Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
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] => [1,2] => [[1,2]] => [2]
[1,1,0,0] => [2,1] => [[1],[2]] => [2]
[1,0,1,0,1,0] => [1,2,3] => [[1,2,3]] => [3]
[1,0,1,1,0,0] => [1,3,2] => [[1,2],[3]] => [2,1]
[1,1,0,0,1,0] => [2,1,3] => [[1,3],[2]] => [3]
[1,1,0,1,0,0] => [2,3,1] => [[1,3],[2]] => [3]
[1,1,1,0,0,0] => [3,2,1] => [[1],[2],[3]] => [3]
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [[1,2,3,4]] => [4]
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [[1,2,3],[4]] => [3,1]
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [[1,2,4],[3]] => [2,2]
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [[1,2,4],[3]] => [2,2]
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [[1,2],[3],[4]] => [2,2]
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [[1,3,4],[2]] => [4]
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [[1,3],[2,4]] => [3,1]
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [[1,3,4],[2]] => [4]
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [[1,3,4],[2]] => [4]
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [[1,3],[2],[4]] => [3,1]
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [[1,4],[2],[3]] => [4]
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [[1,4],[2],[3]] => [4]
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [[1,4],[2],[3]] => [4]
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [[1],[2],[3],[4]] => [4]
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [[1,2,3,4,5]] => [5]
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [[1,2,3,4],[5]] => [4,1]
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [[1,2,3,5],[4]] => [3,2]
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [[1,2,3,5],[4]] => [3,2]
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [[1,2,3],[4],[5]] => [3,2]
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [[1,2,4,5],[3]] => [2,3]
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [[1,2,4],[3,5]] => [2,2,1]
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [[1,2,4,5],[3]] => [2,3]
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [[1,2,4,5],[3]] => [2,3]
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [[1,2,4],[3],[5]] => [2,2,1]
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [[1,2,5],[3],[4]] => [2,3]
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [[1,2,5],[3],[4]] => [2,3]
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [[1,2,5],[3],[4]] => [2,3]
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => [2,3]
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [[1,3,4,5],[2]] => [5]
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [[1,3,4],[2,5]] => [4,1]
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [[1,3,5],[2,4]] => [3,2]
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [[1,3,5],[2,4]] => [3,2]
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [[1,3],[2,4],[5]] => [3,2]
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [[1,3,4,5],[2]] => [5]
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [[1,3,4],[2,5]] => [4,1]
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [[1,3,4,5],[2]] => [5]
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [[1,3,4,5],[2]] => [5]
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [[1,3,4],[2],[5]] => [4,1]
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [[1,3,5],[2],[4]] => [3,2]
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [[1,3,5],[2],[4]] => [3,2]
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [[1,3,5],[2],[4]] => [3,2]
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [[1,3],[2],[4],[5]] => [3,2]
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [[1,4,5],[2],[3]] => [5]
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [[1,4],[2,5],[3]] => [4,1]
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [[1,4,5],[2],[3]] => [5]
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [[1,4,5],[2],[3]] => [5]
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [[1,4],[2,5],[3]] => [4,1]
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [[1,4,5],[2],[3]] => [5]
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [[1,4,5],[2],[3]] => [5]
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [[1,4,5],[2],[3]] => [5]
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [[1,4],[2],[3],[5]] => [4,1]
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [[1,5],[2],[3],[4]] => [5]
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [[1,5],[2],[3],[4]] => [5]
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [[1,5],[2],[3],[4]] => [5]
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [[1,5],[2],[3],[4]] => [5]
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]] => [5]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => [6]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => [5,1]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => [4,2]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [[1,2,3,4,6],[5]] => [4,2]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [[1,2,3,4],[5],[6]] => [4,2]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => [3,3]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [[1,2,3,5],[4,6]] => [3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [[1,2,3,5,6],[4]] => [3,3]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [[1,2,3,5,6],[4]] => [3,3]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [[1,2,3,5],[4],[6]] => [3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [[1,2,3,6],[4],[5]] => [3,3]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [[1,2,3,6],[4],[5]] => [3,3]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [[1,2,3,6],[4],[5]] => [3,3]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [[1,2,3],[4],[5],[6]] => [3,3]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => [2,4]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [[1,2,4,5],[3,6]] => [2,3,1]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [[1,2,4,6],[3,5]] => [2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [[1,2,4,6],[3,5]] => [2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [[1,2,4],[3,5],[6]] => [2,2,2]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [[1,2,4,5,6],[3]] => [2,4]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [[1,2,4,5],[3,6]] => [2,3,1]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [[1,2,4,5,6],[3]] => [2,4]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [[1,2,4,5,6],[3]] => [2,4]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [[1,2,4,5],[3],[6]] => [2,3,1]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [[1,2,4,6],[3],[5]] => [2,2,2]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [[1,2,4,6],[3],[5]] => [2,2,2]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [[1,2,4,6],[3],[5]] => [2,2,2]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [[1,2,4],[3],[5],[6]] => [2,2,2]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [[1,2,5,6],[3],[4]] => [2,4]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [[1,2,5],[3,6],[4]] => [2,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [[1,2,5,6],[3],[4]] => [2,4]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [[1,2,5,6],[3],[4]] => [2,4]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [[1,2,5],[3,6],[4]] => [2,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [[1,2,5,6],[3],[4]] => [2,4]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [[1,2,5,6],[3],[4]] => [2,4]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [[1,2,5,6],[3],[4]] => [2,4]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [[1,2,5],[3],[4],[6]] => [2,3,1]
>>> Load all 1826 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [[1,2,6],[3],[4],[5]] => [2,4]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [[1,2,6],[3],[4],[5]] => [2,4]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [[1,2,6],[3],[4],[5]] => [2,4]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [[1,2,6],[3],[4],[5]] => [2,4]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => [2,4]
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => [6]
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [[1,3,4,5],[2,6]] => [5,1]
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => [4,2]
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [[1,3,4,6],[2,5]] => [4,2]
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [[1,3,4],[2,5],[6]] => [4,2]
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => [3,3]
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => [3,2,1]
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[1,3,5,6],[2,4]] => [3,3]
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [[1,3,5,6],[2,4]] => [3,3]
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [[1,3,5],[2,4],[6]] => [3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [[1,3,6],[2,4],[5]] => [3,3]
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [[1,3,6],[2,4],[5]] => [3,3]
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [[1,3,6],[2,4],[5]] => [3,3]
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => [3,3]
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [[1,3,4,5,6],[2]] => [6]
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [[1,3,4,5],[2,6]] => [5,1]
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [[1,3,4,6],[2,5]] => [4,2]
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [[1,3,4,6],[2,5]] => [4,2]
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [[1,3,4],[2,5],[6]] => [4,2]
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [[1,3,4,5,6],[2]] => [6]
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [[1,3,4,5],[2,6]] => [5,1]
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [[1,3,4,5,6],[2]] => [6]
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [[1,3,4,5,6],[2]] => [6]
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [[1,3,4,5],[2],[6]] => [5,1]
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [[1,3,4,6],[2],[5]] => [4,2]
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [[1,3,4,6],[2],[5]] => [4,2]
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [[1,3,4,6],[2],[5]] => [4,2]
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [[1,3,4],[2],[5],[6]] => [4,2]
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [[1,3,5,6],[2],[4]] => [3,3]
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [[1,3,5],[2,6],[4]] => [3,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [[1,3,5,6],[2],[4]] => [3,3]
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [[1,3,5,6],[2],[4]] => [3,3]
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [[1,3,5],[2,6],[4]] => [3,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [[1,3,5,6],[2],[4]] => [3,3]
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [[1,3,5,6],[2],[4]] => [3,3]
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [[1,3,5,6],[2],[4]] => [3,3]
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [[1,3,5],[2],[4],[6]] => [3,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [[1,3,6],[2],[4],[5]] => [3,3]
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [[1,3,6],[2],[4],[5]] => [3,3]
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [[1,3,6],[2],[4],[5]] => [3,3]
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [[1,3,6],[2],[4],[5]] => [3,3]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [[1,3],[2],[4],[5],[6]] => [3,3]
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => [6]
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [[1,4,5],[2,6],[3]] => [5,1]
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [[1,4,6],[2,5],[3]] => [4,2]
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [[1,4,6],[2,5],[3]] => [4,2]
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => [4,2]
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [[1,4,5,6],[2],[3]] => [6]
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [[1,4,5],[2,6],[3]] => [5,1]
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [[1,4,5,6],[2],[3]] => [6]
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [[1,4,5,6],[2],[3]] => [6]
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [[1,4,5],[2,6],[3]] => [5,1]
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [[1,4,6],[2,5],[3]] => [4,2]
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [[1,4,6],[2,5],[3]] => [4,2]
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [[1,4,6],[2,5],[3]] => [4,2]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [[1,4],[2,5],[3],[6]] => [4,2]
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [[1,4,5,6],[2],[3]] => [6]
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [[1,4,5],[2,6],[3]] => [5,1]
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [[1,4,5,6],[2],[3]] => [6]
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [[1,4,5,6],[2],[3]] => [6]
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [[1,4,5],[2,6],[3]] => [5,1]
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [[1,4,5,6],[2],[3]] => [6]
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [[1,4,5,6],[2],[3]] => [6]
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [[1,4,5,6],[2],[3]] => [6]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [[1,4,5],[2],[3],[6]] => [5,1]
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [[1,4,6],[2],[3],[5]] => [4,2]
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [[1,4,6],[2],[3],[5]] => [4,2]
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [[1,4,6],[2],[3],[5]] => [4,2]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [[1,4,6],[2],[3],[5]] => [4,2]
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [[1,4],[2],[3],[5],[6]] => [4,2]
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]] => [6]
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]] => [5,1]
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [[1,5,6],[2],[3],[4]] => [6]
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [[1,5,6],[2],[3],[4]] => [6]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [[1,5],[2,6],[3],[4]] => [5,1]
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [[1,5,6],[2],[3],[4]] => [6]
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [[1,5,6],[2],[3],[4]] => [6]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[1,5,6],[2],[3],[4]] => [6]
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [[1,5],[2,6],[3],[4]] => [5,1]
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [[1,5,6],[2],[3],[4]] => [6]
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [[1,5,6],[2],[3],[4]] => [6]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [[1,5,6],[2],[3],[4]] => [6]
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [[1,5,6],[2],[3],[4]] => [6]
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [[1,5],[2],[3],[4],[6]] => [5,1]
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => [6]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [[1,6],[2],[3],[4],[5]] => [6]
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [[1,6],[2],[3],[4],[5]] => [6]
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [[1,6],[2],[3],[4],[5]] => [6]
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [[1,6],[2],[3],[4],[5]] => [6]
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => [6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => [7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => [6,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => [5,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,7],[6]] => [5,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [[1,2,3,4,5],[6],[7]] => [5,2]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => [4,3]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [[1,2,3,4,6],[5,7]] => [4,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [[1,2,3,4,6,7],[5]] => [4,3]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [[1,2,3,4,6,7],[5]] => [4,3]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [[1,2,3,4,6],[5],[7]] => [4,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [[1,2,3,4,7],[5],[6]] => [4,3]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [[1,2,3,4,7],[5],[6]] => [4,3]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [[1,2,3,4,7],[5],[6]] => [4,3]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [[1,2,3,4],[5],[6],[7]] => [4,3]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => [3,4]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [[1,2,3,5,7],[4,6]] => [3,2,2]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [[1,2,3,5],[4,6],[7]] => [3,2,2]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [[1,2,3,5,6,7],[4]] => [3,4]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [[1,2,3,5,6],[4,7]] => [3,3,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [[1,2,3,5,6,7],[4]] => [3,4]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [[1,2,3,5,6,7],[4]] => [3,4]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [[1,2,3,5,6],[4],[7]] => [3,3,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [[1,2,3,5,7],[4],[6]] => [3,2,2]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [[1,2,3,5,7],[4],[6]] => [3,2,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [[1,2,3,5,7],[4],[6]] => [3,2,2]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [[1,2,3,5],[4],[6],[7]] => [3,2,2]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [[1,2,3,6,7],[4],[5]] => [3,4]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [[1,2,3,6],[4,7],[5]] => [3,3,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [[1,2,3,6,7],[4],[5]] => [3,4]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [[1,2,3,6,7],[4],[5]] => [3,4]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [[1,2,3,6],[4,7],[5]] => [3,3,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [[1,2,3,6,7],[4],[5]] => [3,4]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [[1,2,3,6,7],[4],[5]] => [3,4]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [[1,2,3,6,7],[4],[5]] => [3,4]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [[1,2,3,6],[4],[5],[7]] => [3,3,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [[1,2,3,7],[4],[5],[6]] => [3,4]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [[1,2,3,7],[4],[5],[6]] => [3,4]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [[1,2,3,7],[4],[5],[6]] => [3,4]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [[1,2,3,7],[4],[5],[6]] => [3,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7]] => [3,4]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => [2,5]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [[1,2,4,5],[3,6],[7]] => [2,3,2]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [[1,2,4,6],[3,5,7]] => [2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [[1,2,4,6,7],[3,5]] => [2,2,3]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [[1,2,4,6],[3,5],[7]] => [2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [[1,2,4,7],[3,5],[6]] => [2,2,3]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [[1,2,4,7],[3,5],[6]] => [2,2,3]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [[1,2,4,7],[3,5],[6]] => [2,2,3]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [[1,2,4],[3,5],[6],[7]] => [2,2,3]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [[1,2,4,5,6,7],[3]] => [2,5]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [[1,2,4,5,7],[3,6]] => [2,3,2]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [[1,2,4,5],[3,6],[7]] => [2,3,2]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [[1,2,4,5,6,7],[3]] => [2,5]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [[1,2,4,5,6],[3,7]] => [2,4,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [[1,2,4,5,6,7],[3]] => [2,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3]] => [2,5]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [[1,2,4,5,6],[3],[7]] => [2,4,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [[1,2,4,5,7],[3],[6]] => [2,3,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [[1,2,4,5,7],[3],[6]] => [2,3,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [[1,2,4,5,7],[3],[6]] => [2,3,2]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [[1,2,4,5],[3],[6],[7]] => [2,3,2]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [[1,2,4,6,7],[3],[5]] => [2,2,3]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [[1,2,4,6],[3,7],[5]] => [2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [[1,2,4,6,7],[3],[5]] => [2,2,3]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [[1,2,4,6,7],[3],[5]] => [2,2,3]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [[1,2,4,6],[3,7],[5]] => [2,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [[1,2,4,6,7],[3],[5]] => [2,2,3]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [[1,2,4,6,7],[3],[5]] => [2,2,3]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [[1,2,4,6,7],[3],[5]] => [2,2,3]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [[1,2,4,6],[3],[5],[7]] => [2,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [[1,2,4,7],[3],[5],[6]] => [2,2,3]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [[1,2,4,7],[3],[5],[6]] => [2,2,3]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [[1,2,4,7],[3],[5],[6]] => [2,2,3]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [[1,2,4,7],[3],[5],[6]] => [2,2,3]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [[1,2,4],[3],[5],[6],[7]] => [2,2,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [[1,2,5,6,7],[3],[4]] => [2,5]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [[1,2,5,6],[3,7],[4]] => [2,4,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [[1,2,5,7],[3,6],[4]] => [2,3,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [[1,2,5,7],[3,6],[4]] => [2,3,2]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [[1,2,5],[3,6],[4,7]] => [2,3,2]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [[1,2,5,6,7],[3],[4]] => [2,5]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [[1,2,5,6],[3,7],[4]] => [2,4,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [[1,2,5,6,7],[3],[4]] => [2,5]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [[1,2,5,6,7],[3],[4]] => [2,5]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [[1,2,5,6],[3,7],[4]] => [2,4,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [[1,2,5,7],[3,6],[4]] => [2,3,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [[1,2,5,7],[3,6],[4]] => [2,3,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [[1,2,5,7],[3,6],[4]] => [2,3,2]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [[1,2,5],[3,6],[4],[7]] => [2,3,2]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [[1,2,5,6,7],[3],[4]] => [2,5]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [[1,2,5,6],[3,7],[4]] => [2,4,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [[1,2,5,6,7],[3],[4]] => [2,5]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [[1,2,5,6,7],[3],[4]] => [2,5]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [[1,2,5,6],[3,7],[4]] => [2,4,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [[1,2,5,6,7],[3],[4]] => [2,5]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [[1,2,5,6,7],[3],[4]] => [2,5]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [[1,2,5,6,7],[3],[4]] => [2,5]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [[1,2,5,6],[3],[4],[7]] => [2,4,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [[1,2,5,7],[3],[4],[6]] => [2,3,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [[1,2,5,7],[3],[4],[6]] => [2,3,2]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [[1,2,5,7],[3],[4],[6]] => [2,3,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [[1,2,5,7],[3],[4],[6]] => [2,3,2]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [[1,2,5],[3],[4],[6],[7]] => [2,3,2]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [[1,2,6,7],[3],[4],[5]] => [2,5]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [[1,2,6],[3,7],[4],[5]] => [2,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [[1,2,6,7],[3],[4],[5]] => [2,5]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [[1,2,6,7],[3],[4],[5]] => [2,5]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [[1,2,6],[3,7],[4],[5]] => [2,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [[1,2,6,7],[3],[4],[5]] => [2,5]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [[1,2,6,7],[3],[4],[5]] => [2,5]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [[1,2,6,7],[3],[4],[5]] => [2,5]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [[1,2,6],[3,7],[4],[5]] => [2,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [[1,2,6,7],[3],[4],[5]] => [2,5]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [[1,2,6,7],[3],[4],[5]] => [2,5]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [[1,2,6,7],[3],[4],[5]] => [2,5]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [[1,2,6,7],[3],[4],[5]] => [2,5]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [[1,2,6],[3],[4],[5],[7]] => [2,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [[1,2,7],[3],[4],[5],[6]] => [2,5]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [[1,2,7],[3],[4],[5],[6]] => [2,5]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [[1,2,7],[3],[4],[5],[6]] => [2,5]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [[1,2,7],[3],[4],[5],[6]] => [2,5]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [[1,2,7],[3],[4],[5],[6]] => [2,5]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => [2,5]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]] => [7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [[1,3,4,5],[2,6],[7]] => [5,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [[1,3,4,6],[2,5],[7]] => [4,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [[1,3,4,7],[2,5],[6]] => [4,3]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [[1,3,4,7],[2,5],[6]] => [4,3]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [[1,3,4,7],[2,5],[6]] => [4,3]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [[1,3,4],[2,5],[6],[7]] => [4,3]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [[1,3,5,7],[2,4,6]] => [3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [[1,3,5],[2,4,6],[7]] => [3,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [[1,3,5,6],[2,4,7]] => [3,3,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [[1,3,5,6,7],[2,4]] => [3,4]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [[1,3,5,6],[2,4],[7]] => [3,3,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [[1,3,5,7],[2,4],[6]] => [3,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [[1,3,5,7],[2,4],[6]] => [3,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [[1,3,5,7],[2,4],[6]] => [3,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [[1,3,5],[2,4],[6],[7]] => [3,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [[1,3,6,7],[2,4],[5]] => [3,4]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [[1,3,6],[2,4,7],[5]] => [3,3,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [[1,3,6,7],[2,4],[5]] => [3,4]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [[1,3,6,7],[2,4],[5]] => [3,4]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [[1,3,6],[2,4,7],[5]] => [3,3,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [[1,3,6,7],[2,4],[5]] => [3,4]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [[1,3,6,7],[2,4],[5]] => [3,4]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [[1,3,6,7],[2,4],[5]] => [3,4]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [[1,3,6],[2,4],[5],[7]] => [3,3,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [[1,3,7],[2,4],[5],[6]] => [3,4]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [[1,3,7],[2,4],[5],[6]] => [3,4]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [[1,3,7],[2,4],[5],[6]] => [3,4]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [[1,3,7],[2,4],[5],[6]] => [3,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => [3,4]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [[1,3,4,5,6,7],[2]] => [7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [[1,3,4,5],[2,6],[7]] => [5,2]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [[1,3,4,6],[2,5,7]] => [4,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [[1,3,4,6,7],[2,5]] => [4,3]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [[1,3,4,6],[2,5],[7]] => [4,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [[1,3,4,7],[2,5],[6]] => [4,3]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [[1,3,4,7],[2,5],[6]] => [4,3]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [[1,3,4,7],[2,5],[6]] => [4,3]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [[1,3,4],[2,5],[6],[7]] => [4,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [[1,3,4,5,6,7],[2]] => [7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [[1,3,4,5,7],[2,6]] => [5,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [[1,3,4,5],[2,6],[7]] => [5,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [[1,3,4,5,6,7],[2]] => [7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [[1,3,4,5,6],[2,7]] => [6,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [[1,3,4,5,6,7],[2]] => [7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2]] => [7]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [[1,3,4,5,6],[2],[7]] => [6,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [[1,3,4,5,7],[2],[6]] => [5,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [[1,3,4,5,7],[2],[6]] => [5,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [[1,3,4,5,7],[2],[6]] => [5,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [[1,3,4,5],[2],[6],[7]] => [5,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [[1,3,4,6,7],[2],[5]] => [4,3]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [[1,3,4,6],[2,7],[5]] => [4,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [[1,3,4,6,7],[2],[5]] => [4,3]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [[1,3,4,6,7],[2],[5]] => [4,3]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [[1,3,4,6],[2,7],[5]] => [4,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [[1,3,4,6,7],[2],[5]] => [4,3]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [[1,3,4,6,7],[2],[5]] => [4,3]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [[1,3,4,6,7],[2],[5]] => [4,3]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [[1,3,4,6],[2],[5],[7]] => [4,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [[1,3,4,7],[2],[5],[6]] => [4,3]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [[1,3,4,7],[2],[5],[6]] => [4,3]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [[1,3,4,7],[2],[5],[6]] => [4,3]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [[1,3,4,7],[2],[5],[6]] => [4,3]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [[1,3,4],[2],[5],[6],[7]] => [4,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => [3,4]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [[1,3,5,6],[2,7],[4]] => [3,3,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [[1,3,5,7],[2,6],[4]] => [3,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [[1,3,5,7],[2,6],[4]] => [3,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => [3,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [[1,3,5,6,7],[2],[4]] => [3,4]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [[1,3,5,6],[2,7],[4]] => [3,3,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [[1,3,5,6,7],[2],[4]] => [3,4]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [[1,3,5,6,7],[2],[4]] => [3,4]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [[1,3,5,6],[2,7],[4]] => [3,3,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [[1,3,5,7],[2,6],[4]] => [3,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [[1,3,5,7],[2,6],[4]] => [3,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [[1,3,5,7],[2,6],[4]] => [3,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [[1,3,5],[2,6],[4],[7]] => [3,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [[1,3,5,6,7],[2],[4]] => [3,4]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [[1,3,5,6],[2,7],[4]] => [3,3,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [[1,3,5,6,7],[2],[4]] => [3,4]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [[1,3,5,6,7],[2],[4]] => [3,4]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [[1,3,5,6],[2,7],[4]] => [3,3,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [[1,3,5,6,7],[2],[4]] => [3,4]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [[1,3,5,6,7],[2],[4]] => [3,4]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [[1,3,5,6,7],[2],[4]] => [3,4]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [[1,3,5,6],[2],[4],[7]] => [3,3,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [[1,3,5,7],[2],[4],[6]] => [3,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [[1,3,5,7],[2],[4],[6]] => [3,2,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [[1,3,5,7],[2],[4],[6]] => [3,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [[1,3,5,7],[2],[4],[6]] => [3,2,2]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [[1,3,5],[2],[4],[6],[7]] => [3,2,2]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [[1,3,6,7],[2],[4],[5]] => [3,4]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [[1,3,6],[2,7],[4],[5]] => [3,3,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [[1,3,6,7],[2],[4],[5]] => [3,4]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [[1,3,6,7],[2],[4],[5]] => [3,4]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [[1,3,6],[2,7],[4],[5]] => [3,3,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [[1,3,6,7],[2],[4],[5]] => [3,4]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [[1,3,6,7],[2],[4],[5]] => [3,4]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [[1,3,6,7],[2],[4],[5]] => [3,4]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [[1,3,6],[2,7],[4],[5]] => [3,3,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [[1,3,6,7],[2],[4],[5]] => [3,4]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [[1,3,6,7],[2],[4],[5]] => [3,4]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [[1,3,6,7],[2],[4],[5]] => [3,4]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [[1,3,6,7],[2],[4],[5]] => [3,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [[1,3,6],[2],[4],[5],[7]] => [3,3,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [[1,3,7],[2],[4],[5],[6]] => [3,4]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [[1,3,7],[2],[4],[5],[6]] => [3,4]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [[1,3,7],[2],[4],[5],[6]] => [3,4]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [[1,3,7],[2],[4],[5],[6]] => [3,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [[1,3,7],[2],[4],[5],[6]] => [3,4]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7]] => [3,4]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [[1,4,5,6],[2,7],[3]] => [6,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [[1,4,5,7],[2,6],[3]] => [5,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [[1,4,5,7],[2,6],[3]] => [5,2]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [[1,4,5],[2,6],[3,7]] => [5,2]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [[1,4,6,7],[2,5],[3]] => [4,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [[1,4,6],[2,5,7],[3]] => [4,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [[1,4,6,7],[2,5],[3]] => [4,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [[1,4,6,7],[2,5],[3]] => [4,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [[1,4,6],[2,5],[3,7]] => [4,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [[1,4,7],[2,5],[3,6]] => [4,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [[1,4,7],[2,5],[3,6]] => [4,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [[1,4,7],[2,5],[3,6]] => [4,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => [4,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [[1,4,5,6],[2,7],[3]] => [6,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [[1,4,5,7],[2,6],[3]] => [5,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [[1,4,5,7],[2,6],[3]] => [5,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [[1,4,5],[2,6],[3,7]] => [5,2]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [[1,4,5,6],[2,7],[3]] => [6,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [[1,4,5,6],[2,7],[3]] => [6,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [[1,4,5,7],[2,6],[3]] => [5,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [[1,4,5,7],[2,6],[3]] => [5,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [[1,4,5,7],[2,6],[3]] => [5,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [[1,4,5],[2,6],[3],[7]] => [5,2]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [[1,4,6,7],[2,5],[3]] => [4,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [[1,4,6],[2,5,7],[3]] => [4,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [[1,4,6,7],[2,5],[3]] => [4,3]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [[1,4,6,7],[2,5],[3]] => [4,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [[1,4,6],[2,5,7],[3]] => [4,2,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [[1,4,6,7],[2,5],[3]] => [4,3]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [[1,4,6,7],[2,5],[3]] => [4,3]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [[1,4,6,7],[2,5],[3]] => [4,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [[1,4,6],[2,5],[3],[7]] => [4,2,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [[1,4,7],[2,5],[3],[6]] => [4,3]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [[1,4,7],[2,5],[3],[6]] => [4,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [[1,4,7],[2,5],[3],[6]] => [4,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [[1,4,7],[2,5],[3],[6]] => [4,3]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [[1,4],[2,5],[3],[6],[7]] => [4,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [[1,4,5,6],[2,7],[3]] => [6,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [[1,4,5,7],[2,6],[3]] => [5,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [[1,4,5,7],[2,6],[3]] => [5,2]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [[1,4,5],[2,6],[3,7]] => [5,2]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [[1,4,5,6],[2,7],[3]] => [6,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [[1,4,5,6],[2,7],[3]] => [6,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [[1,4,5,7],[2,6],[3]] => [5,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [[1,4,5,7],[2,6],[3]] => [5,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [[1,4,5,7],[2,6],[3]] => [5,2]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [[1,4,5],[2,6],[3],[7]] => [5,2]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [[1,4,5,6],[2,7],[3]] => [6,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [[1,4,5,6],[2,7],[3]] => [6,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [[1,4,5,6,7],[2],[3]] => [7]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [[1,4,5,6],[2],[3],[7]] => [6,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [[1,4,5,7],[2],[3],[6]] => [5,2]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [[1,4,5,7],[2],[3],[6]] => [5,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [[1,4,5,7],[2],[3],[6]] => [5,2]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [[1,4,5,7],[2],[3],[6]] => [5,2]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [[1,4,5],[2],[3],[6],[7]] => [5,2]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [[1,4,6,7],[2],[3],[5]] => [4,3]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [[1,4,6],[2,7],[3],[5]] => [4,2,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [[1,4,6,7],[2],[3],[5]] => [4,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [[1,4,6,7],[2],[3],[5]] => [4,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [[1,4,6],[2,7],[3],[5]] => [4,2,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [[1,4,6,7],[2],[3],[5]] => [4,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [[1,4,6,7],[2],[3],[5]] => [4,3]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [[1,4,6,7],[2],[3],[5]] => [4,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [[1,4,6],[2,7],[3],[5]] => [4,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [[1,4,6,7],[2],[3],[5]] => [4,3]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [[1,4,6,7],[2],[3],[5]] => [4,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [[1,4,6,7],[2],[3],[5]] => [4,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [[1,4,6,7],[2],[3],[5]] => [4,3]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [[1,4,6],[2],[3],[5],[7]] => [4,2,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => [4,3]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [[1,4,7],[2],[3],[5],[6]] => [4,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [[1,4,7],[2],[3],[5],[6]] => [4,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [[1,4,7],[2],[3],[5],[6]] => [4,3]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [[1,4,7],[2],[3],[5],[6]] => [4,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [[1,4],[2],[3],[5],[6],[7]] => [4,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [[1,5,6],[2,7],[3],[4]] => [6,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [[1,5,7],[2,6],[3],[4]] => [5,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [[1,5,7],[2,6],[3],[4]] => [5,2]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]] => [5,2]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [[1,5,6],[2,7],[3],[4]] => [6,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [[1,5,7],[2,6],[3],[4]] => [5,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [[1,5,7],[2,6],[3],[4]] => [5,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [[1,5,7],[2,6],[3],[4]] => [5,2]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [[1,5],[2,6],[3,7],[4]] => [5,2]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [[1,5,6],[2,7],[3],[4]] => [6,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [[1,5,6],[2,7],[3],[4]] => [6,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [[1,5,7],[2,6],[3],[4]] => [5,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [[1,5,7],[2,6],[3],[4]] => [5,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [[1,5,7],[2,6],[3],[4]] => [5,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [[1,5,7],[2,6],[3],[4]] => [5,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [[1,5],[2,6],[3],[4],[7]] => [5,2]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [[1,5,6],[2,7],[3],[4]] => [6,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [[1,5,6],[2,7],[3],[4]] => [6,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[1,5,6,7],[2],[3],[4]] => [7]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [[1,5,6],[2],[3],[4],[7]] => [6,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [[1,5,7],[2],[3],[4],[6]] => [5,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [[1,5,7],[2],[3],[4],[6]] => [5,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [[1,5,7],[2],[3],[4],[6]] => [5,2]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [[1,5,7],[2],[3],[4],[6]] => [5,2]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [[1,5,7],[2],[3],[4],[6]] => [5,2]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [[1,5],[2],[3],[4],[6],[7]] => [5,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [[1,6],[2,7],[3],[4],[5]] => [6,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [[1,6],[2,7],[3],[4],[5]] => [6,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [[1,6],[2,7],[3],[4],[5]] => [6,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [[1,6],[2,7],[3],[4],[5]] => [6,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [[1,6,7],[2],[3],[4],[5]] => [7]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [[1,6],[2],[3],[4],[5],[7]] => [6,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6]] => [7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [[1,7],[2],[3],[4],[5],[6]] => [7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [[1,7],[2],[3],[4],[5],[6]] => [7]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [[1,7],[2],[3],[4],[5],[6]] => [7]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [[1,7],[2],[3],[4],[5],[6]] => [7]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [[1,7],[2],[3],[4],[5],[6]] => [7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]] => [7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => [8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => [7,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [[1,2,3,4,5,6,8],[7]] => [6,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,8],[7]] => [6,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [[1,2,3,4,5,6],[7],[8]] => [6,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]] => [5,3]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [[1,2,3,4,5,7],[6,8]] => [5,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [[1,2,3,4,5,7,8],[6]] => [5,3]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [[1,2,3,4,5,7,8],[6]] => [5,3]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [[1,2,3,4,5,7],[6],[8]] => [5,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [[1,2,3,4,5,8],[6],[7]] => [5,3]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [[1,2,3,4,5,8],[6],[7]] => [5,3]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [[1,2,3,4,5,8],[6],[7]] => [5,3]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8]] => [5,3]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => [4,4]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [[1,2,3,4,6,8],[5,7]] => [4,2,2]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => [4,2,2]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [[1,2,3,4,6,7,8],[5]] => [4,4]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [[1,2,3,4,6,7],[5,8]] => [4,3,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [[1,2,3,4,6,7,8],[5]] => [4,4]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [[1,2,3,4,6,7,8],[5]] => [4,4]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [[1,2,3,4,6,7],[5],[8]] => [4,3,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [[1,2,3,4,6,8],[5],[7]] => [4,2,2]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [[1,2,3,4,6,8],[5],[7]] => [4,2,2]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [[1,2,3,4,6,8],[5],[7]] => [4,2,2]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [[1,2,3,4,6],[5],[7],[8]] => [4,2,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [[1,2,3,4,7,8],[5],[6]] => [4,4]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [[1,2,3,4,7],[5,8],[6]] => [4,3,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [[1,2,3,4,7,8],[5],[6]] => [4,4]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [[1,2,3,4,7,8],[5],[6]] => [4,4]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [[1,2,3,4,7],[5,8],[6]] => [4,3,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => [[1,2,3,4,7,8],[5],[6]] => [4,4]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [[1,2,3,4,7,8],[5],[6]] => [4,4]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [[1,2,3,4,7,8],[5],[6]] => [4,4]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [[1,2,3,4,7],[5],[6],[8]] => [4,3,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [[1,2,3,4,8],[5],[6],[7]] => [4,4]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [[1,2,3,4,8],[5],[6],[7]] => [4,4]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [[1,2,3,4,8],[5],[6],[7]] => [4,4]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [[1,2,3,4,8],[5],[6],[7]] => [4,4]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8]] => [4,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => [3,5]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]] => [3,3,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [[1,2,3,5,7,8],[4,6]] => [3,2,3]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [[1,2,3,5,8],[4,6],[7]] => [3,2,3]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [[1,2,3,5,8],[4,6],[7]] => [3,2,3]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => [3,2,3]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [[1,2,3,5,6,8],[4,7]] => [3,3,2]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [[1,2,3,5,6],[4,7],[8]] => [3,3,2]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [[1,2,3,5,6,7,8],[4]] => [3,5]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [[1,2,3,5,6,7],[4,8]] => [3,4,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [[1,2,3,5,6,7,8],[4]] => [3,5]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [[1,2,3,5,6,7,8],[4]] => [3,5]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [[1,2,3,5,6,7],[4],[8]] => [3,4,1]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,6,3] => [[1,2,3,5,6,8],[4],[7]] => [3,3,2]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [[1,2,3,5,6],[4],[7],[8]] => [3,3,2]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [[1,2,3,5,7,8],[4],[6]] => [3,2,3]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,4,6,7,5,3,8] => [[1,2,3,5,7,8],[4],[6]] => [3,2,3]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [[1,2,3,5,7,8],[4],[6]] => [3,2,3]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [[1,2,3,5,7],[4],[6],[8]] => [3,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [[1,2,3,5,8],[4],[6],[7]] => [3,2,3]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => [[1,2,3,5,8],[4],[6],[7]] => [3,2,3]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [[1,2,3,5],[4],[6],[7],[8]] => [3,2,3]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => [3,5]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => [3,4,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [[1,2,3,6,8],[4,7],[5]] => [3,3,2]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => [3,3,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [[1,2,3,6,7,8],[4],[5]] => [3,5]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [[1,2,3,6,7,8],[4],[5]] => [3,5]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [[1,2,3,6,7],[4,8],[5]] => [3,4,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [[1,2,3,6,8],[4,7],[5]] => [3,3,2]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [[1,2,3,6],[4,7],[5],[8]] => [3,3,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,4,7,3,8] => [[1,2,3,6,7,8],[4],[5]] => [3,5]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [[1,2,3,6,7,8],[4],[5]] => [3,5]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,5,6,7,4,3,8] => [[1,2,3,6,7,8],[4],[5]] => [3,5]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [[1,2,3,6,7,8],[4],[5]] => [3,5]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [[1,2,3,6,7,8],[4],[5]] => [3,5]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [[1,2,3,6,7],[4],[5],[8]] => [3,4,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,6,4,3,8] => [[1,2,3,6,8],[4],[5],[7]] => [3,3,2]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,6,4,8,3] => [[1,2,3,6,8],[4],[5],[7]] => [3,3,2]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,6,8,4,3] => [[1,2,3,6,8],[4],[5],[7]] => [3,3,2]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,7,6,4,3] => [[1,2,3,6],[4],[5],[7],[8]] => [3,3,2]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [[1,2,3,7,8],[4],[5],[6]] => [3,5]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [[1,2,3,7,8],[4],[5],[6]] => [3,5]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,5,7,8,4,3] => [[1,2,3,7,8],[4],[5],[6]] => [3,5]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => [[1,2,3,7],[4,8],[5],[6]] => [3,4,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,5,4,3,8] => [[1,2,3,7,8],[4],[5],[6]] => [3,5]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [[1,2,3,7,8],[4],[5],[6]] => [3,5]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [[1,2,3,8],[4],[5],[6],[7]] => [3,5]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [[1,2,3,8],[4],[5],[6],[7]] => [3,5]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,6,5,8,4,3] => [[1,2,3,8],[4],[5],[6],[7]] => [3,5]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [[1,2,3,8],[4],[5],[6],[7]] => [3,5]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [[1,2,3,8],[4],[5],[6],[7]] => [3,5]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8]] => [3,5]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => [2,6]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [[1,2,4,5,6],[3,7],[8]] => [2,4,2]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [[1,2,4,5,7],[3,6],[8]] => [2,3,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [[1,2,4,5,8],[3,6],[7]] => [2,3,3]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [[1,2,4,5,8],[3,6],[7]] => [2,3,3]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]] => [2,3,3]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [[1,2,4,6],[3,5,7],[8]] => [2,2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [[1,2,4,6,7,8],[3,5]] => [2,2,4]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [[1,2,4,6,7],[3,5],[8]] => [2,2,3,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [[1,2,4,6,8],[3,5],[7]] => [2,2,2,2]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [[1,2,4,6,8],[3,5],[7]] => [2,2,2,2]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [[1,2,4,6],[3,5],[7],[8]] => [2,2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]] => [2,2,4]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]] => [2,2,3,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [[1,2,4,7,8],[3,5],[6]] => [2,2,4]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [[1,2,4,7],[3,5,8],[6]] => [2,2,3,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,5,4,8] => [[1,2,4,7,8],[3,5],[6]] => [2,2,4]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [[1,2,4,7,8],[3,5],[6]] => [2,2,4]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,5,4] => [[1,2,4,7,8],[3,5],[6]] => [2,2,4]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,7,5,4] => [[1,2,4,7],[3,5],[6],[8]] => [2,2,3,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [[1,2,4,8],[3,5],[6],[7]] => [2,2,4]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [[1,2,4,8],[3,5],[6],[7]] => [2,2,4]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => [[1,2,4,8],[3,5],[6],[7]] => [2,2,4]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]] => [2,2,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => [2,6]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [[1,2,4,5,7,8],[3,6]] => [2,3,3]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [[1,2,4,5,7],[3,6],[8]] => [2,3,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [[1,2,4,5,8],[3,6],[7]] => [2,3,3]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => [[1,2,4,5,8],[3,6],[7]] => [2,3,3]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]] => [2,3,3]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [[1,2,4,5,6,7,8],[3]] => [2,6]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [[1,2,4,5,6,8],[3,7]] => [2,4,2]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [[1,2,4,5,6],[3,7],[8]] => [2,4,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [[1,2,4,5,6,7,8],[3]] => [2,6]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [[1,2,4,5,6,7],[3,8]] => [2,5,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [[1,2,4,5,6,7,8],[3]] => [2,6]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [[1,2,4,5,6,7,8],[3]] => [2,6]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [[1,2,4,5,6,7],[3],[8]] => [2,5,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [[1,2,4,5,6,8],[3],[7]] => [2,4,2]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [[1,2,4,5,6,8],[3],[7]] => [2,4,2]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [[1,2,4,5,6,8],[3],[7]] => [2,4,2]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [[1,2,4,5,6],[3],[7],[8]] => [2,4,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [[1,2,4,5,7,8],[3],[6]] => [2,3,3]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => [[1,2,4,5,7,8],[3],[6]] => [2,3,3]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,5,8,2] => [[1,2,4,5,7,8],[3],[6]] => [2,3,3]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [[1,2,4,5,7,8],[3],[6]] => [2,3,3]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,7,6,8,5,2] => [[1,2,4,5,8],[3],[6],[7]] => [2,3,3]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [[1,2,4,5],[3],[6],[7],[8]] => [2,3,3]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [[1,2,4,6,7],[3,8],[5]] => [2,2,3,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => [2,2,2,2]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [[1,2,4,6,8],[3,7],[5]] => [2,2,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [[1,2,4,6,8],[3,7],[5]] => [2,2,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [[1,2,4,6,8],[3,7],[5]] => [2,2,2,2]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [[1,2,4,6],[3,7],[5],[8]] => [2,2,2,2]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => [[1,2,4,6,7,8],[3],[5]] => [2,2,4]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,4,2,8] => [[1,2,4,6,7,8],[3],[5]] => [2,2,4]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,4,8,2] => [[1,2,4,6,7,8],[3],[5]] => [2,2,4]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [[1,2,4,6,7,8],[3],[5]] => [2,2,4]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,7,4,2] => [[1,2,4,6,7],[3],[5],[8]] => [2,2,3,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [[1,2,4,6,8],[3],[5],[7]] => [2,2,2,2]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [[1,2,4,6,8],[3],[5],[7]] => [2,2,2,2]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [[1,2,4,6],[3],[5],[7],[8]] => [2,2,2,2]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [[1,2,4,7],[3,8],[5],[6]] => [2,2,3,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [[1,2,4,7,8],[3],[5],[6]] => [2,2,4]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,5,7,4,2,8] => [[1,2,4,7,8],[3],[5],[6]] => [2,2,4]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => [[1,2,4,7,8],[3],[5],[6]] => [2,2,4]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [[1,2,4,7,8],[3],[5],[6]] => [2,2,4]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,5,4,2,8] => [[1,2,4,7,8],[3],[5],[6]] => [2,2,4]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [[1,2,4,7,8],[3],[5],[6]] => [2,2,4]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [[1,2,4,7,8],[3],[5],[6]] => [2,2,4]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,6,8,7,5,4,2] => [[1,2,4,7],[3],[5],[6],[8]] => [2,2,3,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => [[1,2,4,8],[3],[5],[6],[7]] => [2,2,4]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [[1,2,4],[3],[5],[6],[7],[8]] => [2,2,4]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => [2,6]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [[1,2,5,6,7],[3,8],[4]] => [2,5,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [[1,2,5,6,8],[3,7],[4]] => [2,4,2]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [[1,2,5,6,8],[3,7],[4]] => [2,4,2]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => [2,4,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [[1,2,5,7,8],[3,6],[4]] => [2,3,3]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [[1,2,5,7,8],[3,6],[4]] => [2,3,3]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [[1,2,5,7],[3,6],[4,8]] => [2,3,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [[1,2,5,8],[3,6],[4,7]] => [2,3,3]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [[1,2,5,8],[3,6],[4,7]] => [2,3,3]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => [2,3,3]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [[1,2,5,6,7,8],[3],[4]] => [2,6]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [[1,2,5,6,7,8],[3],[4]] => [2,6]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [[1,2,5,6,8],[3,7],[4]] => [2,4,2]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,7,8,6,2] => [[1,2,5,6,8],[3,7],[4]] => [2,4,2]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [[1,2,5,7,8],[3,6],[4]] => [2,3,3]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [[1,2,5,7,8],[3,6],[4]] => [2,3,3]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [[1,2,5,7],[3,6,8],[4]] => [2,3,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,6,7,8,5,2] => [[1,2,5,7,8],[3,6],[4]] => [2,3,3]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,6,8,7,5,2] => [[1,2,5,7],[3,6],[4],[8]] => [2,3,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [[1,2,5,8],[3,6],[4],[7]] => [2,3,3]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [[1,2,5,8],[3,6],[4],[7]] => [2,3,3]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [[1,2,5],[3,6],[4],[7],[8]] => [2,3,3]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,3,2,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => [2,6]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,5,3,2,6,8,7] => [[1,2,5,6,7],[3,8],[4]] => [2,5,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,3,2,7,6,8] => [[1,2,5,6,8],[3,7],[4]] => [2,4,2]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,3,2,7,8,6] => [[1,2,5,6,8],[3,7],[4]] => [2,4,2]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => [2,4,2]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,3,6,2,7,8] => [[1,2,5,6,7,8],[3],[4]] => [2,6]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,3,6,7,2,8] => [[1,2,5,6,7,8],[3],[4]] => [2,6]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [[1,2,5,6,7,8],[3],[4]] => [2,6]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,3,6,8,7,2] => [[1,2,5,6,7],[3,8],[4]] => [2,5,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,3,7,8,6,2] => [[1,2,5,6,8],[3,7],[4]] => [2,4,2]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,3,8,7,6,2] => [[1,2,5,6],[3,7],[4],[8]] => [2,4,2]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,3,2,7,8] => [[1,2,5,6,7,8],[3],[4]] => [2,6]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,5,6,3,8,7,2] => [[1,2,5,6,7],[3,8],[4]] => [2,5,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [[1,2,5,6,7,8],[3],[4]] => [2,6]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [[1,2,5,6,7,8],[3],[4]] => [2,6]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [[1,2,5,6,7,8],[3],[4]] => [2,6]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,7,6,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => [2,4,2]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,5,3,2,7,8] => [[1,2,5,7,8],[3],[4],[6]] => [2,3,3]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,5,3,8,7,2] => [[1,2,5,7],[3,8],[4],[6]] => [2,3,2,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,5,7,3,8,2] => [[1,2,5,7,8],[3],[4],[6]] => [2,3,3]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,5,8,7,3,2] => [[1,2,5,7],[3,8],[4],[6]] => [2,3,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,5,3,2,8] => [[1,2,5,7,8],[3],[4],[6]] => [2,3,3]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,5,3,8,2] => [[1,2,5,7,8],[3],[4],[6]] => [2,3,3]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,5,8,3,2] => [[1,2,5,7,8],[3],[4],[6]] => [2,3,3]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,5,3,2] => [[1,2,5,7,8],[3],[4],[6]] => [2,3,3]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [[1,2,5,7],[3],[4],[6],[8]] => [2,3,2,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,6,5,3,2,8] => [[1,2,5,8],[3],[4],[6],[7]] => [2,3,3]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,6,5,8,3,2] => [[1,2,5,8],[3],[4],[6],[7]] => [2,3,3]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => [[1,2,5,8],[3],[4],[6],[7]] => [2,3,3]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [[1,2,5],[3],[4],[6],[7],[8]] => [2,3,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => [2,4,2]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [[1,2,6,8],[3,7],[4],[5]] => [2,4,2]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => [2,4,2]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [[1,2,6,7],[3,8],[4],[5]] => [2,5,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [[1,2,6],[3,7],[4,8],[5]] => [2,4,2]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,4,6,3,2,7,8] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,4,6,3,2,8,7] => [[1,2,6,7],[3,8],[4],[5]] => [2,5,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,4,6,7,3,2,8] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,4,7,8,6,3,2] => [[1,2,6,8],[3,7],[4],[5]] => [2,4,2]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,4,3,2,7,8] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,4,3,2,8,7] => [[1,2,6,7],[3,8],[4],[5]] => [2,5,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,4,3,8,7,2] => [[1,2,6,7],[3,8],[4],[5]] => [2,5,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,5,6,4,7,3,2,8] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,4,7,3,8,2] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,4,7,8,3,2] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,4,3,2,8] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,4,3,8,2] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [[1,2,6,7,8],[3],[4],[5]] => [2,6]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,6,8,4,3,2] => [[1,2,6,8],[3],[4],[5],[7]] => [2,4,2]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [[1,2,6],[3],[4],[5],[7],[8]] => [2,4,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => [2,6]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => [2,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [[1,2,7],[3,8],[4],[5],[6]] => [2,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,5,4,7,8,3,2] => [[1,2,7,8],[3],[4],[5],[6]] => [2,6]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,5,7,4,3,2,8] => [[1,2,7,8],[3],[4],[5],[6]] => [2,6]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [[1,2,7,8],[3],[4],[5],[6]] => [2,6]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,5,7,8,4,3,2] => [[1,2,7,8],[3],[4],[5],[6]] => [2,6]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,5,8,7,4,3,2] => [[1,2,7],[3,8],[4],[5],[6]] => [2,5,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => [[1,2,7,8],[3],[4],[5],[6]] => [2,6]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,5,4,3,8,2] => [[1,2,7,8],[3],[4],[5],[6]] => [2,6]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [[1,2,7,8],[3],[4],[5],[6]] => [2,6]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [[1,2,7,8],[3],[4],[5],[6]] => [2,6]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [[1,2,7],[3],[4],[5],[6],[8]] => [2,5,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [[1,2,8],[3],[4],[5],[6],[7]] => [2,6]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [[1,2,8],[3],[4],[5],[6],[7]] => [2,6]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [[1,2,8],[3],[4],[5],[6],[7]] => [2,6]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [[1,2,8],[3],[4],[5],[6],[7]] => [2,6]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [[1,2,8],[3],[4],[5],[6],[7]] => [2,6]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [[1,2,8],[3],[4],[5],[6],[7]] => [2,6]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => [2,6]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [[1,3,4,5,6],[2,7],[8]] => [6,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [[1,3,4,5,8],[2,6],[7]] => [5,3]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => [[1,3,4,5,8],[2,6],[7]] => [5,3]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [[1,3,4,5],[2,6],[7],[8]] => [5,3]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [[1,3,4,6,8],[2,5,7]] => [4,2,2]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [[1,3,4,6],[2,5,7],[8]] => [4,2,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [[1,3,4,6,7],[2,5,8]] => [4,3,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [[1,3,4,7],[2,5,8],[6]] => [4,3,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,5,4,8] => [[1,3,4,7,8],[2,5],[6]] => [4,4]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,5,4] => [[1,3,4,7,8],[2,5],[6]] => [4,4]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,6,8,7,5,4] => [[1,3,4,7],[2,5],[6],[8]] => [4,3,1]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,6,5,4] => [[1,3,4,8],[2,5],[6],[7]] => [4,4]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [[1,3,4],[2,5],[6],[7],[8]] => [4,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [[1,3,5,6,8],[2,4,7]] => [3,3,2]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [[1,3,5,6],[2,4,7],[8]] => [3,3,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [[1,3,5,7,8],[2,4,6]] => [3,2,3]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [[1,3,5,7],[2,4,6],[8]] => [3,2,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [[1,3,5,8],[2,4,6],[7]] => [3,2,3]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [[1,3,5,8],[2,4,6],[7]] => [3,2,3]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8]] => [3,2,3]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [[1,3,5,6],[2,4,7],[8]] => [3,3,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [[1,3,5,6,7],[2,4,8]] => [3,4,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4]] => [3,5]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [[1,3,5,6,7],[2,4],[8]] => [3,4,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [[1,3,5,6,8],[2,4],[7]] => [3,3,2]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [[1,3,5,6],[2,4],[7],[8]] => [3,3,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [[1,3,5,7,8],[2,4],[6]] => [3,2,3]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [[1,3,5,7],[2,4,8],[6]] => [3,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [[1,3,5,7],[2,4,8],[6]] => [3,2,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => [[1,3,5,7,8],[2,4],[6]] => [3,2,3]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,5,3] => [[1,3,5,7,8],[2,4],[6]] => [3,2,3]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [[1,3,5,7],[2,4],[6],[8]] => [3,2,2,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [[1,3,5,8],[2,4],[6],[7]] => [3,2,3]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => [[1,3,5,8],[2,4],[6],[7]] => [3,2,3]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [[1,3,5],[2,4],[6],[7],[8]] => [3,2,3]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [[1,3,6,7,8],[2,4],[5]] => [3,5]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [[1,3,6,8],[2,4,7],[5]] => [3,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [[1,3,6,7],[2,4,8],[5]] => [3,4,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [[1,3,6,7,8],[2,4],[5]] => [3,5]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [[1,3,6,7],[2,4,8],[5]] => [3,4,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [[1,3,6,8],[2,4,7],[5]] => [3,3,2]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => [[1,3,6,8],[2,4,7],[5]] => [3,3,2]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [[1,3,6],[2,4,7],[5],[8]] => [3,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,4,3,7,8] => [[1,3,6,7,8],[2,4],[5]] => [3,5]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [[1,3,6,7],[2,4,8],[5]] => [3,4,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => [[1,3,6,7,8],[2,4],[5]] => [3,5]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [[1,3,6,7],[2,4,8],[5]] => [3,4,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,4,3,8] => [[1,3,6,7,8],[2,4],[5]] => [3,5]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => [[1,3,6,7,8],[2,4],[5]] => [3,5]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [[1,3,6,7,8],[2,4],[5]] => [3,5]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,7,4,3] => [[1,3,6,7],[2,4],[5],[8]] => [3,4,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => [[1,3,6,8],[2,4],[5],[7]] => [3,3,2]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [[1,3,6,8],[2,4],[5],[7]] => [3,3,2]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [[1,3,6,8],[2,4],[5],[7]] => [3,3,2]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,7,6,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => [3,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [[1,3,7],[2,4,8],[5],[6]] => [3,4,1]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [[1,3,7],[2,4,8],[5],[6]] => [3,4,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [[1,3,7,8],[2,4],[5],[6]] => [3,5]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [[1,3,7,8],[2,4],[5],[6]] => [3,5]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [[1,3,7],[2,4,8],[5],[6]] => [3,4,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,6,7,5,4,3,8] => [[1,3,7,8],[2,4],[5],[6]] => [3,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,5,4,8,3] => [[1,3,7,8],[2,4],[5],[6]] => [3,5]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [[1,3,7,8],[2,4],[5],[6]] => [3,5]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [[1,3,7,8],[2,4],[5],[6]] => [3,5]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,7,5,4,3] => [[1,3,7],[2,4],[5],[6],[8]] => [3,4,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [[1,3,8],[2,4],[5],[6],[7]] => [3,5]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [[1,3,8],[2,4],[5],[6],[7]] => [3,5]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [[1,3,8],[2,4],[5],[6],[7]] => [3,5]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [[1,3,8],[2,4],[5],[6],[7]] => [3,5]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,6,5,4,3] => [[1,3,8],[2,4],[5],[6],[7]] => [3,5]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => [3,5]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [[1,3,4,5,8],[2,6],[7]] => [5,3]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => [[1,3,4,5,8],[2,6],[7]] => [5,3]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [[1,3,4,5],[2,6],[7],[8]] => [5,3]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [[1,3,4,6,8],[2,5,7]] => [4,2,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [[1,3,4,6,7,8],[2,5]] => [4,4]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [[1,3,4,6,8],[2,5],[7]] => [4,2,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => [[1,3,4,6,8],[2,5],[7]] => [4,2,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [[1,3,4,7,8],[2,5],[6]] => [4,4]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [[1,3,4,7],[2,5,8],[6]] => [4,3,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [[1,3,4,7],[2,5,8],[6]] => [4,3,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,6,7,5,4,8] => [[1,3,4,7,8],[2,5],[6]] => [4,4]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,5,8,4] => [[1,3,4,7,8],[2,5],[6]] => [4,4]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => [[1,3,4,7,8],[2,5],[6]] => [4,4]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,7,5,4] => [[1,3,4,7],[2,5],[6],[8]] => [4,3,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [[1,3,4,8],[2,5],[6],[7]] => [4,4]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => [[1,3,4,8],[2,5],[6],[7]] => [4,4]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [[1,3,4,8],[2,5],[6],[7]] => [4,4]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [[1,3,4],[2,5],[6],[7],[8]] => [4,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [[1,3,4,5,6],[2,7],[8]] => [6,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => [5,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [[1,3,4,5,7,8],[2,6]] => [5,3]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [[1,3,4,5,7],[2,6],[8]] => [5,2,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [[1,3,4,5,8],[2,6],[7]] => [5,3]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [[1,3,4,5,8],[2,6],[7]] => [5,3]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [[1,3,4,5,8],[2,6],[7]] => [5,3]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [[1,3,4,5],[2,6],[7],[8]] => [5,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [[1,3,4,5,6,8],[2,7]] => [6,2]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [[1,3,4,5,6],[2,7],[8]] => [6,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2]] => [8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [[1,3,4,5,6,7],[2],[8]] => [7,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [[1,3,4,5,6,8],[2],[7]] => [6,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [[1,3,4,5,6,8],[2],[7]] => [6,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [[1,3,4,5,6,8],[2],[7]] => [6,2]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [[1,3,4,5,6],[2],[7],[8]] => [6,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => [5,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [[1,3,4,5,7,8],[2],[6]] => [5,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [[1,3,4,5,7,8],[2],[6]] => [5,3]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [[1,3,4,5,7],[2,8],[6]] => [5,2,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => [[1,3,4,5,7,8],[2],[6]] => [5,3]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [[1,3,4,5,7,8],[2],[6]] => [5,3]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [[1,3,4,5,7,8],[2],[6]] => [5,3]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,7,5,1] => [[1,3,4,5,7],[2],[6],[8]] => [5,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [[1,3,4,5,8],[2],[6],[7]] => [5,3]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [[1,3,4,5,8],[2],[6],[7]] => [5,3]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => [[1,3,4,5,8],[2],[6],[7]] => [5,3]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => [[1,3,4,5,8],[2],[6],[7]] => [5,3]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [[1,3,4,5],[2],[6],[7],[8]] => [5,3]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => [4,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [[1,3,4,6,7],[2,8],[5]] => [4,3,1]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => [4,2,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [[1,3,4,6,7,8],[2],[5]] => [4,4]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [[1,3,4,6,7,8],[2],[5]] => [4,4]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [[1,3,4,6,8],[2,7],[5]] => [4,2,2]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,7,8,6,1] => [[1,3,4,6,8],[2,7],[5]] => [4,2,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,4,1,7,8] => [[1,3,4,6,7,8],[2],[5]] => [4,4]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,4,1,8,7] => [[1,3,4,6,7],[2,8],[5]] => [4,3,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,4,7,1,8] => [[1,3,4,6,7,8],[2],[5]] => [4,4]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => [[1,3,4,6,7,8],[2],[5]] => [4,4]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,4,8,7,1] => [[1,3,4,6,7],[2,8],[5]] => [4,3,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,4,1,8] => [[1,3,4,6,7,8],[2],[5]] => [4,4]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [[1,3,4,6,7,8],[2],[5]] => [4,4]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [[1,3,4,6,7,8],[2],[5]] => [4,4]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [[1,3,4,6,7],[2],[5],[8]] => [4,3,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,6,4,1,8] => [[1,3,4,6,8],[2],[5],[7]] => [4,2,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,6,4,8,1] => [[1,3,4,6,8],[2],[5],[7]] => [4,2,2]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,6,8,4,1] => [[1,3,4,6,8],[2],[5],[7]] => [4,2,2]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [[1,3,4,6,8],[2],[5],[7]] => [4,2,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [[1,3,4,7,8],[2],[5],[6]] => [4,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [[1,3,4,7],[2,8],[5],[6]] => [4,3,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [[1,3,4,7,8],[2],[5],[6]] => [4,4]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,6,5,7,4,1,8] => [[1,3,4,7,8],[2],[5],[6]] => [4,4]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => [[1,3,4,7],[2,8],[5],[6]] => [4,3,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,6,7,5,4,1,8] => [[1,3,4,7,8],[2],[5],[6]] => [4,4]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,5,4,1] => [[1,3,4,7,8],[2],[5],[6]] => [4,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => [4,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [[1,3,4,8],[2],[5],[6],[7]] => [4,4]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,6,5,8,4,1] => [[1,3,4,8],[2],[5],[6],[7]] => [4,4]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [[1,3,4],[2],[5],[6],[7],[8]] => [4,4]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => [3,5]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [[1,3,5,6],[2,7],[4,8]] => [3,3,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [[1,3,5,7,8],[2,6],[4]] => [3,2,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]] => [3,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [[1,3,5,7,8],[2,6],[4]] => [3,2,3]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [[1,3,5,7],[2,6],[4,8]] => [3,2,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [[1,3,5,8],[2,6],[4,7]] => [3,2,3]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [[1,3,5,8],[2,6],[4,7]] => [3,2,3]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [[1,3,5],[2,6],[4,7],[8]] => [3,2,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => [3,5]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [[1,3,5,6,8],[2,7],[4]] => [3,3,2]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [[1,3,5,6],[2,7],[4,8]] => [3,3,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [[1,3,5,6,7],[2,8],[4]] => [3,4,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [[1,3,5,6,7,8],[2],[4]] => [3,5]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [[1,3,5,6,7],[2,8],[4]] => [3,4,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [[1,3,5,7,8],[2,6],[4]] => [3,2,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [[1,3,5,7],[2,6,8],[4]] => [3,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [[1,3,5,7,8],[2,6],[4]] => [3,2,3]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [[1,3,5,7,8],[2,6],[4]] => [3,2,3]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [[1,3,5,7],[2,6,8],[4]] => [3,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,6,7,5,8,1] => [[1,3,5,7,8],[2,6],[4]] => [3,2,3]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,6,7,8,5,1] => [[1,3,5,7,8],[2,6],[4]] => [3,2,3]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [[1,3,5,7],[2,6],[4],[8]] => [3,2,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [[1,3,5,8],[2,6],[4],[7]] => [3,2,3]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [[1,3,5],[2,6],[4],[7],[8]] => [3,2,3]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => [3,5]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,4,5,3,1,6,8,7] => [[1,3,5,6,7],[2,8],[4]] => [3,4,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,3,1,7,6,8] => [[1,3,5,6,8],[2,7],[4]] => [3,3,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => [[1,3,5,6,8],[2,7],[4]] => [3,3,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [[1,3,5,6],[2,7],[4,8]] => [3,3,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,3,6,1,8,7] => [[1,3,5,6,7],[2,8],[4]] => [3,4,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [[1,3,5,6,7,8],[2],[4]] => [3,5]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,3,6,8,7,1] => [[1,3,5,6,7],[2,8],[4]] => [3,4,1]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,7,8,6,1] => [[1,3,5,6,8],[2,7],[4]] => [3,3,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,3,1,7,8] => [[1,3,5,6,7,8],[2],[4]] => [3,5]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => [[1,3,5,6,7,8],[2],[4]] => [3,5]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => [[1,3,5,6,7],[2,8],[4]] => [3,4,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => [[1,3,5,6,7,8],[2],[4]] => [3,5]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => [[1,3,5,6,7,8],[2],[4]] => [3,5]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => [[1,3,5,6,7,8],[2],[4]] => [3,5]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,7,3,1] => [[1,3,5,6,7],[2],[4],[8]] => [3,4,1]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,6,3,1] => [[1,3,5,6,8],[2],[4],[7]] => [3,3,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,5,3,1,7,8] => [[1,3,5,7,8],[2],[4],[6]] => [3,2,3]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => [3,2,2,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,5,3,7,8,1] => [[1,3,5,7,8],[2],[4],[6]] => [3,2,3]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [[1,3,5,7],[2,8],[4],[6]] => [3,2,2,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [[1,3,5,7,8],[2],[4],[6]] => [3,2,3]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => [[1,3,5,7,8],[2],[4],[6]] => [3,2,3]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [[1,3,5,7],[2,8],[4],[6]] => [3,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [[1,3,5,7,8],[2],[4],[6]] => [3,2,3]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => [[1,3,5,7,8],[2],[4],[6]] => [3,2,3]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,5,8,3,1] => [[1,3,5,7,8],[2],[4],[6]] => [3,2,3]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [[1,3,5,7,8],[2],[4],[6]] => [3,2,3]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [[1,3,5,7],[2],[4],[6],[8]] => [3,2,2,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => [[1,3,5,8],[2],[4],[6],[7]] => [3,2,3]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [[1,3,5],[2],[4],[6],[7],[8]] => [3,2,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => [3,5]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [[1,3,6,7],[2,8],[4],[5]] => [3,4,1]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [[1,3,6],[2,7],[4,8],[5]] => [3,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [[1,3,6,7],[2,8],[4],[5]] => [3,4,1]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,7,8,6,1] => [[1,3,6,8],[2,7],[4],[5]] => [3,3,2]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [[1,3,6],[2,7],[4,8],[5]] => [3,3,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => [[1,3,6,7,8],[2],[4],[5]] => [3,5]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [[1,3,6,7,8],[2],[4],[5]] => [3,5]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [[1,3,6,7,8],[2],[4],[5]] => [3,5]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,4,6,7,8,3,1] => [[1,3,6,7,8],[2],[4],[5]] => [3,5]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,4,7,6,8,3,1] => [[1,3,6,8],[2,7],[4],[5]] => [3,3,2]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => [[1,3,6,8],[2,7],[4],[5]] => [3,3,2]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,4,8,7,6,3,1] => [[1,3,6],[2,7],[4],[5],[8]] => [3,3,2]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,4,3,1,8,7] => [[1,3,6,7],[2,8],[4],[5]] => [3,4,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,4,3,7,8,1] => [[1,3,6,7,8],[2],[4],[5]] => [3,5]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,4,7,3,1,8] => [[1,3,6,7,8],[2],[4],[5]] => [3,5]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,4,7,8,3,1] => [[1,3,6,7,8],[2],[4],[5]] => [3,5]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => [[1,3,6,7],[2,8],[4],[5]] => [3,4,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,5,6,7,4,3,1,8] => [[1,3,6,7,8],[2],[4],[5]] => [3,5]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => [[1,3,6,7,8],[2],[4],[5]] => [3,5]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => [[1,3,6,7,8],[2],[4],[5]] => [3,5]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [[1,3,6,7,8],[2],[4],[5]] => [3,5]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,5,7,6,4,3,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => [3,3,2]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,7,6,4,3,1] => [[1,3,6],[2],[4],[5],[7],[8]] => [3,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [[1,3,7],[2,8],[4],[5],[6]] => [3,4,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [[1,3,7,8],[2],[4],[5],[6]] => [3,5]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [[1,3,7],[2,8],[4],[5],[6]] => [3,4,1]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,5,4,7,8,3,1] => [[1,3,7,8],[2],[4],[5],[6]] => [3,5]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [[1,3,7],[2,8],[4],[5],[6]] => [3,4,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => [[1,3,7,8],[2],[4],[5],[6]] => [3,5]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,5,4,3,1,8] => [[1,3,7,8],[2],[4],[5],[6]] => [3,5]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [[1,3,7,8],[2],[4],[5],[6]] => [3,5]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,5,4,3,1] => [[1,3,7,8],[2],[4],[5],[6]] => [3,5]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [[1,3,7],[2],[4],[5],[6],[8]] => [3,4,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [[1,3,8],[2],[4],[5],[6],[7]] => [3,5]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [[1,3,8],[2],[4],[5],[6],[7]] => [3,5]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => [[1,3,8],[2],[4],[5],[6],[7]] => [3,5]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,6,8,5,4,3,1] => [[1,3,8],[2],[4],[5],[6],[7]] => [3,5]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [[1,3,8],[2],[4],[5],[6],[7]] => [3,5]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => [3,5]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [[1,4,5,6,8],[2,7],[3]] => [6,2]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => [6,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [[1,4,5,7,8],[2,6],[3]] => [5,3]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [[1,4,5,7],[2,6],[3,8]] => [5,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]] => [5,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [[1,4,5,8],[2,6],[3,7]] => [5,3]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [[1,4,5,8],[2,6],[3,7]] => [5,3]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [[1,4,5],[2,6],[3,7],[8]] => [5,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [[1,4,6,8],[2,5,7],[3]] => [4,2,2]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [[1,4,6,7,8],[2,5],[3]] => [4,4]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [[1,4,6,7,8],[2,5],[3]] => [4,4]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [[1,4,6,7],[2,5],[3,8]] => [4,3,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [[1,4,6,8],[2,5],[3,7]] => [4,2,2]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [[1,4,6,8],[2,5],[3,7]] => [4,2,2]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [[1,4,6,8],[2,5],[3,7]] => [4,2,2]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [[1,4,6],[2,5],[3,7],[8]] => [4,2,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [[1,4,7,8],[2,5],[3,6]] => [4,4]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [[1,4,7],[2,5,8],[3,6]] => [4,3,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [[1,4,7,8],[2,5],[3,6]] => [4,4]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,6,7,8,5,4] => [[1,4,7,8],[2,5],[3,6]] => [4,4]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [[1,4,7],[2,5],[3,6],[8]] => [4,3,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [[1,4,8],[2,5],[3,6],[7]] => [4,4]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [[1,4,8],[2,5],[3,6],[7]] => [4,4]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,7,6,8,5,4] => [[1,4,8],[2,5],[3,6],[7]] => [4,4]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [[1,4,8],[2,5],[3,6],[7]] => [4,4]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => [4,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [[1,4,5,6,8],[2,7],[3]] => [6,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [[1,4,5,6,8],[2,7],[3]] => [6,2]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => [6,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [[1,4,5,7,8],[2,6],[3]] => [5,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [[1,4,5,7],[2,6,8],[3]] => [5,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [[1,4,5,7,8],[2,6],[3]] => [5,3]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [[1,4,5,7,8],[2,6],[3]] => [5,3]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [[1,4,5,7],[2,6],[3,8]] => [5,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]] => [5,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [[1,4,5,8],[2,6],[3,7]] => [5,3]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [[1,4,5,8],[2,6],[3,7]] => [5,3]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [[1,4,5],[2,6],[3,7],[8]] => [5,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => [6,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [[1,4,5,6,8],[2,7],[3]] => [6,2]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,7,8,6,1] => [[1,4,5,6,8],[2,7],[3]] => [6,2]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [[1,4,5,7],[2,6,8],[3]] => [5,2,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,6,7,5,1,8] => [[1,4,5,7,8],[2,6],[3]] => [5,3]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [[1,4,5,8],[2,6],[3],[7]] => [5,3]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [[1,4,5],[2,6],[3],[7],[8]] => [5,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [[1,4,6,7,8],[2,5],[3]] => [4,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [[1,4,6,7],[2,5,8],[3]] => [4,3,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [[1,4,6,8],[2,5,7],[3]] => [4,2,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [[1,4,6,8],[2,5,7],[3]] => [4,2,2]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [[1,4,6],[2,5,7],[3,8]] => [4,2,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [[1,4,6,7],[2,5,8],[3]] => [4,3,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [[1,4,6,7,8],[2,5],[3]] => [4,4]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [[1,4,6,7],[2,5,8],[3]] => [4,3,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [[1,4,6,8],[2,5,7],[3]] => [4,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [[1,4,6,8],[2,5,7],[3]] => [4,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,7,8,6,1] => [[1,4,6,8],[2,5,7],[3]] => [4,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,5,6,4,1,8,7] => [[1,4,6,7],[2,5,8],[3]] => [4,3,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,5,6,4,7,8,1] => [[1,4,6,7,8],[2,5],[3]] => [4,4]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,5,6,7,4,1,8] => [[1,4,6,7,8],[2,5],[3]] => [4,4]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [[1,4,6,7,8],[2,5],[3]] => [4,4]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [[1,4,6,7,8],[2,5],[3]] => [4,4]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,5,7,6,4,1,8] => [[1,4,6,8],[2,5],[3],[7]] => [4,2,2]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => [[1,4,6,8],[2,5],[3],[7]] => [4,2,2]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,5,7,6,8,4,1] => [[1,4,6,8],[2,5],[3],[7]] => [4,2,2]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,5,7,8,6,4,1] => [[1,4,6,8],[2,5],[3],[7]] => [4,2,2]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [[1,4,7],[2,5,8],[3],[6]] => [4,3,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [[1,4,7,8],[2,5],[3],[6]] => [4,4]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [[1,4,7],[2,5,8],[3],[6]] => [4,3,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,6,5,7,4,1,8] => [[1,4,7,8],[2,5],[3],[6]] => [4,4]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [[1,4,7,8],[2,5],[3],[6]] => [4,4]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [[1,4,7,8],[2,5],[3],[6]] => [4,4]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [[1,4,7,8],[2,5],[3],[6]] => [4,4]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => [[1,4,7],[2,5],[3],[6],[8]] => [4,3,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [[1,4,8],[2,5],[3],[6],[7]] => [4,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [[1,4,8],[2,5],[3],[6],[7]] => [4,4]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => [[1,4,8],[2,5],[3],[6],[7]] => [4,4]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [[1,4],[2,5],[3],[6],[7],[8]] => [4,4]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [[1,4,5,7],[2,6,8],[3]] => [5,2,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [[1,4,5,7,8],[2,6],[3]] => [5,3]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [[1,4,5,7],[2,6],[3,8]] => [5,2,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [[1,4,5,8],[2,6],[3,7]] => [5,3]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [[1,4,5,8],[2,6],[3,7]] => [5,3]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [[1,4,5],[2,6],[3,7],[8]] => [5,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => [[1,4,5,6,8],[2,7],[3]] => [6,2]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => [6,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,2,5,7,6,1,8] => [[1,4,5,6,8],[2,7],[3]] => [6,2]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,2,5,7,6,8,1] => [[1,4,5,6,8],[2,7],[3]] => [6,2]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [[1,4,5,6,8],[2,7],[3]] => [6,2]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,2,5,8,7,6,1] => [[1,4,5,6],[2,7],[3],[8]] => [6,2]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,2,6,5,1,8,7] => [[1,4,5,7],[2,6,8],[3]] => [5,2,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,2,6,5,7,8,1] => [[1,4,5,7,8],[2,6],[3]] => [5,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,2,6,7,5,1,8] => [[1,4,5,7,8],[2,6],[3]] => [5,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [[1,4,5,7,8],[2,6],[3]] => [5,3]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,2,7,6,5,8,1] => [[1,4,5,8],[2,6],[3],[7]] => [5,3]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,4,2,7,8,6,5,1] => [[1,4,5,8],[2,6],[3],[7]] => [5,3]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [[1,4,5],[2,6],[3],[7],[8]] => [5,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,2,1,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,5,2,1,7,6,8] => [[1,4,5,6,8],[2,7],[3]] => [6,2]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => [6,2]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,5,2,7,6,1,8] => [[1,4,5,6,8],[2,7],[3]] => [6,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [[1,4,5,6,8],[2,7],[3]] => [6,2]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,2,7,8,6,1] => [[1,4,5,6,8],[2,7],[3]] => [6,2]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,2,1,8,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [[1,4,5,6,7,8],[2],[3]] => [8]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => [[1,4,5,6,7],[2],[3],[8]] => [7,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,6,2,8,1] => [[1,4,5,6,8],[2],[3],[7]] => [6,2]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [[1,4,5,6,8],[2],[3],[7]] => [6,2]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [[1,4,5,6,8],[2],[3],[7]] => [6,2]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,5,2,1,8,7] => [[1,4,5,7],[2,8],[3],[6]] => [5,2,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,5,2,7,1,8] => [[1,4,5,7,8],[2],[3],[6]] => [5,3]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,5,2,7,8,1] => [[1,4,5,7,8],[2],[3],[6]] => [5,3]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [[1,4,5,7,8],[2],[3],[6]] => [5,3]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,5,7,8,2,1] => [[1,4,5,7,8],[2],[3],[6]] => [5,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => [[1,4,5,7,8],[2],[3],[6]] => [5,3]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,5,8,2,1] => [[1,4,5,7,8],[2],[3],[6]] => [5,3]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [[1,4,5,7,8],[2],[3],[6]] => [5,3]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => [5,3]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,6,5,2,8,1] => [[1,4,5,8],[2],[3],[6],[7]] => [5,3]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,6,5,8,2,1] => [[1,4,5,8],[2],[3],[6],[7]] => [5,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,4,2,1,6,8,7] => [[1,4,6,7],[2,8],[3],[5]] => [4,3,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,4,2,1,7,6,8] => [[1,4,6,8],[2,7],[3],[5]] => [4,2,2]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,4,2,1,7,8,6] => [[1,4,6,8],[2,7],[3],[5]] => [4,2,2]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [[1,4,6],[2,7],[3,8],[5]] => [4,2,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,5,4,2,6,1,7,8] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,4,2,6,7,8,1] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [[1,4,6,8],[2,7],[3],[5]] => [4,2,2]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,4,2,7,6,8,1] => [[1,4,6,8],[2,7],[3],[5]] => [4,2,2]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,4,2,7,8,6,1] => [[1,4,6,8],[2,7],[3],[5]] => [4,2,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,4,6,2,7,8,1] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,4,6,7,2,8,1] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,4,6,7,8,2,1] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,4,7,6,2,1,8] => [[1,4,6,8],[2,7],[3],[5]] => [4,2,2]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => [[1,4,6,8],[2,7],[3],[5]] => [4,2,2]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [[1,4,6,8],[2,7],[3],[5]] => [4,2,2]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,4,7,8,6,2,1] => [[1,4,6,8],[2,7],[3],[5]] => [4,2,2]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => [[1,4,6,7],[2,8],[3],[5]] => [4,3,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,4,2,7,1,8] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,4,2,7,8,1] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,4,2,8,7,1] => [[1,4,6,7],[2,8],[3],[5]] => [4,3,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,4,7,2,1,8] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,4,7,8,2,1] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,4,2,1,8] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,4,8,2,1] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [[1,4,6,7,8],[2],[3],[5]] => [4,4]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [[1,4,6,7],[2],[3],[5],[8]] => [4,3,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => [4,2,2]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,6,4,2,8,1] => [[1,4,6,8],[2],[3],[5],[7]] => [4,2,2]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,6,4,8,2,1] => [[1,4,6,8],[2],[3],[5],[7]] => [4,2,2]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,5,7,6,8,4,2,1] => [[1,4,6,8],[2],[3],[5],[7]] => [4,2,2]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [[1,4,6,8],[2],[3],[5],[7]] => [4,2,2]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => [4,2,2]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,5,4,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => [4,4]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [[1,4,7],[2,8],[3],[5],[6]] => [4,3,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,6,5,4,7,2,1,8] => [[1,4,7,8],[2],[3],[5],[6]] => [4,4]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [[1,4,7,8],[2],[3],[5],[6]] => [4,4]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,5,4,7,8,2,1] => [[1,4,7,8],[2],[3],[5],[6]] => [4,4]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,5,4,8,7,2,1] => [[1,4,7],[2,8],[3],[5],[6]] => [4,3,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [[1,4,7],[2],[3],[5],[6],[8]] => [4,3,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [[1,4,8],[2],[3],[5],[6],[7]] => [4,4]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => [[1,4,8],[2],[3],[5],[6],[7]] => [4,4]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => [[1,4,8],[2],[3],[5],[6],[7]] => [4,4]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [[1,4,8],[2],[3],[5],[6],[7]] => [4,4]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => [4,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [[1,5,6,8],[2,7],[3],[4]] => [6,2]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [[1,5,6,8],[2,7],[3],[4]] => [6,2]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [[1,5,6],[2,7],[3,8],[4]] => [6,2]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [[1,5,7,8],[2,6],[3],[4]] => [5,3]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [[1,5,7],[2,6,8],[3],[4]] => [5,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [[1,5,7,8],[2,6],[3],[4]] => [5,3]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [[1,5,7,8],[2,6],[3],[4]] => [5,3]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [[1,5,7],[2,6],[3,8],[4]] => [5,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [[1,5,8],[2,6],[3,7],[4]] => [5,3]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [[1,5,8],[2,6],[3,7],[4]] => [5,3]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [[1,5,8],[2,6],[3,7],[4]] => [5,3]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => [5,3]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [[1,5,6,8],[2,7],[3],[4]] => [6,2]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [[1,5,6],[2,7],[3,8],[4]] => [6,2]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [[1,5,6,8],[2,7],[3],[4]] => [6,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [[1,5,6,8],[2,7],[3],[4]] => [6,2]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,3,2,5,7,8,6,1] => [[1,5,6,8],[2,7],[3],[4]] => [6,2]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [[1,5,6],[2,7],[3,8],[4]] => [6,2]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [[1,5,7,8],[2,6],[3],[4]] => [5,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [[1,5,7],[2,6,8],[3],[4]] => [5,2,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [[1,5,7,8],[2,6],[3],[4]] => [5,3]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [[1,5,7],[2,6,8],[3],[4]] => [5,2,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,3,2,6,7,5,1,8] => [[1,5,7,8],[2,6],[3],[4]] => [5,3]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,6,7,5,8,1] => [[1,5,7,8],[2,6],[3],[4]] => [5,3]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [[1,5,8],[2,6],[3,7],[4]] => [5,3]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,7,8,6,5,1] => [[1,5,8],[2,6],[3,7],[4]] => [5,3]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [[1,5],[2,6],[3,7],[4],[8]] => [5,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,3,5,2,1,6,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,3,5,2,1,8,7,6] => [[1,5,6],[2,7],[3,8],[4]] => [6,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => [[1,5,6,8],[2,7],[3],[4]] => [6,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [[1,5,6,8],[2,7],[3],[4]] => [6,2]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,3,5,6,2,7,1,8] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,3,5,6,7,2,8,1] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,3,6,5,2,1,7,8] => [[1,5,7,8],[2,6],[3],[4]] => [5,3]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [[1,5,7],[2,6,8],[3],[4]] => [5,2,1]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [[1,5,7],[2,6,8],[3],[4]] => [5,2,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,3,6,5,7,2,1,8] => [[1,5,7,8],[2,6],[3],[4]] => [5,3]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [[1,5,7,8],[2,6],[3],[4]] => [5,3]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [[1,5,7,8],[2,6],[3],[4]] => [5,3]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [[1,5,7],[2,6,8],[3],[4]] => [5,2,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [[1,5,7,8],[2,6],[3],[4]] => [5,3]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => [[1,5,8],[2,6],[3],[4],[7]] => [5,3]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,7,6,5,2,8,1] => [[1,5,8],[2,6],[3],[4],[7]] => [5,3]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,7,6,5,8,2,1] => [[1,5,8],[2,6],[3],[4],[7]] => [5,3]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,7,8,6,5,2,1] => [[1,5,8],[2,6],[3],[4],[7]] => [5,3]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => [5,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,3,2,1,6,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,3,2,1,7,6,8] => [[1,5,6,8],[2,7],[3],[4]] => [6,2]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => [[1,5,6],[2,7],[3,8],[4]] => [6,2]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,5,3,2,6,1,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,3,2,6,7,8,1] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,3,2,7,6,1,8] => [[1,5,6,8],[2,7],[3],[4]] => [6,2]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,3,6,7,2,8,1] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [[1,5,6,7,8],[2],[3],[4]] => [8]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,6,3,2,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => [6,2]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => [[1,5,6,8],[2],[3],[4],[7]] => [6,2]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [6,2]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => [[1,5,7],[2,8],[3],[4],[6]] => [5,2,1]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => [[1,5,7],[2,8],[3],[4],[6]] => [5,2,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [[1,5,7,8],[2],[3],[4],[6]] => [5,3]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,5,7,3,2,1,8] => [[1,5,7,8],[2],[3],[4],[6]] => [5,3]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [[1,5,7,8],[2],[3],[4],[6]] => [5,3]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => [[1,5,7,8],[2],[3],[4],[6]] => [5,3]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,5,8,7,3,2,1] => [[1,5,7],[2,8],[3],[4],[6]] => [5,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [[1,5,7,8],[2],[3],[4],[6]] => [5,3]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => [[1,5,7,8],[2],[3],[4],[6]] => [5,3]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [5,2,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => [5,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [[1,5,8],[2],[3],[4],[6],[7]] => [5,3]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [[1,5,8],[2],[3],[4],[6],[7]] => [5,3]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => [[1,5,8],[2],[3],[4],[6],[7]] => [5,3]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,6,5,3,2,1] => [[1,5,8],[2],[3],[4],[6],[7]] => [5,3]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => [5,3]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [[1,6,8],[2,7],[3],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [[1,6,8],[2,7],[3],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [[1,6,8],[2,7],[3],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [[1,6,8],[2,7],[3],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [[1,6,8],[2,7],[3],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [[1,6],[2,7],[3,8],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,4,3,6,2,1,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,4,3,6,2,1,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,4,3,6,2,7,8,1] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,4,3,6,7,2,1,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,4,3,6,8,7,2,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,4,3,7,6,2,1,8] => [[1,6,8],[2,7],[3],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,4,3,7,6,2,8,1] => [[1,6,8],[2,7],[3],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,3,7,8,6,2,1] => [[1,6,8],[2,7],[3],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => [[1,6],[2,7],[3,8],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,4,7,6,3,2,1,8] => [[1,6,8],[2,7],[3],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => [[1,6,8],[2,7],[3],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,4,7,6,8,3,2,1] => [[1,6,8],[2,7],[3],[4],[5]] => [6,2]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,4,7,8,6,3,2,1] => [[1,6,8],[2,7],[3],[4],[5]] => [6,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,6,4,3,2,7,1,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,4,3,8,7,2,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,4,7,3,2,1,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,4,3,2,8,1] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,4,3,8,2,1] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [[1,6,7,8],[2],[3],[4],[5]] => [8]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [7,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => [6,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,6,4,3,2,8,1] => [[1,6,8],[2],[3],[4],[5],[7]] => [6,2]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,6,4,3,8,2,1] => [[1,6,8],[2],[3],[4],[5],[7]] => [6,2]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => [[1,6,8],[2],[3],[4],[5],[7]] => [6,2]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [[1,6,8],[2],[3],[4],[5],[7]] => [6,2]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [[1,6,8],[2],[3],[4],[5],[7]] => [6,2]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => [6,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,5,4,3,8,2,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [[1,7,8],[2],[3],[4],[5],[6]] => [8]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [[1,8],[2],[3],[4],[5],[6],[7]] => [8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [8]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [8]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [8]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [8]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [8]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => [8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => [9]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [10]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,6,5,4,3,2,1,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => [9]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => [2,7]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [2,8]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,7,6,5,4,3,2,1,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [10]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,6,8,5,4,3,2,1,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => [9]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,7,5,4,3,2,1,9] => [[1,7,9],[2],[3],[4],[5],[6],[8]] => [7,2]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,7,9,6,5,4,3,2] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => [2,7]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [2,8]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,6,5,8,4,3,2,1,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => [9]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,7,8,5,4,3,2,1,9] => [[1,7,8,9],[2],[3],[4],[5],[6]] => [9]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,7,8,9,6,5,4,3,2] => [[1,2,8,9],[3],[4],[5],[6],[7]] => [2,7]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,8,10,7,6,5,4,3,2] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [2,8]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,9,6,5,4,3,2,1,10] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [10]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [6,7,5,8,4,3,2,1,9] => [[1,7,8,9],[2],[3],[4],[5],[6]] => [9]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,8,9,10,7,6,5,4,3,2] => [[1,2,9,10],[3],[4],[5],[6],[7],[8]] => [2,8]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [6,5,7,8,4,3,2,1,9] => [[1,7,8,9],[2],[3],[4],[5],[6]] => [9]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,6,8,9,5,4,3,2] => [[1,2,8,9],[3],[4],[5],[6],[7]] => [2,7]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [7,6,8,9,5,4,3,2,1,10] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,6,5,4,3,2,8,1,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => [9]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,9,5,4,3,2] => [[1,2,7,8,9],[3],[4],[5],[6]] => [2,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => [9]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => [2,7]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,7,8,9,10,6,5,4,3,2] => [[1,2,8,9,10],[3],[4],[5],[6],[7]] => [2,8]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [3,6]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,7,6,5,4,3,2,9,1,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [10]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9] => [[1,7,8,9],[2],[3],[4],[5],[6]] => [9]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,7,8,6,5,4,3,2,9] => [[1,2,8,9],[3],[4],[5],[6],[7]] => [2,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [10]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [2,8]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [6,5,4,3,7,8,2,1,9] => [[1,7,8,9],[2],[3],[4],[5],[6]] => [9]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,5,7,8,9,4,3,2] => [[1,2,7,8,9],[3],[4],[5],[6]] => [2,7]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [3,7]
[] => [] => [] => []
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [[1,3,4,5,6,7,8],[2],[9]] => [8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [[1,3,4,5,6,7],[2],[8],[9]] => [7,2]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [[1,3,4],[2],[5],[6],[7],[8],[9]] => [4,5]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => [[1,3,5,6,7,8,9],[2],[4]] => [3,6]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,3,1] => [[1,3,5,6,7,8,9],[2],[4]] => [3,6]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7],[8],[9]] => [3,6]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [[1,4,5,6,7,8,9],[2],[3]] => [9]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => [[1,4,5,6,7,8,9],[2],[3]] => [9]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,2,9,1] => [[1,4,5,6,7,8,9],[2],[3]] => [9]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => [[1,4,5,6,7,8,9],[2],[3]] => [9]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,9,4,2,1] => [[1,4,6,7,8,9],[2],[3],[5]] => [4,5]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [[1,5,6,7,8,9],[2],[3],[4]] => [9]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,6,3,7,8,9,2,1] => [[1,5,6,7,8,9],[2],[3],[4]] => [9]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [[1,5,6,7,8,9],[2],[3],[4]] => [9]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,7,9,8,3,2,1] => [[1,5,6,7,8],[2],[3],[4],[9]] => [8,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => [9]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,8,3,9,2,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => [9]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => [9]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,6,4,7,3,8,2,9,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => [9]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,9,8,4,3,2,1] => [[1,6,7,8],[2],[3],[4],[5],[9]] => [8,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => [9]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => [9]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,7,9,8,5,4,3,2,1] => [[1,7,8],[2],[3],[4],[5],[6],[9]] => [8,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [6,8,7,5,4,3,2,9,1] => [[1,7,9],[2],[3],[4],[5],[6],[8]] => [7,2]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,8,7,9,5,4,3,2,1] => [[1,7,9],[2],[3],[4],[5],[6],[8]] => [7,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => [9]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,6,8,5,4,3,2,9,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => [9]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [7,6,8,5,9,4,3,2,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => [9]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,6,8,9,5,4,3,2,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => [9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,8,6,5,4,3,2,9,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => [9]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,6,5,4,3,2,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => [9]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,8,6,5,4,3,2,1] => [[1,8],[2],[3],[4],[5],[6],[7],[9]] => [8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => [9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => [9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,7,6,5,4,9,3,2,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => [9]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,7,6,5,9,4,3,2,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => [9]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,7,6,9,5,4,3,2,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => [9]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,7,9,6,5,4,3,2,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => [9]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => [9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => [9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [[1,2,3,4,5,6,7,8],[9]] => [8,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [[1,2,3,4,5,6,7,9],[8]] => [7,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [[1,2,4,5,6,7,8,9],[3]] => [2,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => [10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [[1,2,3,4,5,6,7],[8],[9]] => [7,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [[1,2,3,4,5,6,7,8,10],[9]] => [8,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [[1,2,3,4,5,6,9],[7],[8]] => [6,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [[1,2,3,4,5,6,7,9,10],[8]] => [7,3]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [[1,2,3,4,5,6,8,9,10],[7]] => [6,4]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [[1,2,3,4,5,7,8,9,10],[6]] => [5,5]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [[1,2,3,4,6,7,8,9,10],[5]] => [4,6]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [[1,2,5,6,7,8,9],[3],[4]] => [2,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [[1,2,3,5,6,7,8,9,10],[4]] => [3,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [[1,2,4,5,6,7,8,9,10],[3]] => [2,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => [8,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,8,9,7,6] => [[1,2,3,4,5,6,9],[7],[8]] => [6,3]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [[1,2,3,4,5,6],[7],[8],[9]] => [6,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => [10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [7,3]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,10,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => [10]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => [[1,2,4,5,6,7,8,9,10,11,12],[3]] => [2,10]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8],[9]] => [5,4]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [6,4]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,8,3,9,2] => [[1,2,5,6,7,8,9],[3],[4]] => [2,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,2,7,8,9,10,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => [10]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,10,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => [10]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,3,2] => [[1,2,5,6,7,8,9],[3],[4]] => [2,7]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [4,5]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,9,4,3,2] => [[1,2,6,7,8,9],[3],[4],[5]] => [2,7]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [5,5]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,10,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => [10]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,10,3,2] => [[1,2,5,6,7,8,9,10],[3],[4]] => [2,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,9,2,10,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => [10]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,9,10,4,3,2] => [[1,2,6,7,8,9,10],[3],[4],[5]] => [2,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [[1,2,3,4,5,6,7,9],[8]] => [7,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => [2,7]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3],[4]] => [2,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]] => [9]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [[1,5,6,7,8,9],[2],[3],[4]] => [9]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [[1,6,7,8,9],[2],[3],[4],[5]] => [9]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [[1,7,8,9],[2],[3],[4],[5],[6]] => [9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [[1,2,3,4,5,6,7,8,10],[9]] => [8,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => [7,3]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]] => [6,4]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => [5,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]] => [4,6]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]] => [4,2,2,2]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [4,6]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => [3,7]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]] => [2,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => [2,2,2,2,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [9,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => [3,2,2,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [[1,4,5,6,7,8,9,10],[2],[3]] => [10]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [[1,5,6,7,8,9,10],[2],[3],[4]] => [10]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => [10]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => [6,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => [10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [[1,3,4,5,6,7,8,9],[2]] => [9]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [[1,3,5,6,7,8,9],[2],[4]] => [3,6]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [10]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,8,10,9,4,3,2,1] => [[1,6,7,8,9],[2],[3],[4],[5],[10]] => [9,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,7,8,9,10,4,3,2,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => [10]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,7,8,10,9,3,2,1] => [[1,5,6,7,8,9],[2],[3],[4],[10]] => [9,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,9,10,3,2,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => [10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => [9,1]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,10,9,7,6,5,4,3,2,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [9,1]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,8,10,7,6,5,4,3,2,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [10]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [7,8,10,9,6,5,4,3,2,1] => [[1,8,9],[2],[3],[4],[5],[6],[7],[10]] => [9,1]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [8,7,9,10,6,5,4,3,2,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,2,1,9] => [[1,4,5,6,7,8,9],[2],[3]] => [9]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,7,2,1,8,9] => [[1,4,5,6,7,8,9],[2],[3]] => [9]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,6,2,1,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]] => [9]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]] => [9]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]] => [9]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => [3,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [10]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,9,7,6,5,4,3,2,10,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [10]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,5,4,3,2,7,1,8,9] => [[1,7,8,9],[2],[3],[4],[5],[6]] => [9]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,4,3,2,6,1,7,8,9] => [[1,6,7,8,9],[2],[3],[4],[5]] => [9]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8,9] => [[1,5,6,7,8,9],[2],[3],[4]] => [9]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]] => [9]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [10]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,8,3,1,9] => [[1,3,5,6,7,8,9],[2],[4]] => [3,6]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,10,3,1] => [[1,3,5,6,7,8,9,10],[2],[4]] => [3,7]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => [2,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6,9,10] => [[1,2,3,4,5,6,8,9,10],[7]] => [6,4]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,9,6,10] => [[1,2,3,4,5,6,8,9,10],[7]] => [6,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,3,7,8,9,10,1] => [[1,3,5,6,7,8,9,10],[2],[4]] => [3,7]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,9,10,5,4,3,2] => [[1,2,7,8,9,10],[3],[4],[5],[6]] => [2,8]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,9,3,2] => [[1,2,6,7,8,9],[3],[4],[5]] => [2,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [[1,4,5,6,7,8,9],[2],[3]] => [9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [[1,3,4,5,6,7,8],[2,9]] => [8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => [[1,3,4,5,6,7,8],[2],[9],[10]] => [8,2]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => [10]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [10]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,8,7,6,5,4,10,3,2,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [10]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,8,7,6,5,10,4,3,2,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [10]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,8,7,6,10,5,4,3,2,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [10]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,8,7,10,6,5,4,3,2,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [10]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8,9] => [[1,3,4,6,7,8,9],[2,5]] => [4,5]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => [10]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,7,5,8,4,9,3,10,2] => [[1,2,7,8,9,10],[3],[4],[5],[6]] => [2,8]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,6,4,7,3,8,2,9,1,10] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => [10]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9] => [[1,6,7,8,9],[2],[3],[4],[5]] => [9]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8,9] => [[1,5,6,7,8,9],[2],[3],[4]] => [9]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => [2,7]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => [[1,3,4,6,7,8,9],[2,5]] => [4,5]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,6,8,9,7,10] => [[1,2,3,4,5,6,7,9,10],[8]] => [7,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]] => [9]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => [10]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [[1,2,4,5,6,7,8,9],[3]] => [2,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,9,4] => [[1,3,4,6,7,8,9],[2,5]] => [4,5]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8,9,10] => [[1,4,5,6,7,8,9,10],[2],[3]] => [10]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9,10] => [[1,4,5,6,7,8,9,10],[2],[3]] => [10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [9,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9,10] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => [10]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [5,6,4,3,2,7,1,8,9] => [[1,6,7,8,9],[2],[3],[4],[5]] => [9]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9,10] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => [10]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]] => [2,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [[1,2,4,5,6,7,8,9,10],[3]] => [2,8]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,3,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => [3,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,7,8,4,9,10] => [[1,2,3,4,6,7,8,9,10],[5]] => [4,6]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => [[1,2,4,5,6,7,8,9],[3],[10]] => [2,7,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,10,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,10,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [10]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [[1,2,4,6,8,10],[3,5,7,9]] => [2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9,10] => [[1,3,5,6,7,8,9,10],[2],[4]] => [3,7]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => [[1,4,5,6,7,8,9,10],[2],[3]] => [10]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => [[1,2,4,5,6,7,8,9],[3]] => [2,7]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,10,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => [10]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => [3,2,2,2,2,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,4,6,3,7,2,8,1,9] => [[1,6,7,8,9],[2],[3],[4],[5]] => [9]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,5,7,4,8,3,9,2] => [[1,2,7,8,9],[3],[4],[5],[6]] => [2,7]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,7,4,8,3,9,2] => [[1,2,6,7,8,9],[3],[4],[5]] => [2,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,9,8,10] => [[1,2,4,5,6,8,10],[3,7,9]] => [2,4,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,5,3,6,2,7,1,8,9] => [[1,5,6,7,8,9],[2],[3],[4]] => [9]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,12,10] => [[1,2,4,6,8,10,12],[3,5,7,9,11]] => [2,2,2,2,2,2]
Map
to 312-avoiding permutation
Description
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 $T$.
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