6]] => [2,3,1]
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [[1,2,5],[3,4,6]] => [2,3,1]
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [[1,2,5],[3,4,6]] => [2,3,1]
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [[1,2,5,6],[3,4]] => [2,4]
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [[1,2,4,6],[3,5]] => [2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [[1,2,4,6],[3,5]] => [2,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [[1,2,4],[3,5,6]] => [2,2,2]
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [[1,2,4],[3,5,6]] => [2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [[1,2,4,6],[3,5]] => [2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [[1,2,4],[3,5,6]] => [2,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [[1,2,4],[3,5,6]] => [2,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [[1,2,4],[3,5,6]] => [2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [[1,2,4,6],[3,5]] => [2,2,2]
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [[1,2,4,5],[3,6]] => [2,3,1]
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [[1,2,4,5],[3,6]] => [2,3,1]
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [[1,2,4,5],[3,6]] => [2,3,1]
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [[1,2,4,5],[3,6]] => [2,3,1]
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [[1,2,4,5,6],[3]] => [2,4]
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [[1,2,3,5,6],[4]] => [3,3]
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [[1,2,3,5,6],[4]] => [3,3]
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [[1,2,3,5],[4,6]] => [3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [[1,2,3,5],[4,6]] => [3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => [3,3]
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [[1,2,3,6],[4,5]] => [3,3]
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [[1,2,3,6],[4,5]] => [3,3]
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [[1,2,3,6],[4,5]] => [3,3]
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [[1,2,3,6],[4,5]] => [3,3]
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [[1,2,3,6],[4,5]] => [3,3]
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [[1,2,3,5],[4,6]] => [3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [[1,2,3,5],[4,6]] => [3,2,1]
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [[1,2,3,5],[4,6]] => [3,2,1]
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [[1,2,3,5,6],[4]] => [3,3]
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [[1,2,3,6],[4,5]] => [3,3]
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [[1,2,3,6],[4,5]] => [3,3]
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [[1,2,3],[4,5,6]] => [3,3]
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => [[1,2,3],[4,5,6]] => [3,3]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [[1,2,3,6],[4,5]] => [3,3]
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [[1,2,3],[4,5,6]] => [3,3]
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [[1,2,3],[4,5,6]] => [3,3]
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [[1,2,3],[4,5,6]] => [3,3]
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [[1,2,3,6],[4,5]] => [3,3]
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [[1,2,3,5],[4,6]] => [3,2,1]
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [[1,2,3,5],[4,6]] => [3,2,1]
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [[1,2,3,5],[4,6]] => [3,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [[1,2,3,5],[4,6]] => [3,2,1]
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [[1,2,3,5,6],[4]] => [3,3]
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [[1,2,3,4,6],[5]] => [4,2]
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => [4,2]
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [[1,2,3,4],[5,6]] => [4,2]
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [[1,2,3,4],[5,6]] => [4,2]
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [[1,2,3,4,6],[5]] => [4,2]
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [[1,2,3,4],[5,6]] => [4,2]
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [[1,2,3,4],[5,6]] => [4,2]
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [[1,2,3,4],[5,6]] => [4,2]
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [[1,2,3,4,6],[5]] => [4,2]
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [[1,2,3,4],[5,6]] => [4,2]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [[1,2,3,4],[5,6]] => [4,2]
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [[1,2,3,4],[5,6]] => [4,2]
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [[1,2,3,4],[5,6]] => [4,2]
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [[1,2,3,4,6],[5]] => [4,2]
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => [5,1]
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [[1,2,3,4,5],[6]] => [5,1]
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [[1,2,3,4,5],[6]] => [5,1]
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [[1,2,3,4,5],[6]] => [5,1]
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [[1,2,3,4,5],[6]] => [5,1]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => [6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2]] => [7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7] => [[1,3,4,5,6,7],[2]] => [7]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => [[1,3,4,5,6,7],[2]] => [7]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [[1,3,4,5,6,7],[2]] => [7]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,7,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [[1,3,4,5,6,7],[2]] => [7]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,7,3,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,7] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,1,7,3] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,1,3,7] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,1,3,7,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,7,1,3,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,7,3,5] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5,7] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,6,1,3,7,5] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,5,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,5,1,3,6,7,4] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,5,1,3,6,4,7] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,5,1,6,7,3,4] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,4,7] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,6,1,3,7,4] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,5,6,1,7,3,4] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => [[1,3,4,7],[2,5,6]] => [4,3]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1,3,4,7,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,5,1,3,7,4,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,4,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,6,1,3,4,7,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6,1,3,7,4,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => [[1,3,4,5],[2,6,7]] => [5,2]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]] => [7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3]] => [2,5]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [[1,2,4,5,6,7],[3]] => [2,5]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [[1,2,4,5,6,7],[3]] => [2,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [[1,2,4,5,6,7],[3]] => [2,5]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => [2,5]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,2,7] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,5,7,2,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,5,2,6,7] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,6,2,5,7] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,7,2,5,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,6,2,7] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,7,2,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,6,7] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,1,6,7,2] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,7] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,2] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,2] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,1,2,7,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5,7] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,6,1,2,7,5] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => [[1,2,5,7],[3,4,6]] => [2,3,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,5,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => [[1,2,5,6],[3,4,7]] => [2,4,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [[1,2,5,6,7],[3,4]] => [2,5]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,6,7,2,4] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,6,2,4,7] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,7,2,4,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,4,6,7] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,5,1,2,6,7,4] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,6,4,7] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,4,7] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,5,6,1,2,7,4] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,5,6,1,7,2,4] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => [[1,2,4,7],[3,5,6]] => [2,2,3]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,7,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,7,4,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,4,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,7,2,4,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,4,5,7] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1,2,4,7,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,6,1,2,7,4,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => [[1,2,4,5],[3,6,7]] => [2,3,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,4,5,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => [2,5]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [[1,2,3,5,6,7],[4]] => [3,4]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [[1,2,3,5,6,7],[4]] => [3,4]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [[1,2,3,5,6,7],[4]] => [3,4]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => [3,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [[1,2,3,5,6,7],[4]] => [3,4]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,6,7,3] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,6,3,7] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,7,3,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,3,6,7] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,6,2,3,7] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,7,2,3,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,3,6,7] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,1,2,6,7,3] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,6,3,7] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,1,2,3] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [[1,2,3,7],[4,5,6]] => [3,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,1,2,3,7,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,1,2,7,3,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => [[1,2,3,6],[4,5,7]] => [3,3,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => [[1,2,3,6,7],[4,5]] => [3,4]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,6,7,3,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5,7] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5,7] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => [[1,2,3,5],[4,6,7]] => [3,2,2]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,2,7,3,5,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,3,5,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [[1,2,3,5,6,7],[4]] => [3,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [[1,2,3,4,6,7],[5]] => [4,3]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [[1,2,3,4,6,7],[5]] => [4,3]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => [4,3]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [[1,2,3,4,6,7],[5]] => [4,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [[1,2,3,4,6,7],[5]] => [4,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,2,3,6,7,4] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,1,2,3,6,4,7] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,2,6,7,3,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,1,2,6,3,4,7] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,3,4,7] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,1,2,3,4] => [[1,2,3,4],[5,6,7]] => [4,3]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => [[1,2,3,4,7],[5,6]] => [4,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,2,3,7,4,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,1,2,7,3,4,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,3,4,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => [[1,2,3,4,6,7],[5]] => [4,3]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,7],[6]] => [5,2]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => [5,2]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [[1,2,3,4,5,7],[6]] => [5,2]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [[1,2,3,4,5,7],[6]] => [5,2]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [[1,2,3,4,5,7],[6]] => [5,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,1,2,3,7,4,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,1,2,7,3,4,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => [[1,2,3,4,5],[6,7]] => [5,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => [[1,2,3,4,5,7],[6]] => [5,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => [6,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,6],[7]] => [6,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [[1,2,3,4,5,6],[7]] => [6,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [[1,2,3,4,5,6],[7]] => [6,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [[1,2,3,4,5,6],[7]] => [6,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7]] => [6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => [7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,1,8] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,8,1,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,1,7,8] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,8,6] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,7,1,8,6] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,7,8,1,6] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,1,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,1,8,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,8,1,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,5] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,4,1,6,7,5,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,8,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,1,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,4,6,1,7,8,5] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,1,5] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,4,6,7,1,5,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,8,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,4,6,8,1,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,4,1,5,7,8,6] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,4,1,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,1,7,5,8,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,1,7,8,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,4,1,7,5,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,4,7,1,5,8,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,4,7,1,8,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,7,8,1,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,4,1,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,4,1,5,8,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,4] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,5,6,7,4,8] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,5,6,8,4,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,5,6,4,7,8] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => [[1,3,4,6,8],[2,5,7]] => [4,2,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,7,8,4,6] => [[1,3,4,6,8],[2,5,7]] => [4,2,2]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,5,4,6,7,8] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,4] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,5,1,6,4,8,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,5,1,6,8,4,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,5,6,1,7,8,4] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,1,4] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,6,7,1,4,8] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,6,1,8,4,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,8,1,4,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6,8] => [[1,3,4,6,8],[2,5,7]] => [4,2,2]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,7,4,8,6] => [[1,3,4,6,8],[2,5,7]] => [4,2,2]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,7,8,1,4,6] => [[1,3,4,6,8],[2,5,7]] => [4,2,2]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6,8] => [[1,3,4,6,8],[2,5,7]] => [4,2,2]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,5,1,4,8,6,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,8,1,4,6,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,1,4,6,7,8] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,5] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,4,6,7,5,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,8] => [[1,3,4,5,8],[2,6,7]] => [5,3]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,4,5] => [[1,3,4,5,8],[2,6,7]] => [5,3]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,4,8,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,1,6,8,4,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,1,6,4,5,7,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,1,4,7,8,5] => [[1,3,4,5,8],[2,6,7]] => [5,3]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,1,7,8,4,5] => [[1,3,4,5,8],[2,6,7]] => [5,3]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,6,7,1,8,4,5] => [[1,3,4,5,8],[2,6,7]] => [5,3]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,6,7,8,1,4,5] => [[1,3,4,5,8],[2,6,7]] => [5,3]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,8,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,6,1,4,8,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,6,1,8,4,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,6,1,4,5,7,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,4,5,7,8,6] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,1,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,4,7,8,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,1,4,7,5,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,7,4,5,8,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,7,8,4,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,1,4,5,8,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,1,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,1,4,8,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,1,8,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,7,3,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,3,8,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,4,5,6,8,3,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,7,3,8,6] => [[1,3,5,6,8],[2,4,7]] => [3,3,2]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,3,6,8,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4,5,8,3,6,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4,5,3,6,7,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,8,5,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,7,8] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,6,3,7,8,5] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,6,3,7,5,8] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,7,3,8,5] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,6,7,8,3,5] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,8,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,8,5,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,8,3,5,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,6,3,5,7,8] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [[1,3,5,6,8],[2,4,7]] => [3,3,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => [[1,3,5,6],[2,4,7,8]] => [3,3,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [[1,3,5,6],[2,4,7,8]] => [3,3,2]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,7,3,5,8,6] => [[1,3,5,6],[2,4,7,8]] => [3,3,2]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,4,7,8,3,5,6] => [[1,3,5,6],[2,4,7,8]] => [3,3,2]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,3,5,6,8,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,3,5,8,6,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,3,8,5,6,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,8,3,5,6,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,5,6,7,3,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,4,1,5,6,3,8,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,5,6,8,3,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,4,1,5,6,3,7,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,5,3,7,8,6] => [[1,3,5,6,8],[2,4,7]] => [3,3,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,8] => [[1,3,5,6,8],[2,4,7]] => [3,3,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,4,1,5,7,3,8,6] => [[1,3,5,6,8],[2,4,7]] => [3,3,2]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,3,6,8,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,4,1,5,8,3,6,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,3,6,7,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,4,5,1,6,7,8,3] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,4,5,1,6,3,8,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,4,5,1,6,8,3,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,4,5,1,6,3,7,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,6,1,7,8,3] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,6,1,7,3,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,1,8,3] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,1,3] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,7,1,3,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,6,1,3,8,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,6,1,8,3,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,6,8,1,3,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,4,5,1,3,7,8,6] => [[1,3,5,6,8],[2,4,7]] => [3,3,2]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6,8] => [[1,3,5,6,8],[2,4,7]] => [3,3,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,4,5,1,7,3,8,6] => [[1,3,5,6,8],[2,4,7]] => [3,3,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,4,5,1,7,8,3,6] => [[1,3,5,6,8],[2,4,7]] => [3,3,2]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6,8] => [[1,3,5,6,8],[2,4,7]] => [3,3,2]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,7,8,1,3,6] => [[1,3,5,6,8],[2,4,7]] => [3,3,2]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,1,3,6,7,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,6,7,8,5] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,8,5,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,6,5,7,8] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,8,5] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,8] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,6,7,3,8,5] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,7,8,3,5] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,8,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,8,3,5,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,6,3,5,7,8] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,6,1,3,7,5,8] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,6,1,7,3,8,5] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,6,7,1,3,8,5] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,6,7,8,1,3,5] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,8,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,8,5,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,6,1,3,5,7,8] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,3,5,7,8,6] => [[1,3,5,6,8],[2,4,7]] => [3,3,2]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,3,7,5,8,6] => [[1,3,5,6],[2,4,7,8]] => [3,3,2]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,3,7,8,5,6] => [[1,3,5,6],[2,4,7,8]] => [3,3,2]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,7,3,5,8,6] => [[1,3,5,6],[2,4,7,8]] => [3,3,2]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,7,3,8,5,6] => [[1,3,5,6],[2,4,7,8]] => [3,3,2]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,7,8,3,5,6] => [[1,3,5,6],[2,4,7,8]] => [3,3,2]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,4,7,1,8,3,5,6] => [[1,3,5,6],[2,4,7,8]] => [3,3,2]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1,3,8,5,6,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1,8,3,5,6,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,8,1,3,5,6,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,4] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,6,4,8,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,8,4,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,7,8,6] => [[1,3,4,6,8],[2,5,7]] => [4,2,2]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,1,3,5,8,4,6,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,1,5,3,6,7,4,8] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7] => [[1,3,4,7],[2,5,6,8]] => [4,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,1,5,3,6,8,4,7] => [[1,3,4,7],[2,5,6,8]] => [4,3,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,1,5,6,3,7,8,4] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,1,5,6,3,7,4,8] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,1,5,6,7,3,8,4] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,3,4] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,1,5,6,7,3,4,8] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,8,7] => [[1,3,4,7],[2,5,6,8]] => [4,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,1,5,6,8,3,4,7] => [[1,3,4,7],[2,5,6,8]] => [4,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,1,5,3,7,4,8,6] => [[1,3,4,6],[2,5,7,8]] => [4,2,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,1,5,3,7,8,4,6] => [[1,3,4,6],[2,5,7,8]] => [4,2,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,5,7,3,4,8,6] => [[1,3,4,6],[2,5,7,8]] => [4,2,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,5,7,3,8,4,6] => [[1,3,4,6],[2,5,7,8]] => [4,2,2]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,5,7,8,3,4,6] => [[1,3,4,6],[2,5,7,8]] => [4,2,2]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6,8] => [[1,3,4,6,8],[2,5,7]] => [4,2,2]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,5,3,4,6,8,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,1,5,3,8,4,6,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,1,5,8,3,4,6,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,5,3,4,6,7,8] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,1,3,6,7,8,4] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,5,1,3,6,4,8,7] => [[1,3,4,7],[2,5,6,8]] => [4,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,5,1,3,6,8,4,7] => [[1,3,4,7],[2,5,6,8]] => [4,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,1,3,6,4,7,8] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,5,1,6,3,7,8,4] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,5,1,6,3,7,4,8] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,1,6,7,3,8,4] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,1,6,7,8,3,4] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,1,6,7,3,4,8] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,5,1,6,3,4,8,7] => [[1,3,4,7],[2,5,6,8]] => [4,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,1,6,8,3,4,7] => [[1,3,4,7],[2,5,6,8]] => [4,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,5,6,1,3,7,8,4] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,5,6,1,3,7,4,8] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,5,6,1,7,8,3,4] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,5,6,7,1,3,8,4] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,5,6,7,1,8,3,4] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,1,3,4] => [[1,3,4,7,8],[2,5,6]] => [4,4]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,5,6,1,3,4,8,7] => [[1,3,4,7],[2,5,6,8]] => [4,3,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,5,6,1,3,8,4,7] => [[1,3,4,7],[2,5,6,8]] => [4,3,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => [[1,3,4,7],[2,5,6,8]] => [4,3,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,7,4,8,6] => [[1,3,4,6],[2,5,7,8]] => [4,2,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,7,8,4,6] => [[1,3,4,6],[2,5,7,8]] => [4,2,2]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,5,1,7,3,4,8,6] => [[1,3,4,6],[2,5,7,8]] => [4,2,2]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,5,1,7,8,3,4,6] => [[1,3,4,6],[2,5,7,8]] => [4,2,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,5,7,1,3,4,8,6] => [[1,3,4,6],[2,5,7,8]] => [4,2,2]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,5,7,1,8,3,4,6] => [[1,3,4,6],[2,5,7,8]] => [4,2,2]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [[1,3,4,6],[2,5,7,8]] => [4,2,2]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,5,1,3,8,4,6,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,5,1,8,3,4,6,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,4,6,7,8] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,5] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,3,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,1,3,6,7,4,8,5] => [[1,3,4,5,8],[2,6,7]] => [5,3]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,6,7,8,4,5] => [[1,3,4,5,8],[2,6,7]] => [5,3]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,1,3,6,4,5,8,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,1,3,6,4,5,7,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [[1,3,4,5,8],[2,6,7]] => [5,3]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,6,3,7,4,8,5] => [[1,3,4,5],[2,6,7,8]] => [5,3]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,6,3,7,8,4,5] => [[1,3,4,5],[2,6,7,8]] => [5,3]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,6,7,3,4,8,5] => [[1,3,4,5],[2,6,7,8]] => [5,3]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,3,4,5] => [[1,3,4,5],[2,6,7,8]] => [5,3]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,8,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,1,6,3,4,8,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,1,6,3,8,4,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,1,6,8,3,4,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,1,3,4,7,8,5] => [[1,3,4,5,8],[2,6,7]] => [5,3]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,1,3,4,7,5,8] => [[1,3,4,5,8],[2,6,7]] => [5,3]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,6,1,3,7,4,8,5] => [[1,3,4,5],[2,6,7,8]] => [5,3]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,1,3,7,8,4,5] => [[1,3,4,5],[2,6,7,8]] => [5,3]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,6,1,7,3,4,8,5] => [[1,3,4,5],[2,6,7,8]] => [5,3]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,6,1,7,3,8,4,5] => [[1,3,4,5],[2,6,7,8]] => [5,3]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,6,1,7,8,3,4,5] => [[1,3,4,5],[2,6,7,8]] => [5,3]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,6,1,7,3,4,5,8] => [[1,3,4,5,8],[2,6,7]] => [5,3]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,6,7,1,3,4,8,5] => [[1,3,4,5],[2,6,7,8]] => [5,3]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,6,7,1,3,8,4,5] => [[1,3,4,5],[2,6,7,8]] => [5,3]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,6,7,1,8,3,4,5] => [[1,3,4,5],[2,6,7,8]] => [5,3]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => [[1,3,4,5],[2,6,7,8]] => [5,3]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,8,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,8,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,6,1,3,8,4,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,6,1,8,3,4,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,6,1,3,4,5,7,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,7,8,6] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,4,7,5,8,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,1,3,4,7,8,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,3,4,7,5,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,1,3,7,4,8,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,1,3,7,8,4,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,7,3,4,5,8,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,1,7,3,4,8,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,1,7,3,8,4,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,7,8,3,4,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,7,1,3,4,5,8,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,7,1,3,8,4,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,7,1,8,3,4,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [[1,3,4,5,6],[2,7,8]] => [6,2]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,3,4,5,8,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,1,3,4,8,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,2] => [[1,2,4,5,6,7,8],[3]] => [2,6]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,2,8] => [[1,2,4,5,6,7,8],[3]] => [2,6]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,6,2,8,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,8,2,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,2,7,8] => [[1,2,4,5,6,7,8],[3]] => [2,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,5,2,7,8,6] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,7,8,2,6] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,5,2,8,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,5,8,2,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [[1,2,4,5,6,7,8],[3]] => [2,6]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,4,2,6,7,8,5] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,6,7,5,8] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,6,2,7,5,8] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,6,7,2,8,5] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,7,2,5,8] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,4,6,8,2,5,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,4,6,2,5,7,8] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,4,2,5,7,8,6] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,4,2,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,2,7,5,8,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,4,2,7,8,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,4,7,8,2,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,2,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,3,4,2,5,8,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,2,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => [2,6]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,6,7,8,4] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,5,6,7,4,8] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,5,6,4,8,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,5,6,4,7,8] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,8,6] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,7,8,4,6] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,5,8,4,6,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,5,2,6,7,4,8] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,5,2,6,8,4,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,5,6,2,7,4,8] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,5,6,7,2,8,4] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,8,2,4] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,6,7,2,4,8] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,5,6,2,4,8,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,5,6,2,8,4,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,6,8,2,4,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,7,4,8,6] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,7,8,4,6] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,7,2,4,8,6] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,7,2,8,4,6] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,7,8,2,4,6] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,5,2,4,6,8,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,5,2,4,8,6,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,2,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,4,6,7,8,5] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,4,6,8,5,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,4,6,5,7,8] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,8] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,3,2,6,7,4,8,5] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,7,8,4,5] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,2,6,7,4,5,8] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,6,8,4,5,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,2,6,4,5,7,8] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,2,7,4,8,5] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,2,7,8,4,5] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,7,4,5,8] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,6,7,8,2,4,5] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,6,2,4,8,5,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,6,2,4,5,7,8] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,3,2,4,5,7,8,6] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,3,2,4,7,5,8,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,4,7,8,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,7,4,8,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,3,2,7,4,5,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,3,7,2,4,5,8,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,3,7,2,4,8,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,3,7,8,2,4,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,3,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,3,2,4,8,5,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,3,2,8,4,5,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => [2,6]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,2] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,2,8] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,5,6,2,8,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,4,5,6,8,2,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,5,2,7,8,6] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6,8] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,5,7,2,8,6] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4,5,7,8,2,6] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4,5,8,2,6,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,2,6,7,8] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,4,2,6,7,5,8] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,8,5,7] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,6,2,7,8,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,6,7,2,8,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,4,6,7,8,2,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,8,7] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,8,5,7] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,4,6,8,2,5,7] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,7,8,6] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,7,5,8,6] => [[1,2,5,6],[3,4,7,8]] => [2,4,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,4,2,7,8,5,6] => [[1,2,5,6],[3,4,7,8]] => [2,4,2]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,4,2,7,5,6,8] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,7,2,5,8,6] => [[1,2,5,6],[3,4,7,8]] => [2,4,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,2,5,8,6,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,4,2,8,5,6,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,1,4,8,2,5,6,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,2,5,6,7,8] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,2] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,5,6,7,2,8] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,4,1,5,6,2,8,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,5,6,8,2,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,4,1,5,6,2,7,8] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6,8] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,4,1,5,7,2,8,6] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,7,8,2,6] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6,8] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,2,8,6,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4,1,5,8,2,6,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4,1,5,2,6,7,8] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,2] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,5,1,6,7,2,8] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,1,6,2,8,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,5,1,6,2,7,8] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,1,7,8,2] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,6,1,7,2,8] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,1,8,2] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,1,2] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,1,2,8] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,6,1,2,8,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,6,1,8,2,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,6,8,1,2,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,5,1,2,7,8,6] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,5,1,7,8,2,6] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,5,7,1,2,8,6] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,5,7,8,1,2,6] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6,8] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,5,1,2,6,8,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,5,1,2,8,6,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,6,7,8,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,6,7,5,8] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,8,5,7] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,6,5,7,8] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,4,1,6,2,7,8,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,6,2,7,5,8] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,4,1,6,7,2,8,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,6,7,8,2,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,4,1,6,7,2,5,8] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,8,7] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,8,5,7] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,8,2,5,7] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,4,6,1,2,7,8,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,4,6,1,2,7,5,8] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,4,6,1,7,2,8,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,4,6,1,7,8,2,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,4,6,7,1,2,8,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,4,6,7,1,8,2,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,6,7,8,1,2,5] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,7,1,2,5,8] => [[1,2,5,7,8],[3,4,6]] => [2,3,3]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,8,7] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,4,1,2,5,7,8,6] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,7,6,8] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,4,1,2,7,5,8,6] => [[1,2,5,6],[3,4,7,8]] => [2,4,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,2,7,8,5,6] => [[1,2,5,6],[3,4,7,8]] => [2,4,2]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,4,1,2,7,5,6,8] => [[1,2,5,6,8],[3,4,7]] => [2,4,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,4,7,1,2,5,8,6] => [[1,2,5,6],[3,4,7,8]] => [2,4,2]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [[1,2,5,6],[3,4,7,8]] => [2,4,2]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => [[1,2,5,6],[3,4,7,8]] => [2,4,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1,2,5,6,8,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1,2,5,8,6,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1,2,8,5,6,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1,8,2,5,6,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,8,1,2,5,6,7] => [[1,2,5,6,7],[3,4,8]] => [2,5,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [[1,2,5,6,7,8],[3,4]] => [2,6]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,5,6,7,8,4] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,5,6,7,4,8] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,5,6,8,4,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,7,4,8,6] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,5,4,6,8,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,5,8,4,6,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,7,8,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,5,2,6,8,4,7] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,5,6,2,7,8,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,5,6,7,2,8,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,5,6,7,8,2,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,5,6,2,4,8,7] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,5,6,2,8,4,7] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,5,6,8,2,4,7] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,5,6,2,4,7,8] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,8,6] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,7,8,4,6] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,7,2,4,8,6] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,7,2,8,4,6] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,7,8,2,4,6] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,5,2,4,8,6,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,5,2,8,4,6,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,5,8,2,4,6,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,5,1,2,6,7,8,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,5,1,2,6,4,8,7] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,5,1,2,6,8,4,7] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,5,1,6,2,7,8,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,5,1,6,2,7,4,8] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,5,1,6,7,2,8,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,5,1,6,7,8,2,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,5,1,6,7,2,4,8] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,5,1,6,8,2,4,7] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,5,1,6,2,4,7,8] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,5,6,1,2,7,8,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,5,6,1,2,7,4,8] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,5,6,1,7,2,8,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,5,6,1,7,8,2,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,5,6,1,7,2,4,8] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,5,6,7,1,2,8,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,5,6,7,1,8,2,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,1,2,4] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,5,6,1,2,4,8,7] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,5,6,1,2,8,4,7] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,5,6,1,2,4,7,8] => [[1,2,4,7,8],[3,5,6]] => [2,2,4]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,7,8,6] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,7,4,8,6] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,7,8,4,6] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,7,8,2,4,6] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,7,1,2,4,8,6] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,5,1,2,4,6,8,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,5,1,2,4,8,6,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,5,1,2,8,4,6,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,5,1,8,2,4,6,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,5,1,2,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,4,6,7,8,5] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,7,5,8] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [3,1,2,6,4,7,8,5] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [3,1,2,6,4,7,5,8] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,6,7,4,8,5] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,2,6,7,8,4,5] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [3,1,2,6,4,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [3,1,2,6,8,4,5,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,7,8,5] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,6,2,7,4,8,5] => [[1,2,4,5],[3,6,7,8]] => [2,3,3]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [3,1,6,7,2,8,4,5] => [[1,2,4,5],[3,6,7,8]] => [2,3,3]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,1,6,7,2,4,5,8] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [3,1,6,2,4,8,5,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,6,8,2,4,5,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,6,1,2,4,7,8,5] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => [[1,2,4,5,8],[3,6,7]] => [2,3,3]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,6,1,2,7,4,8,5] => [[1,2,4,5],[3,6,7,8]] => [2,3,3]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [3,6,1,2,7,8,4,5] => [[1,2,4,5],[3,6,7,8]] => [2,3,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,6,1,7,2,4,8,5] => [[1,2,4,5],[3,6,7,8]] => [2,3,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => [[1,2,4,5],[3,6,7,8]] => [2,3,3]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [3,6,1,7,8,2,4,5] => [[1,2,4,5],[3,6,7,8]] => [2,3,3]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [3,6,7,1,2,4,8,5] => [[1,2,4,5],[3,6,7,8]] => [2,3,3]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [3,6,7,1,2,8,4,5] => [[1,2,4,5],[3,6,7,8]] => [2,3,3]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [[1,2,4,5],[3,6,7,8]] => [2,3,3]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,8,5,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [3,6,1,2,8,4,5,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,6,1,8,2,4,5,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,6,8,1,2,4,5,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,6,1,2,4,5,7,8] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,2,4,5,7,8,6] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,4,7,5,8,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,2,4,7,8,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [3,1,2,4,7,5,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [3,1,2,7,4,8,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,2,7,8,4,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,1,2,7,4,5,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,7,2,4,5,8,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [3,1,7,2,8,4,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,7,8,2,4,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,7,1,2,4,5,8,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [3,7,1,2,4,8,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [3,7,1,2,8,4,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,7,1,8,2,4,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => [[1,2,4,5,6],[3,7,8]] => [2,4,2]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,2,4,5,8,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,2,4,8,5,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,2,8,4,5,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => [2,6]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,3] => [[1,2,3,5,6,7,8],[4]] => [3,5]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,7,3,8] => [[1,2,3,5,6,7,8],[4]] => [3,5]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,4,5,6,3,8,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,6,8,3,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,4,5,6,3,7,8] => [[1,2,3,5,6,7,8],[4]] => [3,5]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,5,3,7,8,6] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,7,3,8,6] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,7,8,3,6] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,4,5,3,8,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,4,5,8,3,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,5] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,6,7,5,8] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,8,3,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,4,3,5,7,8,6] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,3,7,5,8,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,4,3,7,8,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,4,3,7,5,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,7,3,5,8,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,4,7,3,8,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,4,7,8,3,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,3,5,8,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => [3,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,3] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,4,2,5,6,7,3,8] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,4,2,5,6,8,3,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,4,2,5,7,3,8,6] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,4,2,5,7,8,3,6] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,4,2,5,3,6,8,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,4,2,5,8,3,6,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,4,2,5,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,5,2,6,7,8,3] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,5,2,6,7,3,8] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,5,2,6,3,8,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,5,2,6,8,3,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,5,2,6,3,7,8] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,4,5,6,2,7,8,3] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,4,5,6,2,7,3,8] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,2,8,3] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,2,3] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,2,3,8] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,6,8,2,3,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3,7,8] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,4,5,2,3,7,8,6] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6,8] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,5,2,7,3,8,6] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,4,5,2,7,8,3,6] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6,8] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,4,5,7,8,2,3,6] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6,8] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,4,5,2,3,8,6,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,4,5,2,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,6,7,8,5] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,6,7,5,8] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,8] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,7,8,3,5] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,6,7,3,5,8] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,8,3,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,6,3,5,7,8] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,4,6,2,3,7,8,5] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,4,6,2,7,3,8,5] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,6,2,7,8,3,5] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,7,3,5,8] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,4,6,7,2,8,3,5] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,4,6,7,8,2,3,5] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,8,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,8,3,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,6,2,3,5,7,8] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,4,2,3,5,7,8,6] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,4,2,3,7,5,8,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,3,7,8,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2,3,7,5,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,4,2,7,3,5,8,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,7,3,8,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2,7,3,5,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,4,7,2,3,5,8,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,7,2,3,8,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,7,2,8,3,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,7,8,2,3,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,4,2,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,2,3,8,5,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => [3,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,3] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,2,5,6,7,3,8] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,5,6,3,8,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,5,6,8,3,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3,7,8] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,5,3,7,8,6] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6,8] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,5,7,3,8,6] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,5,7,8,3,6] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6,8] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,5,3,8,6,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,1,2,5,8,3,6,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,5,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [[1,2,3,7],[4,5,6,8]] => [3,4,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,5,2,6,8,3,7] => [[1,2,3,7],[4,5,6,8]] => [3,4,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,1,5,2,6,3,7,8] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,5,6,7,2,8,3] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,2,3] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,5,6,2,3,8,7] => [[1,2,3,7],[4,5,6,8]] => [3,4,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [4,1,5,6,2,8,3,7] => [[1,2,3,7],[4,5,6,8]] => [3,4,1]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [4,1,5,6,8,2,3,7] => [[1,2,3,7],[4,5,6,8]] => [3,4,1]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,1,5,6,2,3,7,8] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6,8] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => [[1,2,3,6],[4,5,7,8]] => [3,3,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => [[1,2,3,6],[4,5,7,8]] => [3,3,2]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6,8] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,1,5,7,2,8,3,6] => [[1,2,3,6],[4,5,7,8]] => [3,3,2]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,1,5,2,3,8,6,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,1,5,2,8,3,6,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,1,5,2,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,5,1,2,6,7,8,3] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => [[1,2,3,7],[4,5,6,8]] => [3,4,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [4,5,1,2,6,8,3,7] => [[1,2,3,7],[4,5,6,8]] => [3,4,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,5,1,6,2,7,8,3] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,5,1,6,2,7,3,8] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,5,1,6,7,2,8,3] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,5,1,6,7,8,2,3] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [4,5,1,6,2,3,8,7] => [[1,2,3,7],[4,5,6,8]] => [3,4,1]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [4,5,1,6,8,2,3,7] => [[1,2,3,7],[4,5,6,8]] => [3,4,1]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,1,6,2,3,7,8] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,6,1,2,7,8,3] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,6,1,2,7,3,8] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,1,7,2,8,3] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,6,1,7,8,2,3] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,6,1,7,2,3,8] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,1,2,8,3] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,1,8,2,3] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,1,2,3] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => [[1,2,3,7],[4,5,6,8]] => [3,4,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,6,1,2,8,3,7] => [[1,2,3,7],[4,5,6,8]] => [3,4,1]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [[1,2,3,7],[4,5,6,8]] => [3,4,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [[1,2,3,7],[4,5,6,8]] => [3,4,1]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [[1,2,3,7,8],[4,5,6]] => [3,5]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6,8] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [4,5,1,2,7,8,3,6] => [[1,2,3,6],[4,5,7,8]] => [3,3,2]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6,8] => [[1,2,3,6,8],[4,5,7]] => [3,3,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,5,1,7,2,3,8,6] => [[1,2,3,6],[4,5,7,8]] => [3,3,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [4,5,1,7,2,8,3,6] => [[1,2,3,6],[4,5,7,8]] => [3,3,2]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [4,5,1,7,8,2,3,6] => [[1,2,3,6],[4,5,7,8]] => [3,3,2]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => [[1,2,3,6],[4,5,7,8]] => [3,3,2]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [[1,2,3,6],[4,5,7,8]] => [3,3,2]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [4,5,1,2,3,8,6,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,5,1,2,8,3,6,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,5,1,8,2,3,6,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [[1,2,3,6,7],[4,5,8]] => [3,4,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => [3,5]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,6,7,5,8] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,8,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,6,3,7,8,5] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5,8] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,6,7,3,8,5] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,6,7,3,5,8] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,8,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,6,2,3,7,5,8] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => [[1,2,3,5],[4,6,7,8]] => [3,2,3]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,6,2,7,3,5,8] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,6,7,2,3,8,5] => [[1,2,3,5],[4,6,7,8]] => [3,2,3]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,6,7,8,2,3,5] => [[1,2,3,5],[4,6,7,8]] => [3,2,3]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,6,7,2,3,5,8] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,8,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,8,3,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,8,2,3,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,6,2,3,5,7,8] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [4,6,1,2,7,8,3,5] => [[1,2,3,5],[4,6,7,8]] => [3,2,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [4,6,1,7,2,8,3,5] => [[1,2,3,5],[4,6,7,8]] => [3,2,3]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [4,6,1,7,8,2,3,5] => [[1,2,3,5],[4,6,7,8]] => [3,2,3]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,6,1,7,2,3,5,8] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [4,6,7,1,2,3,8,5] => [[1,2,3,5],[4,6,7,8]] => [3,2,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [4,6,7,1,2,8,3,5] => [[1,2,3,5],[4,6,7,8]] => [3,2,3]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [[1,2,3,5],[4,6,7,8]] => [3,2,3]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [[1,2,3,5],[4,6,7,8]] => [3,2,3]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,6,7,1,2,3,5,8] => [[1,2,3,5,8],[4,6,7]] => [3,2,3]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,8,3,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,8,2,3,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,8,1,2,3,5,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [4,6,1,2,3,5,7,8] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,3,7,5,8,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,3,7,8,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,3,7,5,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,7,3,5,8,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [4,1,2,7,8,3,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,1,2,7,3,5,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,7,2,3,5,8,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [4,1,7,2,3,8,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [4,1,7,2,8,3,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,1,7,8,2,3,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [4,7,1,2,3,5,8,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [4,7,1,2,3,8,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [4,7,1,2,8,3,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,7,1,8,2,3,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,7,8,1,2,3,5,6] => [[1,2,3,5,6],[4,7,8]] => [3,3,2]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [4,1,2,3,5,8,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,8,3,5,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => [3,5]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4] => [[1,2,3,4,6,7,8],[5]] => [4,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,4,8] => [[1,2,3,4,6,7,8],[5]] => [4,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,2,3,5,6,4,8,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,8,4,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,5,6,4,7,8] => [[1,2,3,4,6,7,8],[5]] => [4,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,7,8,6] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,2,3,5,7,4,8,6] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,2,3,5,7,8,4,6] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6,8] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,5,4,6,8,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,5,8,4,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => [4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,4] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,2,5,3,6,4,8,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,2,5,3,6,4,7,8] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,2,5,6,3,7,8,4] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,2,5,6,3,7,4,8] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,2,5,6,7,3,8,4] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,6,7,8,3,4] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,2,5,6,3,4,8,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,2,5,6,3,8,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,7,8,6] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6,8] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,2,5,3,7,4,8,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6,8] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,2,5,7,3,4,8,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,2,5,7,3,8,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,2,5,7,8,3,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,2,5,3,4,6,8,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4,8,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,2,5,3,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => [4,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,5,2,3,6,7,8,4] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,5,2,3,6,7,4,8] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,5,2,3,6,4,8,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,5,2,3,6,8,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,2,3,6,4,7,8] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,5,2,6,3,7,8,4] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,7,8,3,4] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,2,6,7,3,4,8] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,5,2,6,3,4,8,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,3,8,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,2,6,8,3,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,2,6,3,4,7,8] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,5,6,2,3,7,8,4] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,5,6,2,7,8,3,4] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,5,6,7,2,3,8,4] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,6,7,2,8,3,4] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,2,3,4] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,4,8] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,5,6,2,3,4,8,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,6,2,3,8,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,5,6,2,8,3,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,5,6,8,2,3,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,5,6,2,3,4,7,8] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,7,8,6] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,7,4,8,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,7,8,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6,8] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,5,2,7,3,4,8,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,5,2,7,8,3,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6,8] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,5,7,2,3,4,8,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,7,2,3,8,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,5,7,8,2,3,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,5,2,3,4,6,8,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,5,2,3,8,4,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => [4,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,4] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,6,7,4,8] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,1,2,3,6,8,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,6,4,7,8] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,2,6,3,7,8,4] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,1,2,6,3,7,4,8] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,7,3,8,4] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,1,2,6,7,8,3,4] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,1,2,6,7,3,4,8] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,3,4,8,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,1,2,6,3,8,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,1,2,6,8,3,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,2,6,3,4,7,8] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,1,6,2,3,7,4,8] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => [[1,2,3,4],[5,6,7,8]] => [4,4]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,1,6,2,7,3,4,8] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,6,7,2,3,8,4] => [[1,2,3,4],[5,6,7,8]] => [4,4]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [5,1,6,7,2,8,3,4] => [[1,2,3,4],[5,6,7,8]] => [4,4]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,2,3,4] => [[1,2,3,4],[5,6,7,8]] => [4,4]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [5,1,6,2,3,4,8,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [5,1,6,2,3,8,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,1,6,2,8,3,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [5,1,6,2,3,4,7,8] => [[1,2,3,4,7,8],[5,6]] => [4,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,6,1,2,3,7,8,4] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1,2,7,3,8,4] => [[1,2,3,4],[5,6,7,8]] => [4,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [5,6,1,2,7,8,3,4] => [[1,2,3,4],[5,6,7,8]] => [4,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,6,1,7,2,3,8,4] => [[1,2,3,4],[5,6,7,8]] => [4,4]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,6,1,7,8,2,3,4] => [[1,2,3,4],[5,6,7,8]] => [4,4]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,1,7,2,3,4,8] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,6,7,1,2,3,8,4] => [[1,2,3,4],[5,6,7,8]] => [4,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [5,6,7,1,2,8,3,4] => [[1,2,3,4],[5,6,7,8]] => [4,4]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [[1,2,3,4],[5,6,7,8]] => [4,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [[1,2,3,4],[5,6,7,8]] => [4,4]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => [[1,2,3,4,8],[5,6,7]] => [4,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,8,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [5,6,1,2,3,8,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,6,1,2,8,3,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,6,1,8,2,3,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => [[1,2,3,4,7],[5,6,8]] => [4,3,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,7,8,6] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,7,4,8,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,7,8,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,7,3,4,8,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,7,3,8,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,7,8,3,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6,8] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [5,1,7,2,3,4,8,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [5,1,7,2,3,8,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,1,7,8,2,3,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6,8] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,7,1,2,3,4,8,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [5,7,1,2,3,8,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,7,1,2,8,3,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,7,1,8,2,3,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [[1,2,3,4,6],[5,7,8]] => [4,2,2]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6,8] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,1,2,3,4,8,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,8,4,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,1,2,8,3,4,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [5,1,8,2,3,4,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => [4,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,5] => [[1,2,3,4,5,7,8],[6]] => [5,3]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,6,7,5,8] => [[1,2,3,4,5,7,8],[6]] => [5,3]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,6,8,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]] => [5,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,6,4,7,8,5] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,2,3,6,7,4,8,5] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,2,3,6,7,8,4,5] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,2,3,6,7,4,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,6,4,5,8,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,2,3,6,4,8,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,2,3,6,8,4,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [[1,2,3,4,5,7,8],[6]] => [5,3]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,2,6,3,4,7,8,5] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,2,6,3,4,7,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,2,6,3,7,4,8,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,2,6,3,7,8,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,2,6,3,7,4,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,2,6,7,3,8,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,7,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,8,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,2,6,3,4,8,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,3,4,5,7,8] => [[1,2,3,4,5,7,8],[6]] => [5,3]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,6,2,3,4,7,8,5] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,6,2,3,7,4,8,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,3,7,8,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,2,3,7,4,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,6,2,7,3,4,8,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,6,2,7,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,6,2,7,3,4,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,6,7,2,3,4,8,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,7,2,3,8,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,6,7,2,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,6,7,2,3,4,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,8,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,6,2,3,8,4,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,6,2,8,3,4,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,6,2,3,4,5,7,8] => [[1,2,3,4,5,7,8],[6]] => [5,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,7,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,3,7,4,8,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,1,2,3,7,8,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [6,1,2,3,7,4,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,7,3,4,8,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,1,2,7,3,8,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,1,2,7,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [6,1,2,7,3,4,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,7,2,3,4,8,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,1,7,2,3,8,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,1,7,2,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [6,1,7,8,2,3,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [6,1,7,2,3,4,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,7,1,2,3,8,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,7,1,2,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,1,8,2,3,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [[1,2,3,4,5],[6,7,8]] => [5,3]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5,8] => [[1,2,3,4,5,8],[6,7]] => [5,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,8,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,8,4,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [6,1,2,8,3,4,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => [[1,2,3,4,5,7,8],[6]] => [5,3]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,8],[7]] => [6,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8] => [[1,2,3,4,5,6,8],[7]] => [6,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,7,8,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,7,5,6,8] => [[1,2,3,4,5,6,8],[7]] => [6,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,3,7,8,4,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [[1,2,3,4,5,6,8],[7]] => [6,2]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,2,7,3,4,8,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6,8] => [[1,2,3,4,5,6,8],[7]] => [6,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,7,2,3,8,4,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,7,2,8,3,4,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8] => [[1,2,3,4,5,6,8],[7]] => [6,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,1,2,3,8,4,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [7,1,2,8,3,4,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8]] => [6,2]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => [[1,2,3,4,5,6,8],[7]] => [6,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => [7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,7],[8]] => [7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,3,4,8,5,6,7] => [[1,2,3,4,5,6,7],[8]] => [7,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,5,6,7],[8]] => [7,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8]] => [7,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8]] => [7,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8]] => [7,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => [8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => [[1,2,3,4,5,6,7,8],[9]] => [8,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [8,2]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [9,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [1,2,8,3,4,5,6,9,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [7,8,1,2,3,4,5,9,6] => [[1,2,3,4,5,6],[7,8,9]] => [6,3]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,8,9,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2,8,9]] => [7,2]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [9,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [1,2,9,3,4,5,6,7,10,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [8,2]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [8,9,1,2,3,4,5,6,10,7] => [[1,2,3,4,5,6,7],[8,9,10]] => [7,3]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,9,10,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2,9,10]] => [8,2]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [1,2,3,4,8,5,6,9,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,1,3,4,5,9,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [2,8,1,3,9,4,5,6,7] => [[1,3,4,5,6,7],[2,8,9]] => [7,2]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [2,1,8,9,3,4,5,6,7] => [[1,3,4,5,6,7],[2,8,9]] => [7,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,8,6,9,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,8,1,2,3,4,9,5] => [[1,2,3,4,5],[6,7,8,9]] => [5,4]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,9] => [[1,2,3,4,5,6,7,9],[8]] => [7,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,9,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,7,8,9,1,3,4,5,6] => [[1,3,4,5,6],[2,7,8,9]] => [6,3]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => [2,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [1,2,3,4,5,9,6,7,10,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [8,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,8,9,7] => [[1,2,3,4,5,6,7,9],[8]] => [7,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [7,1,2,3,4,8,5,9,6] => [[1,2,3,4,5,6],[7,8,9]] => [6,3]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,8,6,9] => [[1,2,3,4,5,6,9],[7,8]] => [6,3]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,8,9,10,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2,8,9,10]] => [7,3]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,6,9,7,10,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [8,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8,10] => [[1,2,3,4,5,6,7,8,10],[9]] => [8,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,8,9,6] => [[1,2,3,4,5,6,9],[7,8]] => [6,3]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [2,8,1,3,4,5,6,9,7] => [[1,3,4,5,6,7],[2,8,9]] => [7,2]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,7,10,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [9,1]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,9,1,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]] => [2,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,9,10,8] => [[1,2,3,4,5,6,7,8,10],[9]] => [8,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1,2,3,4,5,9,6,10,7] => [[1,2,3,4,5,6,7],[8,9,10]] => [7,3]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [9,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [2,1,7,8,9,3,4,5,6] => [[1,3,4,5,6],[2,7,8,9]] => [6,3]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,3,1,9,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[] => [] => [] => []
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,1,2] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,1,2,9] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,6,7,1,9,2,8] => [[1,2,5,6,7,8],[3,4,9]] => [2,6,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,6,7,9,1,2,8] => [[1,2,5,6,7,8],[3,4,9]] => [2,6,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,7,1,2,8,9] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,5,6,1,2,9,7,8] => [[1,2,5,6,7,8],[3,4,9]] => [2,6,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,6,9,1,2,7,8] => [[1,2,5,6,7,8],[3,4,9]] => [2,6,1]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7,8,9] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8,9] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => [2,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,9,2,3] => [[1,2,3,6,7,8,9],[4,5]] => [3,6]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,9,2,3] => [[1,2,3,7,8,9],[4,5,6]] => [3,6]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,5,6,1,7,8,9,2,3] => [[1,2,3,7,8,9],[4,5,6]] => [3,6]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,8,1,9,2,3] => [[1,2,3,7,8,9],[4,5,6]] => [3,6]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,1,2,3] => [[1,2,3,7,8,9],[4,5,6]] => [3,6]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => [[1,2,3,7,8,9],[4,5,6]] => [3,6]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,6,7,1,9,2,3,8] => [[1,2,3,7,8],[4,5,6,9]] => [3,5,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,7,9,1,2,3,8] => [[1,2,3,7,8],[4,5,6,9]] => [3,5,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,5,2,6,7,8,9,3,4] => [[1,2,3,4,8,9],[5,6,7]] => [4,5]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,9,2,3,4] => [[1,2,3,4,8,9],[5,6,7]] => [4,5]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [5,1,6,7,8,2,9,3,4] => [[1,2,3,4,9],[5,6,7,8]] => [4,5]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,9,2,3,4] => [[1,2,3,4,9],[5,6,7,8]] => [4,5]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,6,1,7,8,9,2,3,4] => [[1,2,3,4,9],[5,6,7,8]] => [4,5]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,7,1,8,2,3,4,9] => [[1,2,3,4,9],[5,6,7,8]] => [4,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,8,1,9,2,3,4] => [[1,2,3,4,9],[5,6,7,8]] => [4,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [[1,2,3,4,9],[5,6,7,8]] => [4,5]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [[1,2,3,4,9],[5,6,7,8]] => [4,5]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [1,6,7,8,2,9,3,4,5] => [[1,2,3,4,5],[6,7,8,9]] => [5,4]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,9,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9]] => [5,4]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,1,7,2,8,3,9,4,5] => [[1,2,3,4,5],[6,7,8,9]] => [5,4]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [6,1,7,8,9,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9]] => [5,4]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,8,1,9,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9]] => [5,4]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9]] => [5,4]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,8,1,2,3,4,5,9] => [[1,2,3,4,5,9],[6,7,8]] => [5,4]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [1,2,3,4,7,8,5,6,9] => [[1,2,3,4,5,6,9],[7,8]] => [6,3]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,7,8,9,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9]] => [6,3]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [7,1,8,2,3,9,4,5,6] => [[1,2,3,4,5,6],[7,8,9]] => [6,3]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [7,1,8,2,9,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9]] => [6,3]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [7,1,8,9,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9]] => [6,3]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [7,1,8,2,3,4,5,6,9] => [[1,2,3,4,5,6,9],[7,8]] => [6,3]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [7,8,1,9,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9]] => [6,3]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9]] => [6,3]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6,9] => [[1,2,3,4,5,6,9],[7,8]] => [6,3]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,5,8,9,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [1,2,3,4,8,5,9,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [1,2,3,4,8,9,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0] => [1,2,3,8,4,5,9,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,9,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,8,2,9,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7,9] => [[1,2,3,4,5,6,7,9],[8]] => [7,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,9,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,9,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [8,1,2,3,9,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [8,1,2,9,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [8,1,9,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [7,2]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9] => [[1,2,3,4,5,6,7,9],[8]] => [7,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,9,7,8] => [[1,2,3,4,5,6,7,8],[9]] => [8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,9,6,7,8] => [[1,2,3,4,5,6,7,8],[9]] => [8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9]] => [8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9]] => [8,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9]] => [8,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9]] => [8,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9]] => [8,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => [9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,1,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,9,1,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,9,1,4] => [[1,3,4,6,7,8,9],[2,5]] => [4,5]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,1,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,10,1,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [9,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,6,1,9,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,5,1,8,9,6,7] => [[1,3,4,5,6,7],[2,8,9]] => [7,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,9,10,1,4] => [[1,3,4,6,7,8,9,10],[2,5]] => [4,6]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,1,2] => [[1,2,5,6,7,8,9,10],[3,4]] => [2,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,9,1,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,9,10,2,3] => [[1,2,3,6,7,8,9,10],[4,5]] => [3,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,7,10,1,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [9,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,5,8,9,1,6,7] => [[1,3,4,5,6,7],[2,8,9]] => [7,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,9,1,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,9,10,1,7,8] => [[1,3,4,5,6,7,8],[2,9,10]] => [8,2]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,10,1,7,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [9,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,5,6,1,7,8,9,10,2,3] => [[1,2,3,7,8,9,10],[4,5,6]] => [3,7]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,9,1,5,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,10,1,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [9,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,8,9,1,10,2,3] => [[1,2,3,7,8,9,10],[4,5,6]] => [3,7]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,5,6,1,2,3,9,10,7,8] => [[1,2,3,7,8],[4,5,6,9,10]] => [3,5,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,4,5,1,6,7,9,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,9,4] => [[1,3,4,6,7,8,9],[2,5]] => [4,5]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,5,4,6,7,8,9] => [[1,3,4,6,7,8,9],[2,5]] => [4,5]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,1,4,5,6,7,9,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,9,4] => [[1,3,4,6,7,8,9],[2,5]] => [4,5]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,2] => [[1,2,4,5,6,7,8,9],[3]] => [2,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,8,2,9] => [[1,2,4,5,6,7,8,9],[3]] => [2,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,7,2,8,9] => [[1,2,4,5,6,7,8,9],[3]] => [2,7]
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,5,2,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => [2,7]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,2,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => [2,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,8,1,10,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [9,1]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,9,10,4] => [[1,3,4,6,7,8,9,10],[2,5]] => [4,6]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => [3,2,2,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,2] => [[1,2,4,5,6,7,8,9,10],[3]] => [2,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,8,9,2,10] => [[1,2,4,5,6,7,8,9,10],[3]] => [2,8]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,4,2,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]] => [2,8]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,6,9,10,8] => [[1,2,4,6,8,10],[3,5,7,9]] => [2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => [2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,8,9,10,7] => [[1,2,4,6,7,9,10],[3,5,8]] => [2,2,3,3]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,10,3] => [[1,2,3,5,6,7,8,9,10],[4]] => [3,7]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => [3,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,10,4] => [[1,2,3,4,6,7,8,9,10],[5]] => [4,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]] => [4,2,2,2]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]] => [4,6]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,10,5] => [[1,2,3,4,5,7,8,9,10],[6]] => [5,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => [5,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,10,6] => [[1,2,3,4,5,6,8,9,10],[7]] => [6,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,8,9,6,10] => [[1,2,3,4,5,6,8,9,10],[7]] => [6,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,7,8,6,9,10] => [[1,2,3,4,5,6,8,9,10],[7]] => [6,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]] => [6,4]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,6,8,9,10,7] => [[1,2,3,4,5,6,7,9,10],[8]] => [7,3]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,9,7,10] => [[1,2,3,4,5,6,7,9,10],[8]] => [7,3]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => [7,3]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => [10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,2] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,9,2] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,9,2] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,6,1,7,8,9,2] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,1,8,9,2] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,1,9,2] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => [[1,2,5,6,7,8,9,10],[3,4]] => [2,8]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,9,10,2] => [[1,2,5,6,7,8,9,10],[3,4]] => [2,8]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,9,10,2] => [[1,2,5,6,7,8,9,10],[3,4]] => [2,8]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,5,6,1,7,8,9,10,2] => [[1,2,5,6,7,8,9,10],[3,4]] => [2,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,6,7,1,8,9,10,2] => [[1,2,5,6,7,8,9,10],[3,4]] => [2,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,6,7,1,2,9,8] => [[1,2,5,6,7,8],[3,4,9]] => [2,6,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,8,1,9,10,2] => [[1,2,5,6,7,8,9,10],[3,4]] => [2,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,1,10,2] => [[1,2,5,6,7,8,9,10],[3,4]] => [2,8]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5,10] => [[1,2,3,4,5,10],[6,7,8,9]] => [5,5]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,7,8,9,10,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => [6,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4,10] => [[1,2,3,4,9,10],[5,6,7,8]] => [4,6]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,9,10,2,3,4,5] => [[1,2,3,4,5,10],[6,7,8,9]] => [5,5]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => [[1,2,5,6,7,8,9,10],[3,4]] => [2,8]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8,10] => [[1,2,3,4,5,6,7,8,10],[9]] => [8,2]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [[1,2,3,4,5,6,7,10],[8,9]] => [7,3]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [8,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,4,5,6,7,9,2,8] => [[1,2,5,6,7,8],[3,4,9]] => [2,6,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,8,2,9] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,8,1,2,9,3] => [[1,2,3,7,8,9],[4,5,6]] => [3,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,6,7,1,2,8,9,3] => [[1,2,3,7,8,9],[4,5,6]] => [3,6]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,5,6,1,2,7,8,9,3] => [[1,2,3,7,8,9],[4,5,6]] => [3,6]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,5,1,2,6,7,8,9,3] => [[1,2,3,7,8,9],[4,5,6]] => [3,6]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,9,3] => [[1,2,3,6,7,8,9],[4,5]] => [3,6]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]] => [2,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,10,8,9] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,10,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [8,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,4,7,5,8,9,6] => [[1,2,3,4,5,6,9],[7,8]] => [6,3]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,9,4] => [[1,2,3,4,7,8,9],[5,6]] => [4,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,9,3] => [[1,2,3,6,7,8,9],[4,5]] => [3,6]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => [7,3]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]] => [6,4]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => [5,5]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]] => [4,6]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => [3,7]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,6,7,1,2,8,3,9] => [[1,2,3,7,8,9],[4,5,6]] => [3,6]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,2,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,3,6,7,8,9] => [[1,2,3,6,7,8,9],[4,5]] => [3,6]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,4,7,8,9] => [[1,2,3,4,7,8,9],[5,6]] => [4,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,9,4] => [[1,3,4,6,7,8,9],[2,5]] => [4,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,4,5,1,6,7,8,2,9] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => [[1,3,4,5,6],[2,7,8,9,10]] => [6,4]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,8,2,9,3] => [[1,2,3,6,7,8,9],[4,5]] => [3,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,5,6,1,7,2,8,9] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,7,8,1,2,9,10] => [[1,2,5,6,7,8,9,10],[3,4]] => [2,8]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,1,6,2,7,8,9] => [[1,2,5,6,7,8,9],[3,4]] => [2,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,6,7,10,1,2,8,9] => [[1,2,5,6,7,8,9],[3,4,10]] => [2,7,1]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,1,5,9,2,6,7,8] => [[1,2,5,6,7,8],[3,4,9]] => [2,6,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [[1,2,3,4,9,10],[5,6,7,8]] => [4,6]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,4,7,5,8,6,9] => [[1,2,3,4,5,6,9],[7,8]] => [6,3]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,9,10,4] => [[1,3,4,6,7,8,9,10],[2,5]] => [4,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,6,1,7,2,9,8] => [[1,2,5,6,7,8],[3,4,9]] => [2,6,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => [2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,9,6,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => [2,2,2,2,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [[1,2,5,7,9],[3,4,6,8,10]] => [2,3,2,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [[1,2,3,7,8,9,10],[4,5,6]] => [3,7]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,9,10,2,3,4] => [[1,2,3,4,8,9,10],[5,6,7]] => [4,6]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8,10] => [[1,2,3,4,5,6,7,8,10],[9]] => [8,2]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => [[1,3,5,7,9],[2,4,6,8,10]] => [3,2,2,2,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [5,5]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,4,6,8,10,12,1,3,5,7,9,11] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => [3,2,2,2,2,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1,8,2,9,3,10,4,11,5,12,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [6,6]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,8,9,1,2,10,3] => [[1,2,3,7,8,9,10],[4,5,6]] => [3,7]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => [[1,2,4,5,6,7,8,9,10,11,12],[3]] => [2,10]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,4,6,7,8,9] => [[1,3,4,6,7,8,9],[2,5]] => [4,5]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [5,5]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [1,8,9,10,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9,10]] => [7,3]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [9,1,10,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [8,2]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,10,1,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [9,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,10,1,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [9,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,9,4] => [[1,2,3,4,7,8,9],[5,6]] => [4,5]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,4,5,8,1,6,9,7] => [[1,3,4,5,6,7],[2,8,9]] => [7,2]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [8,2]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => [6,4]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9,10]] => [7,3]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,1,4,9,2,5,6,7,8] => [[1,2,5,6,7,8],[3,4,9]] => [2,6,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [7,8,9,1,10,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => [6,4]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [7,8,1,9,10,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => [6,4]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [7,1,8,9,10,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => [6,4]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [1,9,2,10,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [8,2]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,9,10,3] => [[1,2,3,6,7,8,9,10],[4,5]] => [3,7]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,7,8,9,10,5] => [[1,2,3,4,5,8,9,10],[6,7]] => [5,5]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,2,3,7,4,8,9,5] => [[1,2,3,4,5,9],[6,7,8]] => [5,4]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,2,3,4,5,8,9,10,6] => [[1,2,3,4,5,6,9,10],[7,8]] => [6,4]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,7,8,10,1,2,3,4,9] => [[1,2,3,4,9],[5,6,7,8,10]] => [4,5,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [7,8,9,1,2,10,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => [6,4]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,5,6,1,7,8,9,10,4] => [[1,3,4,6,7,8,9,10],[2,5]] => [4,6]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [2,1,7,8,9,10,3,4,5,6] => [[1,3,4,5,6],[2,7,8,9,10]] => [6,4]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,1,7,8,9,4,5,6] => [[1,3,4,5,6],[2,7,8,9]] => [6,3]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [3,4,1,2,8,9,10,5,6,7] => [[1,2,5,6,7],[3,4,8,9,10]] => [2,5,3]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,6,7,8,1,2,3,4,10,9] => [[1,2,3,4,9],[5,6,7,8,10]] => [4,5,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,5,6,7,9,2,8] => [[1,2,5,6,7,8],[3,4,9]] => [2,6,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,7,1,8,2,9,3] => [[1,2,3,7,8,9],[4,5,6]] => [3,6]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,2,3,4,5,6,9,10,7] => [[1,2,3,4,5,6,7,10],[8,9]] => [7,3]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,5,1,8,6,9,7] => [[1,3,4,5,6,7],[2,8,9]] => [7,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,7,8,10,1,2,3,9] => [[1,2,3,7,8,9],[4,5,6,10]] => [3,6,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,9,10,2,3,4] => [[1,2,3,4,9,10],[5,6,7,8]] => [4,6]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,5,6,9,10,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [8,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => [[1,3,5,7,9],[2,4,6,8,10]] => [3,2,2,2,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,5,1,9,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,1,8,2,9,3,10,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => [6,4]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,3,8,1,4,5,6,9,7] => [[1,3,4,5,6,7],[2,8,9]] => [7,2]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,7,2,8,3,9,4,10,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => [6,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,6,7,1,8,2,10,9] => [[1,2,5,6,7,8,9],[3,4,10]] => [2,7,1]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,7,8,9,1,10,2,3,4,6] => [[1,2,3,4,6],[5,7,8,9,10]] => [4,2,4]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,8,9,1,2,10,3,4,7] => [[1,2,3,4,7],[5,6,8,9,10]] => [4,3,3]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [5,6,7,9,1,2,3,10,4,8] => [[1,2,3,4,8],[5,6,7,9,10]] => [4,4,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => [1,2,3,4,5,9,6,10,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [8,2]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,8,9,1,2,3,4,10,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => [6,4]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,9,10,7,8,12,11] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => [4,4,3,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,5,2,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => [2,2,2,2,2]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [2,9,1,3,4,5,6,7,10,8] => [[1,3,4,5,6,7,8],[2,9,10]] => [8,2]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,6,1,2,3,7,8,9,10,4] => [[1,2,3,4,8,9,10],[5,6,7]] => [4,6]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [7,1,2,8,3,9,4,10,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => [6,4]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,3,5,7,2,4,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => [2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,5,7,2,9,4,6,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => [2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,5,7,9,1,2,4,6,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => [2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,9,6,11,8,10,12] => [[1,2,4,6,8,10,12],[3,5,7,9,11]] => [2,2,2,2,2,2]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => [3,2,2,2,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,6,1,2,3,7,8,9,4] => [[1,2,3,4,8,9],[5,6,7]] => [4,5]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => [3,2,2,2,2,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,6,2,7,3,8,4,9,5] => [[1,2,3,4,5],[6,7,8,9]] => [5,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,6,2,7,3,8,4,9] => [[1,2,3,4,9],[5,6,7,8]] => [4,5]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [8,1,9,2,10,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9,10]] => [7,3]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => [[1,2,4,5,6,7,8,9,10,11,12],[3]] => [2,10]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0] => [1,7,8,9,2,10,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => [6,4]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [3,6,1,7,9,2,4,10,5,8] => [[1,2,4,5,8],[3,6,7,9,10]] => [2,3,3,2]
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
Map
peak composition
Description
The composition corresponding to the peak set of a standard tableau.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a peak, if $i-1$ is an ascent and $i$ is a descent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the peak set of $T$.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a peak, if $i-1$ is an ascent and $i$ is a descent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the peak set of $T$.
searching the database
Sorry, this map was not found in the database.