Identifier
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Images
[1,0] => [1] => [1] => [[1]]
[1,0,1,0] => [2,1] => [2,1] => [[1],[2]]
[1,1,0,0] => [1,2] => [1,2] => [[1,2]]
[1,0,1,0,1,0] => [2,3,1] => [3,2,1] => [[1],[2],[3]]
[1,0,1,1,0,0] => [2,1,3] => [2,1,3] => [[1,3],[2]]
[1,1,0,0,1,0] => [1,3,2] => [1,3,2] => [[1,2],[3]]
[1,1,0,1,0,0] => [3,1,2] => [2,3,1] => [[1,3],[2]]
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [[1,2,3]]
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [4,2,3,1] => [[1,3],[2],[4]]
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [3,2,1,4] => [[1,4],[2],[3]]
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [2,1,4,3] => [[1,3],[2,4]]
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [3,2,4,1] => [[1,4],[2],[3]]
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [[1,3,4],[2]]
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [1,4,3,2] => [[1,2],[3],[4]]
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [1,3,2,4] => [[1,2,4],[3]]
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [3,4,1,2] => [[1,2],[3,4]]
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [2,4,3,1] => [[1,3],[2],[4]]
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [2,3,1,4] => [[1,3,4],[2]]
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [1,2,4,3] => [[1,2,3],[4]]
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,3,4,2] => [[1,2,4],[3]]
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [2,3,4,1] => [[1,3,4],[2]]
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [[1,2,3,4]]
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => [5,2,3,4,1] => [[1,3,4],[2],[5]]
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [4,2,3,1,5] => [[1,3,5],[2],[4]]
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [3,2,1,5,4] => [[1,4],[2,5],[3]]
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [4,2,3,5,1] => [[1,3,5],[2],[4]]
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [3,2,1,4,5] => [[1,4,5],[2],[3]]
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [2,1,5,4,3] => [[1,3],[2,4],[5]]
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [2,1,4,3,5] => [[1,3,5],[2,4]]
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [4,2,5,1,3] => [[1,3],[2,5],[4]]
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [3,2,5,4,1] => [[1,4],[2,5],[3]]
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [3,2,4,1,5] => [[1,4,5],[2],[3]]
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [2,1,3,5,4] => [[1,3,4],[2,5]]
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [2,1,4,5,3] => [[1,3,5],[2,4]]
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [3,2,4,5,1] => [[1,4,5],[2],[3]]
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[1,3,4,5],[2]]
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [1,5,3,4,2] => [[1,2,4],[3],[5]]
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [1,4,3,2,5] => [[1,2,5],[3],[4]]
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [1,3,2,5,4] => [[1,2,4],[3,5]]
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [1,4,3,5,2] => [[1,2,5],[3],[4]]
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => [[1,2,4,5],[3]]
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [3,5,1,4,2] => [[1,2],[3,4],[5]]
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [3,4,1,2,5] => [[1,2,5],[3,4]]
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [4,5,3,1,2] => [[1,2],[3,5],[4]]
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [2,5,3,4,1] => [[1,3,4],[2],[5]]
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [2,4,3,1,5] => [[1,3,5],[2],[4]]
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [2,3,1,5,4] => [[1,3,4],[2,5]]
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [3,4,1,5,2] => [[1,2,5],[3,4]]
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [2,4,3,5,1] => [[1,3,5],[2],[4]]
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [2,3,1,4,5] => [[1,3,4,5],[2]]
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [1,2,5,4,3] => [[1,2,3],[4],[5]]
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => [[1,2,3,5],[4]]
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [1,4,5,2,3] => [[1,2,3],[4,5]]
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [1,3,5,4,2] => [[1,2,4],[3],[5]]
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [1,3,4,2,5] => [[1,2,4,5],[3]]
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [2,4,5,1,3] => [[1,3,5],[2,4]]
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [4,3,5,1,2] => [[1,2],[3,5],[4]]
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [2,3,5,4,1] => [[1,3,4],[2],[5]]
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [2,3,4,1,5] => [[1,3,4,5],[2]]
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [1,2,3,5,4] => [[1,2,3,4],[5]]
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [1,2,4,5,3] => [[1,2,3,5],[4]]
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [1,3,4,5,2] => [[1,2,4,5],[3]]
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [2,3,4,5,1] => [[1,3,4,5],[2]]
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [[1,2,3,4,5]]
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [[1,3,4,5],[2],[6]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [[1,3,4,6],[2],[5]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [[1,3,5],[2,6],[4]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [5,2,3,4,6,1] => [[1,3,4,6],[2],[5]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [[1,3,5,6],[2],[4]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [[1,4,6],[2,5],[3]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [5,2,3,6,1,4] => [[1,3,4],[2,6],[5]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [4,2,3,6,5,1] => [[1,3,5],[2,6],[4]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [4,2,3,5,1,6] => [[1,3,5,6],[2],[4]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [[1,4,5],[2,6],[3]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [3,2,1,5,6,4] => [[1,4,6],[2,5],[3]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [4,2,3,5,6,1] => [[1,3,5,6],[2],[4]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [[1,4,5,6],[2],[3]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [[1,3,5],[2,4],[6]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [[1,3,6],[2,4],[5]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [2,1,5,4,6,3] => [[1,3,6],[2,4],[5]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [4,2,6,1,5,3] => [[1,3],[2,5],[4,6]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => [[1,3,6],[2,5],[4]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [5,2,6,4,1,3] => [[1,3],[2,4],[5,6]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [3,2,6,4,5,1] => [[1,4,5],[2,6],[3]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [3,2,5,4,1,6] => [[1,4,6],[2,5],[3]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [3,2,4,1,6,5] => [[1,4,5],[2,6],[3]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [4,2,5,1,6,3] => [[1,3,6],[2,5],[4]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [3,2,5,4,6,1] => [[1,4,6],[2,5],[3]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [3,2,4,1,5,6] => [[1,4,5,6],[2],[3]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [[1,3,4],[2,5],[6]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [[1,3,4,6],[2,5]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [2,1,5,6,3,4] => [[1,3,4],[2,5,6]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [2,1,4,6,5,3] => [[1,3,5],[2,4],[6]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [2,1,4,5,3,6] => [[1,3,5,6],[2,4]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [3,2,5,6,1,4] => [[1,4,6],[2,5],[3]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [5,2,4,6,1,3] => [[1,3,6],[2,4],[5]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [3,2,4,6,5,1] => [[1,4,5],[2,6],[3]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [3,2,4,5,1,6] => [[1,4,5,6],[2],[3]]
>>> Load all 1855 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [[1,3,4,5],[2,6]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [2,1,3,5,6,4] => [[1,3,4,6],[2,5]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [2,1,4,5,6,3] => [[1,3,5,6],[2,4]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [3,2,4,5,6,1] => [[1,4,5,6],[2],[3]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]]
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [[1,2,4,5],[3],[6]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [[1,2,4,6],[3],[5]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [[1,2,5],[3,6],[4]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [1,5,3,4,6,2] => [[1,2,4,6],[3],[5]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [[1,2,5,6],[3],[4]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [[1,2,4],[3,5],[6]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [[1,2,4,6],[3,5]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [1,5,3,6,2,4] => [[1,2,4],[3,6],[5]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [1,4,3,6,5,2] => [[1,2,5],[3,6],[4]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,4,3,5,2,6] => [[1,2,5,6],[3],[4]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [[1,2,4,5],[3,6]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => [[1,2,4,6],[3,5]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [1,4,3,5,6,2] => [[1,2,5,6],[3],[4]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [3,6,1,4,5,2] => [[1,2,5],[3,4],[6]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [3,5,1,4,2,6] => [[1,2,6],[3,4],[5]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [3,4,1,2,6,5] => [[1,2,5],[3,4,6]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [3,5,1,4,6,2] => [[1,2,6],[3,4],[5]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => [[1,2,5,6],[3,4]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [4,6,3,1,5,2] => [[1,2],[3,5],[4,6]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [4,5,3,1,2,6] => [[1,2,6],[3,5],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [5,6,3,4,1,2] => [[1,2],[3,4],[5,6]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [2,6,3,4,5,1] => [[1,3,4,5],[2],[6]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [2,5,3,4,1,6] => [[1,3,4,6],[2],[5]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [2,4,3,1,6,5] => [[1,3,5],[2,6],[4]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [4,5,3,1,6,2] => [[1,2,6],[3,5],[4]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [2,5,3,4,6,1] => [[1,3,4,6],[2],[5]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [2,4,3,1,5,6] => [[1,3,5,6],[2],[4]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [2,3,1,6,5,4] => [[1,3,4],[2,5],[6]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => [[1,3,4,6],[2,5]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [3,5,1,6,2,4] => [[1,2,4],[3,5,6]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [3,4,1,6,5,2] => [[1,2,5],[3,4],[6]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [3,4,1,5,2,6] => [[1,2,5,6],[3,4]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [2,5,3,6,1,4] => [[1,3,4],[2,6],[5]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [5,4,3,6,1,2] => [[1,2],[3,6],[4],[5]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [2,4,3,6,5,1] => [[1,3,5],[2,6],[4]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [2,4,3,5,1,6] => [[1,3,5,6],[2],[4]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => [[1,3,4,5],[2,6]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [2,3,1,5,6,4] => [[1,3,4,6],[2,5]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [3,4,1,5,6,2] => [[1,2,5,6],[3,4]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [2,4,3,5,6,1] => [[1,3,5,6],[2],[4]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [[1,3,4,5,6],[2]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [[1,2,3,5],[4],[6]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [[1,2,3,6],[4],[5]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [[1,2,3,5],[4,6]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [1,2,5,4,6,3] => [[1,2,3,6],[4],[5]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [1,4,6,2,5,3] => [[1,2,3],[4,5],[6]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [1,4,5,2,3,6] => [[1,2,3,6],[4,5]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [1,5,6,4,2,3] => [[1,2,3],[4,6],[5]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [1,3,6,4,5,2] => [[1,2,4,5],[3],[6]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [1,3,5,4,2,6] => [[1,2,4,6],[3],[5]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => [[1,2,4,5],[3,6]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [1,4,5,2,6,3] => [[1,2,3,6],[4,5]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [1,3,5,4,6,2] => [[1,2,4,6],[3],[5]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => [[1,2,4,5,6],[3]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [2,4,6,1,5,3] => [[1,3,5],[2,4],[6]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [2,4,5,1,3,6] => [[1,3,5,6],[2,4]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => [[1,2,3],[4,5,6]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => [4,3,6,1,5,2] => [[1,2],[3,5],[4,6]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [4,3,5,1,2,6] => [[1,2,6],[3,5],[4]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [2,5,6,4,1,3] => [[1,3,6],[2,4],[5]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [5,3,6,4,1,2] => [[1,2],[3,4],[5,6]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [2,3,6,4,5,1] => [[1,3,4,5],[2],[6]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [2,3,5,4,1,6] => [[1,3,4,6],[2],[5]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => [[1,3,4,5],[2,6]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [2,4,5,1,6,3] => [[1,3,5,6],[2,4]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [4,3,5,1,6,2] => [[1,2,6],[3,5],[4]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [2,3,5,4,6,1] => [[1,3,4,6],[2],[5]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [[1,3,4,5,6],[2]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [[1,2,3,4],[5],[6]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [1,2,5,6,3,4] => [[1,2,3,4],[5,6]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [1,2,4,6,5,3] => [[1,2,3,5],[4],[6]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => [[1,2,3,5,6],[4]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [1,3,5,6,2,4] => [[1,2,4,6],[3,5]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [1,5,4,6,2,3] => [[1,2,3],[4,6],[5]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [1,3,4,6,5,2] => [[1,2,4,5],[3],[6]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => [[1,2,4,5,6],[3]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [2,3,5,6,1,4] => [[1,3,4,6],[2,5]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [2,5,4,6,1,3] => [[1,3,6],[2,4],[5]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [5,3,4,6,1,2] => [[1,2,6],[3,4],[5]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [2,3,4,6,5,1] => [[1,3,4,5],[2],[6]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [[1,3,4,5,6],[2]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => [[1,2,3,4,6],[5]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => [[1,2,3,5,6],[4]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => [[1,2,4,5,6],[3]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [[1,3,4,5,6],[2]]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [[1,3,4,5,7],[2],[6]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [[1,3,4,6],[2,7],[5]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => [6,2,3,4,5,7,1] => [[1,3,4,5,7],[2],[6]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [[1,3,4,6,7],[2],[5]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [[1,3,5],[2,6],[4,7]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [[1,3,5,7],[2,6],[4]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => [6,2,3,4,7,1,5] => [[1,3,4,5],[2,7],[6]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => [5,2,3,4,7,6,1] => [[1,3,4,6],[2,7],[5]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => [5,2,3,4,6,1,7] => [[1,3,4,6,7],[2],[5]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [[1,3,5,6],[2,7],[4]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => [4,2,3,1,6,7,5] => [[1,3,5,7],[2,6],[4]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => [5,2,3,4,6,7,1] => [[1,3,4,6,7],[2],[5]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [[1,3,5,6,7],[2],[4]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [[1,4,6],[2,5],[3,7]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [[1,4,7],[2,5],[3,6]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [[1,4,6],[2,5,7],[3]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => [3,2,1,6,5,7,4] => [[1,4,7],[2,5],[3,6]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [[1,4,6,7],[2,5],[3]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => [5,2,3,7,1,6,4] => [[1,3,4],[2,6],[5,7]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => [5,2,3,6,1,4,7] => [[1,3,4,7],[2,6],[5]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => [6,2,3,7,5,1,4] => [[1,3,4],[2,5],[6,7]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => [4,2,3,7,5,6,1] => [[1,3,5,6],[2,7],[4]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => [4,2,3,6,5,1,7] => [[1,3,5,7],[2,6],[4]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,7,6] => [4,2,3,5,1,7,6] => [[1,3,5,6],[2,7],[4]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => [5,2,3,6,1,7,4] => [[1,3,4,7],[2,6],[5]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => [4,2,3,6,5,7,1] => [[1,3,5,7],[2,6],[4]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => [4,2,3,5,1,6,7] => [[1,3,5,6,7],[2],[4]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [[1,4,5],[2,6],[3,7]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [[1,4,5,7],[2,6],[3]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [3,2,1,6,7,4,5] => [[1,4,5],[2,6,7],[3]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => [3,2,1,5,7,6,4] => [[1,4,6],[2,5],[3,7]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => [3,2,1,5,6,4,7] => [[1,4,6,7],[2,5],[3]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => [4,2,3,6,7,1,5] => [[1,3,5,7],[2,6],[4]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => [6,2,3,5,7,1,4] => [[1,3,4,7],[2,5],[6]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => [4,2,3,5,7,6,1] => [[1,3,5,6],[2,7],[4]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => [4,2,3,5,6,1,7] => [[1,3,5,6,7],[2],[4]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [[1,4,5,6],[2,7],[3]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => [3,2,1,4,6,7,5] => [[1,4,5,7],[2,6],[3]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => [3,2,1,5,6,7,4] => [[1,4,6,7],[2,5],[3]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => [4,2,3,5,6,7,1] => [[1,3,5,6,7],[2],[4]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [[1,3,5,6],[2,4],[7]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [[1,3,5,7],[2,4],[6]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [[1,3,6],[2,4,7],[5]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => [2,1,6,4,5,7,3] => [[1,3,5,7],[2,4],[6]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [[1,3,6,7],[2,4],[5]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [[1,3,5],[2,4,6],[7]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [[1,3,5,7],[2,4,6]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [2,1,6,4,7,3,5] => [[1,3,5],[2,4,7],[6]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => [2,1,5,4,7,6,3] => [[1,3,6],[2,4,7],[5]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => [2,1,5,4,6,3,7] => [[1,3,6,7],[2,4],[5]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [[1,3,5,6],[2,4,7]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [2,1,4,3,6,7,5] => [[1,3,5,7],[2,4,6]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => [2,1,5,4,6,7,3] => [[1,3,6,7],[2,4],[5]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [[1,3,5,6,7],[2,4]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => [4,2,7,1,5,6,3] => [[1,3,6],[2,5],[4,7]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => [4,2,6,1,5,3,7] => [[1,3,7],[2,5],[4,6]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => [4,2,5,1,3,7,6] => [[1,3,6],[2,5,7],[4]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,7,3,6] => [4,2,6,1,5,7,3] => [[1,3,7],[2,5],[4,6]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => [4,2,5,1,3,6,7] => [[1,3,6,7],[2,5],[4]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => [5,2,7,4,1,6,3] => [[1,3,6],[2,4],[5,7]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,7] => [5,2,6,4,1,3,7] => [[1,3,7],[2,4],[5,6]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,1,7,3] => [6,2,7,4,5,1,3] => [[1,3,5],[2,4],[6,7]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => [3,2,7,4,5,6,1] => [[1,4,5,6],[2,7],[3]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,1,3,7] => [3,2,6,4,5,1,7] => [[1,4,5,7],[2,6],[3]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,1,3,7,6] => [3,2,5,4,1,7,6] => [[1,4,6],[2,5,7],[3]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,6] => [5,2,6,4,1,7,3] => [[1,3,7],[2,4],[5,6]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,7,1,3,6] => [3,2,6,4,5,7,1] => [[1,4,5,7],[2,6],[3]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => [3,2,5,4,1,6,7] => [[1,4,6,7],[2,5],[3]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => [3,2,4,1,7,6,5] => [[1,4,5],[2,6],[3,7]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => [3,2,4,1,6,5,7] => [[1,4,5,7],[2,6],[3]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => [4,2,6,1,7,3,5] => [[1,3,5],[2,6,7],[4]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,7,3,5] => [4,2,5,1,7,6,3] => [[1,3,6],[2,5],[4,7]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5,7] => [4,2,5,1,6,3,7] => [[1,3,6,7],[2,5],[4]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,6,1,3,7,5] => [3,2,6,4,7,1,5] => [[1,4,5],[2,6,7],[3]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => [6,2,5,4,7,1,3] => [[1,3,7],[2,4],[5],[6]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => [3,2,5,4,7,6,1] => [[1,4,6],[2,5,7],[3]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => [3,2,5,4,6,1,7] => [[1,4,6,7],[2,5],[3]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => [3,2,4,1,5,7,6] => [[1,4,5,6],[2,7],[3]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => [3,2,4,1,6,7,5] => [[1,4,5,7],[2,6],[3]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,5,6] => [4,2,5,1,6,7,3] => [[1,3,6,7],[2,5],[4]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => [3,2,5,4,6,7,1] => [[1,4,6,7],[2,5],[3]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [3,2,4,1,5,6,7] => [[1,4,5,6,7],[2],[3]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [[1,3,4,6],[2,5],[7]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [[1,3,4,7],[2,5],[6]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [[1,3,4,6],[2,5,7]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => [2,1,3,6,5,7,4] => [[1,3,4,7],[2,5],[6]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [[1,3,4,6,7],[2,5]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [2,1,5,7,3,6,4] => [[1,3,4],[2,5,6],[7]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [2,1,5,6,3,4,7] => [[1,3,4,7],[2,5,6]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [2,1,6,7,5,3,4] => [[1,3,4],[2,5,7],[6]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => [2,1,4,7,5,6,3] => [[1,3,5,6],[2,4],[7]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => [2,1,4,6,5,3,7] => [[1,3,5,7],[2,4],[6]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [2,1,4,5,3,7,6] => [[1,3,5,6],[2,4,7]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [2,1,5,6,3,7,4] => [[1,3,4,7],[2,5,6]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => [2,1,4,6,5,7,3] => [[1,3,5,7],[2,4],[6]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => [2,1,4,5,3,6,7] => [[1,3,5,6,7],[2,4]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,5,1,3,6,7,4] => [3,2,5,7,1,6,4] => [[1,4,6],[2,5],[3,7]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,5,1,3,6,4,7] => [3,2,5,6,1,4,7] => [[1,4,6,7],[2,5],[3]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => [5,2,6,7,1,3,4] => [[1,3,4],[2,6,7],[5]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,5,1,6,7,3,4] => [5,2,4,7,1,6,3] => [[1,3,6],[2,4],[5,7]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,4,7] => [5,2,4,6,1,3,7] => [[1,3,6,7],[2,4],[5]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,6,1,3,7,4] => [3,2,6,7,5,1,4] => [[1,4,7],[2,5],[3,6]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,5,6,1,7,3,4] => [6,2,4,7,5,1,3] => [[1,3,5],[2,4],[6,7]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => [3,2,4,7,5,6,1] => [[1,4,5,6],[2,7],[3]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => [3,2,4,6,5,1,7] => [[1,4,5,7],[2,6],[3]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1,3,4,7,6] => [3,2,4,5,1,7,6] => [[1,4,5,6],[2,7],[3]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,5,1,3,7,4,6] => [3,2,5,6,1,7,4] => [[1,4,6,7],[2,5],[3]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,4,6] => [5,2,4,6,1,7,3] => [[1,3,6,7],[2,4],[5]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => [3,2,4,6,5,7,1] => [[1,4,5,7],[2,6],[3]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => [3,2,4,5,1,6,7] => [[1,4,5,6,7],[2],[3]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [[1,3,4,5],[2,6],[7]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [[1,3,4,5,7],[2,6]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [2,1,3,6,7,4,5] => [[1,3,4,5],[2,6,7]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => [2,1,3,5,7,6,4] => [[1,3,4,6],[2,5],[7]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => [2,1,3,5,6,4,7] => [[1,3,4,6,7],[2,5]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [2,1,4,6,7,3,5] => [[1,3,5,7],[2,4,6]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [2,1,6,5,7,3,4] => [[1,3,4],[2,5,7],[6]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => [2,1,4,5,7,6,3] => [[1,3,5,6],[2,4],[7]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => [2,1,4,5,6,3,7] => [[1,3,5,6,7],[2,4]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,6,1,3,4,7,5] => [3,2,4,6,7,1,5] => [[1,4,5,7],[2,6],[3]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6,1,3,7,4,5] => [3,2,6,5,7,1,4] => [[1,4,7],[2,5],[3,6]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => [6,2,4,5,7,1,3] => [[1,3,5,7],[2,4],[6]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => [3,2,4,5,7,6,1] => [[1,4,5,6],[2,7],[3]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => [3,2,4,5,6,1,7] => [[1,4,5,6,7],[2],[3]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => [2,1,3,4,6,7,5] => [[1,3,4,5,7],[2,6]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => [2,1,3,5,6,7,4] => [[1,3,4,6,7],[2,5]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => [2,1,4,5,6,7,3] => [[1,3,5,6,7],[2,4]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [3,2,4,5,6,7,1] => [[1,4,5,6,7],[2],[3]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [[1,2,4,5,6],[3],[7]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [[1,2,4,5,7],[3],[6]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [[1,2,4,6],[3,7],[5]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [1,6,3,4,5,7,2] => [[1,2,4,5,7],[3],[6]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [[1,2,4,6,7],[3],[5]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [[1,2,5],[3,6],[4,7]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [[1,2,5,7],[3,6],[4]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [1,6,3,4,7,2,5] => [[1,2,4,5],[3,7],[6]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [1,5,3,4,7,6,2] => [[1,2,4,6],[3,7],[5]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [1,5,3,4,6,2,7] => [[1,2,4,6,7],[3],[5]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [[1,2,5,6],[3,7],[4]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [1,4,3,2,6,7,5] => [[1,2,5,7],[3,6],[4]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [1,5,3,4,6,7,2] => [[1,2,4,6,7],[3],[5]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [[1,2,5,6,7],[3],[4]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [[1,2,4,6],[3,5],[7]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [[1,2,4,7],[3,5],[6]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [[1,2,4,6],[3,5,7]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [1,3,2,6,5,7,4] => [[1,2,4,7],[3,5],[6]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [[1,2,4,6,7],[3,5]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [1,5,3,7,2,6,4] => [[1,2,4],[3,6],[5,7]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [1,5,3,6,2,4,7] => [[1,2,4,7],[3,6],[5]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [1,6,3,7,5,2,4] => [[1,2,4],[3,5],[6,7]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [1,4,3,7,5,6,2] => [[1,2,5,6],[3,7],[4]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [1,4,3,6,5,2,7] => [[1,2,5,7],[3,6],[4]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [1,4,3,5,2,7,6] => [[1,2,5,6],[3,7],[4]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [1,5,3,6,2,7,4] => [[1,2,4,7],[3,6],[5]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [1,4,3,6,5,7,2] => [[1,2,5,7],[3,6],[4]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [1,4,3,5,2,6,7] => [[1,2,5,6,7],[3],[4]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [[1,2,4,5],[3,6],[7]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [[1,2,4,5,7],[3,6]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [1,3,2,6,7,4,5] => [[1,2,4,5],[3,6,7]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [1,3,2,5,7,6,4] => [[1,2,4,6],[3,5],[7]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [1,3,2,5,6,4,7] => [[1,2,4,6,7],[3,5]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [1,4,3,6,7,2,5] => [[1,2,5,7],[3,6],[4]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [1,6,3,5,7,2,4] => [[1,2,4,7],[3,5],[6]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [1,4,3,5,7,6,2] => [[1,2,5,6],[3,7],[4]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [1,4,3,5,6,2,7] => [[1,2,5,6,7],[3],[4]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,6,7,5] => [[1,2,4,5,7],[3,6]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [1,3,2,5,6,7,4] => [[1,2,4,6,7],[3,5]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [1,4,3,5,6,7,2] => [[1,2,5,6,7],[3],[4]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => [3,7,1,4,5,6,2] => [[1,2,5,6],[3,4],[7]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,2,7] => [3,6,1,4,5,2,7] => [[1,2,5,7],[3,4],[6]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => [3,5,1,4,2,7,6] => [[1,2,6],[3,4,7],[5]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,5,7,2,6] => [3,6,1,4,5,7,2] => [[1,2,5,7],[3,4],[6]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,5,2,6,7] => [3,5,1,4,2,6,7] => [[1,2,6,7],[3,4],[5]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [3,4,1,2,7,6,5] => [[1,2,5],[3,4,6],[7]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [3,4,1,2,6,5,7] => [[1,2,5,7],[3,4,6]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [3,6,1,4,7,2,5] => [[1,2,5],[3,4,7],[6]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => [3,5,1,4,7,6,2] => [[1,2,6],[3,4,7],[5]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,6,2,5,7] => [3,5,1,4,6,2,7] => [[1,2,6,7],[3,4],[5]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [3,4,1,2,5,7,6] => [[1,2,5,6],[3,4,7]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [3,4,1,2,6,7,5] => [[1,2,5,7],[3,4,6]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,7,2,5,6] => [3,5,1,4,6,7,2] => [[1,2,6,7],[3,4],[5]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => [[1,2,5,6,7],[3,4]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => [4,7,3,1,5,6,2] => [[1,2,6],[3,5],[4,7]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,6,2,7] => [4,6,3,1,5,2,7] => [[1,2,7],[3,5],[4,6]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => [4,5,3,1,2,7,6] => [[1,2,6],[3,5,7],[4]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,7,2,6] => [4,6,3,1,5,7,2] => [[1,2,7],[3,5],[4,6]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,6,7] => [4,5,3,1,2,6,7] => [[1,2,6,7],[3,5],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,1,6,7,2] => [5,7,3,4,1,6,2] => [[1,2,6],[3,4],[5,7]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,7] => [5,6,3,4,1,2,7] => [[1,2,7],[3,4],[5,6]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,2] => [6,7,3,4,5,1,2] => [[1,2,5],[3,4],[6,7]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,2] => [2,7,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => [2,6,3,4,5,1,7] => [[1,3,4,5,7],[2],[6]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,1,2,7,6] => [2,5,3,4,1,7,6] => [[1,3,4,6],[2,7],[5]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,6] => [5,6,3,4,1,7,2] => [[1,2,7],[3,4],[5,6]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => [2,6,3,4,5,7,1] => [[1,3,4,5,7],[2],[6]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => [2,5,3,4,1,6,7] => [[1,3,4,6,7],[2],[5]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => [2,4,3,1,7,6,5] => [[1,3,5],[2,6],[4,7]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => [2,4,3,1,6,5,7] => [[1,3,5,7],[2,6],[4]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => [4,6,3,1,7,2,5] => [[1,2,5],[3,6,7],[4]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => [4,5,3,1,7,6,2] => [[1,2,6],[3,5],[4,7]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5,7] => [4,5,3,1,6,2,7] => [[1,2,6,7],[3,5],[4]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,6,1,2,7,5] => [2,6,3,4,7,1,5] => [[1,3,4,5],[2,7],[6]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => [6,5,3,4,7,1,2] => [[1,2,7],[3,4],[5],[6]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => [2,5,3,4,7,6,1] => [[1,3,4,6],[2,7],[5]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => [2,5,3,4,6,1,7] => [[1,3,4,6,7],[2],[5]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => [2,4,3,1,5,7,6] => [[1,3,5,6],[2,7],[4]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => [2,4,3,1,6,7,5] => [[1,3,5,7],[2,6],[4]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,5,6] => [4,5,3,1,6,7,2] => [[1,2,6,7],[3,5],[4]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => [2,5,3,4,6,7,1] => [[1,3,4,6,7],[2],[5]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [2,4,3,1,5,6,7] => [[1,3,5,6,7],[2],[4]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => [2,3,1,7,5,6,4] => [[1,3,4,6],[2,5],[7]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => [2,3,1,6,5,4,7] => [[1,3,4,7],[2,5],[6]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [2,3,1,5,4,7,6] => [[1,3,4,6],[2,5,7]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => [2,3,1,6,5,7,4] => [[1,3,4,7],[2,5],[6]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => [2,3,1,5,4,6,7] => [[1,3,4,6,7],[2,5]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [3,5,1,7,2,6,4] => [[1,2,4],[3,5,6],[7]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => [3,5,1,6,2,4,7] => [[1,2,4,7],[3,5,6]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [3,6,1,7,5,2,4] => [[1,2,4],[3,5,7],[6]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,6,7,2,4] => [3,4,1,7,5,6,2] => [[1,2,5,6],[3,4],[7]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,6,2,4,7] => [3,4,1,6,5,2,7] => [[1,2,5,7],[3,4],[6]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => [3,4,1,5,2,7,6] => [[1,2,5,6],[3,4,7]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => [3,5,1,6,2,7,4] => [[1,2,4,7],[3,5,6]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,7,2,4,6] => [3,4,1,6,5,7,2] => [[1,2,5,7],[3,4],[6]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,4,6,7] => [3,4,1,5,2,6,7] => [[1,2,5,6,7],[3,4]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,5,1,2,6,7,4] => [2,5,3,7,1,6,4] => [[1,3,4],[2,6],[5,7]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,6,4,7] => [2,5,3,6,1,4,7] => [[1,3,4,7],[2,6],[5]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [5,6,3,7,1,2,4] => [[1,2,4],[3,6,7],[5]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => [5,4,3,7,1,6,2] => [[1,2],[3,6],[4,7],[5]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,4,7] => [5,4,3,6,1,2,7] => [[1,2,7],[3,6],[4],[5]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,5,6,1,2,7,4] => [2,6,3,7,5,1,4] => [[1,3,4],[2,5],[6,7]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,5,6,1,7,2,4] => [6,4,3,7,5,1,2] => [[1,2],[3,5],[4,7],[6]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => [2,4,3,7,5,6,1] => [[1,3,5,6],[2,7],[4]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => [2,4,3,6,5,1,7] => [[1,3,5,7],[2,6],[4]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,7,6] => [2,4,3,5,1,7,6] => [[1,3,5,6],[2,7],[4]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,7,4,6] => [2,5,3,6,1,7,4] => [[1,3,4,7],[2,6],[5]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,4,6] => [5,4,3,6,1,7,2] => [[1,2,7],[3,6],[4],[5]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => [2,4,3,6,5,7,1] => [[1,3,5,7],[2,6],[4]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => [2,4,3,5,1,6,7] => [[1,3,5,6,7],[2],[4]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => [2,3,1,4,7,6,5] => [[1,3,4,5],[2,6],[7]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => [2,3,1,4,6,5,7] => [[1,3,4,5,7],[2,6]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [2,3,1,6,7,4,5] => [[1,3,4,5],[2,6,7]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => [2,3,1,5,7,6,4] => [[1,3,4,6],[2,5],[7]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => [2,3,1,5,6,4,7] => [[1,3,4,6,7],[2,5]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => [3,4,1,6,7,2,5] => [[1,2,5,7],[3,4,6]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => [3,6,1,5,7,2,4] => [[1,2,4],[3,5,7],[6]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,7,2,4,5] => [3,4,1,5,7,6,2] => [[1,2,5,6],[3,4],[7]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,4,5,7] => [3,4,1,5,6,2,7] => [[1,2,5,6,7],[3,4]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1,2,4,7,5] => [2,4,3,6,7,1,5] => [[1,3,5,7],[2,6],[4]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,6,1,2,7,4,5] => [2,6,3,5,7,1,4] => [[1,3,4,7],[2,5],[6]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => [6,4,3,5,7,1,2] => [[1,2,7],[3,5],[4],[6]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => [2,4,3,5,7,6,1] => [[1,3,5,6],[2,7],[4]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => [2,4,3,5,6,1,7] => [[1,3,5,6,7],[2],[4]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [2,3,1,4,5,7,6] => [[1,3,4,5,6],[2,7]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => [2,3,1,4,6,7,5] => [[1,3,4,5,7],[2,6]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => [2,3,1,5,6,7,4] => [[1,3,4,6,7],[2,5]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,4,5,6] => [3,4,1,5,6,7,2] => [[1,2,5,6,7],[3,4]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => [2,4,3,5,6,7,1] => [[1,3,5,6,7],[2],[4]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [[1,3,4,5,6,7],[2]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [[1,2,3,5,6],[4],[7]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [[1,2,3,5,7],[4],[6]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [[1,2,3,6],[4,7],[5]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [1,2,6,4,5,7,3] => [[1,2,3,5,7],[4],[6]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [[1,2,3,6,7],[4],[5]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [[1,2,3,5],[4,6],[7]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [[1,2,3,5,7],[4,6]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [1,2,6,4,7,3,5] => [[1,2,3,5],[4,7],[6]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [1,2,5,4,7,6,3] => [[1,2,3,6],[4,7],[5]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [1,2,5,4,6,3,7] => [[1,2,3,6,7],[4],[5]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,6,7,5] => [[1,2,3,5,7],[4,6]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [1,2,5,4,6,7,3] => [[1,2,3,6,7],[4],[5]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [1,4,7,2,5,6,3] => [[1,2,3,6],[4,5],[7]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [1,4,6,2,5,3,7] => [[1,2,3,7],[4,5],[6]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [1,4,5,2,3,7,6] => [[1,2,3,6],[4,5,7]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [1,4,6,2,5,7,3] => [[1,2,3,7],[4,5],[6]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [1,4,5,2,3,6,7] => [[1,2,3,6,7],[4,5]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [1,5,7,4,2,6,3] => [[1,2,3],[4,6],[5,7]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [1,5,6,4,2,3,7] => [[1,2,3,7],[4,6],[5]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [1,6,7,4,5,2,3] => [[1,2,3],[4,5],[6,7]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [1,3,7,4,5,6,2] => [[1,2,4,5,6],[3],[7]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [1,3,6,4,5,2,7] => [[1,2,4,5,7],[3],[6]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [1,3,5,4,2,7,6] => [[1,2,4,6],[3,7],[5]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [1,5,6,4,2,7,3] => [[1,2,3,7],[4,6],[5]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [1,3,6,4,5,7,2] => [[1,2,4,5,7],[3],[6]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [1,3,5,4,2,6,7] => [[1,2,4,6,7],[3],[5]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [1,3,4,2,7,6,5] => [[1,2,4,5],[3,6],[7]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7] => [[1,2,4,5,7],[3,6]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [1,4,6,2,7,3,5] => [[1,2,3,5],[4,6,7]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [1,4,5,2,7,6,3] => [[1,2,3,6],[4,5],[7]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [1,4,5,2,6,3,7] => [[1,2,3,6,7],[4,5]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [1,3,6,4,7,2,5] => [[1,2,4,5],[3,7],[6]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [1,6,5,4,7,2,3] => [[1,2,3],[4,7],[5],[6]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [1,3,5,4,7,6,2] => [[1,2,4,6],[3,7],[5]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [1,3,5,4,6,2,7] => [[1,2,4,6,7],[3],[5]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [1,3,4,2,5,7,6] => [[1,2,4,5,6],[3,7]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,3,4,2,6,7,5] => [[1,2,4,5,7],[3,6]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [1,4,5,2,6,7,3] => [[1,2,3,6,7],[4,5]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [1,3,5,4,6,7,2] => [[1,2,4,6,7],[3],[5]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => [[1,2,4,5,6,7],[3]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,6,7,3] => [2,4,7,1,5,6,3] => [[1,3,5,6],[2,4],[7]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,6,3,7] => [2,4,6,1,5,3,7] => [[1,3,5,7],[2,4],[6]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => [2,4,5,1,3,7,6] => [[1,3,5,6],[2,4,7]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,7,3,6] => [2,4,6,1,5,7,3] => [[1,3,5,7],[2,4],[6]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,3,6,7] => [2,4,5,1,3,6,7] => [[1,3,5,6,7],[2,4]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [4,5,7,1,2,6,3] => [[1,2,3],[4,5,6],[7]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => [[1,2,3,7],[4,5,6]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [4,6,7,1,5,2,3] => [[1,2,3],[4,5,7],[6]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => [4,3,7,1,5,6,2] => [[1,2,6],[3,5],[4,7]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,6,2,3,7] => [4,3,6,1,5,2,7] => [[1,2,7],[3,5],[4,6]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => [4,3,5,1,2,7,6] => [[1,2,6],[3,5,7],[4]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => [4,5,6,1,2,7,3] => [[1,2,3,7],[4,5,6]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,7,2,3,6] => [4,3,6,1,5,7,2] => [[1,2,7],[3,5],[4,6]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,3,6,7] => [4,3,5,1,2,6,7] => [[1,2,6,7],[3,5],[4]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,1,2,6,7,3] => [2,5,7,4,1,6,3] => [[1,3,6],[2,4],[5,7]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,6,3,7] => [2,5,6,4,1,3,7] => [[1,3,6,7],[2,4],[5]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => [5,6,7,4,1,2,3] => [[1,2,3],[4,6,7],[5]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => [5,3,7,4,1,6,2] => [[1,2,6],[3,4],[5,7]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => [5,3,6,4,1,2,7] => [[1,2,7],[3,4],[5,6]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => [2,6,7,4,5,1,3] => [[1,3,5],[2,4],[6,7]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => [6,3,7,4,5,1,2] => [[1,2,5],[3,4],[6,7]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,1,2,3] => [2,3,7,4,5,6,1] => [[1,3,4,5,6],[2],[7]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [2,3,6,4,5,1,7] => [[1,3,4,5,7],[2],[6]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,1,2,3,7,6] => [2,3,5,4,1,7,6] => [[1,3,4,6],[2,7],[5]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,1,2,7,3,6] => [2,5,6,4,1,7,3] => [[1,3,6,7],[2,4],[5]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => [5,3,6,4,1,7,2] => [[1,2,7],[3,4],[5,6]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => [2,3,6,4,5,7,1] => [[1,3,4,5,7],[2],[6]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => [2,3,5,4,1,6,7] => [[1,3,4,6,7],[2],[5]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => [2,3,4,1,7,6,5] => [[1,3,4,5],[2,6],[7]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => [2,3,4,1,6,5,7] => [[1,3,4,5,7],[2,6]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [2,4,6,1,7,3,5] => [[1,3,5,7],[2,4,6]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,6,7,3,5] => [2,4,5,1,7,6,3] => [[1,3,5,6],[2,4],[7]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5,7] => [2,4,5,1,6,3,7] => [[1,3,5,6,7],[2,4]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => [4,3,6,1,7,2,5] => [[1,2,5],[3,6,7],[4]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [4,6,5,1,7,2,3] => [[1,2,3],[4,5,7],[6]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => [4,3,5,1,7,6,2] => [[1,2,6],[3,5],[4,7]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5,7] => [4,3,5,1,6,2,7] => [[1,2,6,7],[3,5],[4]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => [2,3,6,4,7,1,5] => [[1,3,4,5],[2,7],[6]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => [2,6,5,4,7,1,3] => [[1,3,7],[2,4],[5],[6]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => [6,3,5,4,7,1,2] => [[1,2,7],[3,4],[5],[6]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => [2,3,5,4,7,6,1] => [[1,3,4,6],[2,7],[5]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => [2,3,5,4,6,1,7] => [[1,3,4,6,7],[2],[5]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [2,3,4,1,5,7,6] => [[1,3,4,5,6],[2,7]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => [2,3,4,1,6,7,5] => [[1,3,4,5,7],[2,6]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,2,7,3,5,6] => [2,4,5,1,6,7,3] => [[1,3,5,6,7],[2,4]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,3,5,6] => [4,3,5,1,6,7,2] => [[1,2,6,7],[3,5],[4]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => [2,3,5,4,6,7,1] => [[1,3,4,6,7],[2],[5]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [[1,3,4,5,6,7],[2]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [[1,2,3,4,6],[5],[7]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [[1,2,3,4,7],[5],[6]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [[1,2,3,4,6],[5,7]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [1,2,3,6,5,7,4] => [[1,2,3,4,7],[5],[6]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [1,2,5,7,3,6,4] => [[1,2,3,4],[5,6],[7]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [1,2,5,6,3,4,7] => [[1,2,3,4,7],[5,6]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [1,2,6,7,5,3,4] => [[1,2,3,4],[5,7],[6]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [1,2,4,7,5,6,3] => [[1,2,3,5,6],[4],[7]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [1,2,4,6,5,3,7] => [[1,2,3,5,7],[4],[6]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [1,2,4,5,3,7,6] => [[1,2,3,5,6],[4,7]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [1,2,5,6,3,7,4] => [[1,2,3,4,7],[5,6]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [1,2,4,6,5,7,3] => [[1,2,3,5,7],[4],[6]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => [[1,2,3,5,6,7],[4]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [1,3,5,7,2,6,4] => [[1,2,4,6],[3,5],[7]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [1,3,5,6,2,4,7] => [[1,2,4,6,7],[3,5]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [1,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [1,5,4,7,2,6,3] => [[1,2,3],[4,6],[5,7]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [1,5,4,6,2,3,7] => [[1,2,3,7],[4,6],[5]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [1,3,6,7,5,2,4] => [[1,2,4,7],[3,5],[6]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [1,6,4,7,5,2,3] => [[1,2,3],[4,5],[6,7]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [1,3,4,7,5,6,2] => [[1,2,4,5,6],[3],[7]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [1,3,4,6,5,2,7] => [[1,2,4,5,7],[3],[6]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [1,3,4,5,2,7,6] => [[1,2,4,5,6],[3,7]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,3,5,6,2,7,4] => [[1,2,4,6,7],[3,5]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [1,5,4,6,2,7,3] => [[1,2,3,7],[4,6],[5]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [1,3,4,6,5,7,2] => [[1,2,4,5,7],[3],[6]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => [[1,2,4,5,6,7],[3]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,2,3,6,7,4] => [2,3,5,7,1,6,4] => [[1,3,4,6],[2,5],[7]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,1,2,3,6,4,7] => [2,3,5,6,1,4,7] => [[1,3,4,6,7],[2,5]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [2,5,6,7,1,3,4] => [[1,3,4,7],[2,5,6]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,2,6,7,3,4] => [2,5,4,7,1,6,3] => [[1,3,6],[2,4],[5,7]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,1,2,6,3,4,7] => [2,5,4,6,1,3,7] => [[1,3,6,7],[2,4],[5]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => [5,3,6,7,1,2,4] => [[1,2,4],[3,6,7],[5]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => [5,6,4,7,1,2,3] => [[1,2,3],[4,6,7],[5]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => [5,3,4,7,1,6,2] => [[1,2,6],[3,4],[5,7]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,3,4,7] => [5,3,4,6,1,2,7] => [[1,2,6,7],[3,4],[5]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => [2,3,6,7,5,1,4] => [[1,3,4,7],[2,5],[6]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => [2,6,4,7,5,1,3] => [[1,3,5],[2,4],[6,7]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => [6,3,4,7,5,1,2] => [[1,2,5],[3,4],[6,7]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,1,2,3,4] => [2,3,4,7,5,6,1] => [[1,3,4,5,6],[2],[7]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => [2,3,4,6,5,1,7] => [[1,3,4,5,7],[2],[6]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [2,3,4,5,1,7,6] => [[1,3,4,5,6],[2,7]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,2,3,7,4,6] => [2,3,5,6,1,7,4] => [[1,3,4,6,7],[2,5]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,1,2,7,3,4,6] => [2,5,4,6,1,7,3] => [[1,3,6,7],[2,4],[5]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,3,4,6] => [5,3,4,6,1,7,2] => [[1,2,6,7],[3,4],[5]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => [2,3,4,6,5,7,1] => [[1,3,4,5,7],[2],[6]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [[1,3,4,5,6,7],[2]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [[1,2,3,4,5],[6],[7]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [1,2,3,5,7,6,4] => [[1,2,3,4,6],[5],[7]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => [[1,2,3,4,6,7],[5]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [1,2,4,6,7,3,5] => [[1,2,3,5,7],[4,6]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [1,2,6,5,7,3,4] => [[1,2,3,4],[5,7],[6]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [1,2,4,5,7,6,3] => [[1,2,3,5,6],[4],[7]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => [[1,2,3,5,6,7],[4]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [1,3,4,6,7,2,5] => [[1,2,4,5,7],[3,6]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,3,6,5,7,2,4] => [[1,2,4,7],[3,5],[6]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [1,6,4,5,7,2,3] => [[1,2,3,7],[4,5],[6]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [1,3,4,5,7,6,2] => [[1,2,4,5,6],[3],[7]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => [[1,2,4,5,6,7],[3]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [2,3,4,6,7,1,5] => [[1,3,4,5,7],[2,6]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,1,2,3,7,4,5] => [2,3,6,5,7,1,4] => [[1,3,4,7],[2,5],[6]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,1,2,7,3,4,5] => [2,6,4,5,7,1,3] => [[1,3,5,7],[2,4],[6]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => [6,3,4,5,7,1,2] => [[1,2,5,7],[3,4],[6]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => [2,3,4,5,7,6,1] => [[1,3,4,5,6],[2],[7]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [[1,3,4,5,6,7],[2]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,7],[6]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => [[1,2,3,4,6,7],[5]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => [[1,2,3,5,6,7],[4]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => [[1,3,4,5,7],[2,8],[6]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,8,1,7] => [7,2,3,4,5,6,8,1] => [[1,3,4,5,6,8],[2],[7]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,7,1,8,6] => [7,2,3,4,5,8,1,6] => [[1,3,4,5,6],[2,8],[7]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,7,8,1,6] => [6,2,3,4,5,8,7,1] => [[1,3,4,5,7],[2,8],[6]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,1,6,8,7] => [5,2,3,4,1,6,8,7] => [[1,3,4,6,7],[2,8],[5]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,1,8,6,7] => [5,2,3,4,1,7,8,6] => [[1,3,4,6,8],[2,7],[5]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,8,1,6,7] => [6,2,3,4,5,7,8,1] => [[1,3,4,5,7,8],[2],[6]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,8,5,7] => [4,2,3,1,7,6,8,5] => [[1,3,5,8],[2,6],[4,7]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,4,6,7,1,8,5] => [7,2,3,4,8,6,1,5] => [[1,3,4,5],[2,6],[7,8]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,1,5] => [5,2,3,4,8,6,7,1] => [[1,3,4,6,7],[2,8],[5]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,4,6,7,1,5,8] => [5,2,3,4,7,6,1,8] => [[1,3,4,6,8],[2,7],[5]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,8,7] => [5,2,3,4,6,1,8,7] => [[1,3,4,6,7],[2,8],[5]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => [5,2,3,4,6,1,7,8] => [[1,3,4,6,7,8],[2],[5]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,4,1,5,7,6,8] => [4,2,3,1,5,7,6,8] => [[1,3,5,6,8],[2,7],[4]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,1,7,5,8,6] => [4,2,3,1,7,8,5,6] => [[1,3,5,6],[2,7,8],[4]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,1,7,8,5,6] => [4,2,3,1,6,8,7,5] => [[1,3,5,7],[2,6],[4,8]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,4,7,1,8,5,6] => [7,2,3,4,6,8,1,5] => [[1,3,4,5,8],[2,6],[7]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [5,2,3,4,6,7,1,8] => [[1,3,4,6,7,8],[2],[5]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,4,1,5,8,6,7] => [4,2,3,1,5,7,8,6] => [[1,3,5,6,8],[2,7],[4]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [4,2,3,1,6,7,8,5] => [[1,3,5,7,8],[2,6],[4]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [5,2,3,4,6,7,8,1] => [[1,3,4,6,7,8],[2],[5]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [[1,4,6,7],[2,5],[3,8]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,5,6,8,4,7] => [3,2,1,7,5,6,8,4] => [[1,4,6,8],[2,5],[3,7]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [[1,4,6,8],[2,5,7],[3]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,7,8,4,6] => [3,2,1,6,5,8,7,4] => [[1,4,7],[2,5,8],[3,6]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,5,8,4,6,7] => [3,2,1,6,5,7,8,4] => [[1,4,7,8],[2,5],[3,6]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,4] => [5,2,3,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,5,1,6,4,8,7] => [5,2,3,6,1,4,8,7] => [[1,3,4,7],[2,6,8],[5]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,5,1,6,8,4,7] => [5,2,3,7,1,6,8,4] => [[1,3,4,8],[2,6],[5,7]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,5,6,1,7,8,4] => [6,2,3,8,5,1,7,4] => [[1,3,4,7],[2,5],[6,8]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,5,6,1,7,4,8] => [6,2,3,7,5,1,4,8] => [[1,3,4,8],[2,5],[6,7]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,5,6,7,1,8,4] => [7,2,3,8,5,6,1,4] => [[1,3,4,6],[2,5],[7,8]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,1,4] => [4,2,3,8,5,6,7,1] => [[1,3,5,6,7],[2,8],[4]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,8,1,4,7] => [4,2,3,7,5,6,8,1] => [[1,3,5,6,8],[2,7],[4]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,7,8,6] => [4,2,3,5,1,8,7,6] => [[1,3,5,6],[2,7],[4,8]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,7,4,8,6] => [5,2,3,7,1,8,4,6] => [[1,3,4,6],[2,7,8],[5]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,7,8,1,4,6] => [4,2,3,6,5,8,7,1] => [[1,3,5,7],[2,6,8],[4]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => [5,2,3,6,1,7,8,4] => [[1,3,4,7,8],[2,6],[5]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,1,4,6,7,8] => [4,2,3,5,1,6,7,8] => [[1,3,5,6,7,8],[2],[4]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => [[1,4,5,7],[2,6],[3,8]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,1,4,6,8,5,7] => [3,2,1,4,7,6,8,5] => [[1,4,5,8],[2,6],[3,7]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,4,7,5,8] => [3,2,1,6,7,4,5,8] => [[1,4,5,8],[2,6,7],[3]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,3,1,6,7,4,8,5] => [3,2,1,7,8,6,4,5] => [[1,4,5],[2,6,8],[3,7]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,4,5] => [3,2,1,5,8,6,7,4] => [[1,4,6,7],[2,5],[3,8]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,1,6,7,4,5,8] => [3,2,1,5,7,6,4,8] => [[1,4,6,8],[2,5],[3,7]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,4,8,5,7] => [3,2,1,6,7,4,8,5] => [[1,4,5,8],[2,6,7],[3]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,1,6,8,4,5,7] => [3,2,1,5,7,6,8,4] => [[1,4,6,8],[2,5],[3,7]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,1,6,4,5,7,8] => [3,2,1,5,6,4,7,8] => [[1,4,6,7,8],[2,5],[3]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,3,6,1,7,4,8,5] => [6,2,3,7,8,1,4,5] => [[1,3,4,5],[2,7,8],[6]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,1,7,8,4,5] => [6,2,3,5,8,1,7,4] => [[1,3,4,7],[2,5],[6,8]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,8,7] => [4,2,3,5,6,1,8,7] => [[1,3,5,6,7],[2,8],[4]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,6,1,4,5,7,8] => [4,2,3,5,6,1,7,8] => [[1,3,5,6,7,8],[2],[4]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,4,7,8,5,6] => [3,2,1,4,6,8,7,5] => [[1,4,5,7],[2,6],[3,8]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,7,4,5,8,6] => [3,2,1,5,7,8,4,6] => [[1,4,6,8],[2,5,7],[3]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => [3,2,1,7,6,8,4,5] => [[1,4,5],[2,6,8],[3,7]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,7,8,4,5,6] => [3,2,1,5,6,8,7,4] => [[1,4,6,7],[2,5],[3,8]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [4,2,3,5,6,8,7,1] => [[1,3,5,6,7],[2,8],[4]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6,8] => [4,2,3,5,6,7,1,8] => [[1,3,5,6,7,8],[2],[4]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => [3,2,1,4,5,7,8,6] => [[1,4,5,6,8],[2,7],[3]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,1,4,8,5,6,7] => [3,2,1,4,6,7,8,5] => [[1,4,5,7,8],[2,6],[3]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,1,8,4,5,6,7] => [3,2,1,5,6,7,8,4] => [[1,4,6,7,8],[2,5],[3]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [4,2,3,5,6,7,8,1] => [[1,3,5,6,7,8],[2],[4]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,3] => [2,1,8,4,5,6,7,3] => [[1,3,5,6,7],[2,4],[8]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [[1,3,5,7],[2,4,8],[6]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,7,3,8,6] => [2,1,7,4,5,8,3,6] => [[1,3,5,6],[2,4,8],[7]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4,5,7,8,3,6] => [2,1,6,4,5,8,7,3] => [[1,3,5,7],[2,4,8],[6]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4,5,8,3,6,7] => [2,1,6,4,5,7,8,3] => [[1,3,5,7,8],[2,4],[6]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4,5,3,6,7,8] => [2,1,5,4,3,6,7,8] => [[1,3,6,7,8],[2,4],[5]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [[1,3,5,7],[2,4,6],[8]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,8,5,7] => [2,1,4,3,7,6,8,5] => [[1,3,5,8],[2,4,6],[7]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [[1,3,5,7,8],[2,4,6]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,6,3,7,8,5] => [2,1,6,4,8,3,7,5] => [[1,3,5],[2,4,7],[6,8]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,7,3,8,5] => [2,1,7,4,8,6,3,5] => [[1,3,5],[2,4,6],[7,8]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,6,7,8,3,5] => [2,1,5,4,8,6,7,3] => [[1,3,6,7],[2,4,8],[5]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,8,7] => [2,1,5,4,6,3,8,7] => [[1,3,6,7],[2,4,8],[5]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,8,5,7] => [2,1,6,4,7,3,8,5] => [[1,3,5,8],[2,4,7],[6]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,8,3,5,7] => [2,1,5,4,7,6,8,3] => [[1,3,6,8],[2,4,7],[5]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,7,6] => [[1,3,5,6],[2,4,7],[8]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => [2,1,4,3,7,8,5,6] => [[1,3,5,6],[2,4,7,8]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [2,1,4,3,6,8,7,5] => [[1,3,5,7],[2,4,6],[8]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,4,7,3,8,5,6] => [2,1,7,4,6,8,3,5] => [[1,3,5,8],[2,4,6],[7]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,4,7,8,3,5,6] => [2,1,5,4,6,8,7,3] => [[1,3,6,7],[2,4,8],[5]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [[1,3,5,6,7],[2,4,8]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,3,5,8,6,7] => [2,1,4,3,5,7,8,6] => [[1,3,5,6,8],[2,4,7]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,3,8,5,6,7] => [2,1,4,3,6,7,8,5] => [[1,3,5,7,8],[2,4,6]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,8,3,5,6,7] => [2,1,5,4,6,7,8,3] => [[1,3,6,7,8],[2,4],[5]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,3] => [4,2,8,1,5,6,7,3] => [[1,3,6,7],[2,5],[4,8]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,4,1,5,6,3,8,7] => [4,2,6,1,5,3,8,7] => [[1,3,7],[2,5,8],[4,6]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,5,6,8,3,7] => [4,2,7,1,5,6,8,3] => [[1,3,6,8],[2,5],[4,7]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,4,1,5,6,3,7,8] => [4,2,6,1,5,3,7,8] => [[1,3,7,8],[2,5],[4,6]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,5,3,7,8,6] => [4,2,5,1,3,8,7,6] => [[1,3,6],[2,5,7],[4,8]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,8] => [4,2,5,1,3,7,6,8] => [[1,3,6,8],[2,5,7],[4]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,4,1,5,7,3,8,6] => [4,2,7,1,5,8,3,6] => [[1,3,6],[2,5,8],[4,7]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,3,6,8,7] => [4,2,5,1,3,6,8,7] => [[1,3,6,7],[2,5,8],[4]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,5,3,8,6,7] => [4,2,5,1,3,7,8,6] => [[1,3,6,8],[2,5,7],[4]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,4,1,5,8,3,6,7] => [4,2,6,1,5,7,8,3] => [[1,3,7,8],[2,5],[4,6]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,3,6,7,8] => [4,2,5,1,3,6,7,8] => [[1,3,6,7,8],[2,5],[4]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,4,5,1,6,7,8,3] => [5,2,8,4,1,6,7,3] => [[1,3,6,7],[2,4],[5,8]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,4,5,1,6,7,3,8] => [5,2,7,4,1,6,3,8] => [[1,3,6,8],[2,4],[5,7]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,4,5,1,6,3,8,7] => [5,2,6,4,1,3,8,7] => [[1,3,7],[2,4,8],[5,6]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,4,5,1,6,8,3,7] => [5,2,7,4,1,6,8,3] => [[1,3,6,8],[2,4],[5,7]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,4,5,1,6,3,7,8] => [5,2,6,4,1,3,7,8] => [[1,3,7,8],[2,4],[5,6]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,6,1,7,8,3] => [6,2,8,4,5,1,7,3] => [[1,3,5,7],[2,4],[6,8]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,6,1,7,3,8] => [6,2,7,4,5,1,3,8] => [[1,3,5,8],[2,4],[6,7]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,1,8,3] => [7,2,8,4,5,6,1,3] => [[1,3,5,6],[2,4],[7,8]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,1,3] => [3,2,8,4,5,6,7,1] => [[1,4,5,6,7],[2,8],[3]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,7,1,3,8] => [3,2,7,4,5,6,1,8] => [[1,4,5,6,8],[2,7],[3]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,6,1,3,8,7] => [3,2,6,4,5,1,8,7] => [[1,4,5,7],[2,6,8],[3]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,6,1,8,3,7] => [6,2,7,4,5,1,8,3] => [[1,3,5,8],[2,4],[6,7]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,4,5,1,3,7,8,6] => [3,2,5,4,1,8,7,6] => [[1,4,6],[2,5,7],[3,8]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6,8] => [3,2,5,4,1,7,6,8] => [[1,4,6,8],[2,5,7],[3]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,4,5,1,7,3,8,6] => [5,2,7,4,1,8,3,6] => [[1,3,6],[2,4,8],[5,7]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,4,5,1,7,8,3,6] => [5,2,6,4,1,8,7,3] => [[1,3,7],[2,4,8],[5,6]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,7,1,3,8,6] => [3,2,7,4,5,8,1,6] => [[1,4,5,6],[2,7,8],[3]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,7,1,8,3,6] => [7,2,6,4,5,8,1,3] => [[1,3,5,8],[2,4],[6],[7]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [5,2,6,4,1,7,8,3] => [[1,3,7,8],[2,4],[5,6]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,1,3,6,7,8] => [3,2,5,4,1,6,7,8] => [[1,4,6,7,8],[2,5],[3]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,6,7,8,5] => [3,2,4,1,8,6,7,5] => [[1,4,5,7],[2,6],[3,8]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,6,7,5,8] => [3,2,4,1,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7] => [3,2,4,1,6,5,8,7] => [[1,4,5,7],[2,6,8],[3]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,8,5,7] => [3,2,4,1,7,6,8,5] => [[1,4,5,8],[2,6],[3,7]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,6,5,7,8] => [3,2,4,1,6,5,7,8] => [[1,4,5,7,8],[2,6],[3]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,8,5] => [4,2,6,1,8,3,7,5] => [[1,3,5],[2,6,7],[4,8]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5,8] => [4,2,6,1,7,3,5,8] => [[1,3,5,8],[2,6,7],[4]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,6,7,3,8,5] => [4,2,7,1,8,6,3,5] => [[1,3,5],[2,6,8],[4,7]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,7,8,3,5] => [4,2,5,1,8,6,7,3] => [[1,3,6,7],[2,5],[4,8]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,8,7] => [4,2,5,1,6,3,8,7] => [[1,3,6,7],[2,5,8],[4]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,7] => [4,2,6,1,7,3,8,5] => [[1,3,5,8],[2,6,7],[4]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,8,3,5,7] => [4,2,5,1,7,6,8,3] => [[1,3,6,8],[2,5],[4,7]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,6,3,5,7,8] => [4,2,5,1,6,3,7,8] => [[1,3,6,7,8],[2,5],[4]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,6,1,3,7,8,5] => [3,2,6,4,8,1,7,5] => [[1,4,5],[2,6,7],[3,8]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,6,1,3,7,5,8] => [3,2,6,4,7,1,5,8] => [[1,4,5,8],[2,6,7],[3]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,6,1,7,3,8,5] => [6,2,7,4,8,1,3,5] => [[1,3,5],[2,4,8],[6,7]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,6,7,1,3,8,5] => [3,2,7,4,8,6,1,5] => [[1,4,5],[2,6,8],[3,7]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,6,7,1,8,3,5] => [7,2,5,4,8,6,1,3] => [[1,3,6],[2,4],[5,8],[7]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,6,7,8,1,3,5] => [3,2,5,4,8,6,7,1] => [[1,4,6,7],[2,5,8],[3]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [3,2,5,4,7,6,1,8] => [[1,4,6,8],[2,5,7],[3]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,8,7] => [3,2,5,4,6,1,8,7] => [[1,4,6,7],[2,5,8],[3]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,8,5,7] => [3,2,6,4,7,1,8,5] => [[1,4,5,8],[2,6,7],[3]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [6,2,5,4,7,1,8,3] => [[1,3,7,8],[2,4],[5],[6]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [3,2,5,4,7,6,8,1] => [[1,4,6,8],[2,5,7],[3]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,3,5,7,8,6] => [3,2,4,1,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,4,1,3,5,7,6,8] => [3,2,4,1,5,7,6,8] => [[1,4,5,6,8],[2,7],[3]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,3,7,5,8,6] => [3,2,4,1,7,8,5,6] => [[1,4,5,6],[2,7,8],[3]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,3,7,8,5,6] => [3,2,4,1,6,8,7,5] => [[1,4,5,7],[2,6],[3,8]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,4,1,3,7,5,6,8] => [3,2,4,1,6,7,5,8] => [[1,4,5,7,8],[2,6],[3]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,7,3,5,8,6] => [4,2,5,1,7,8,3,6] => [[1,3,6,8],[2,5,7],[4]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,7,3,8,5,6] => [4,2,7,1,6,8,3,5] => [[1,3,5],[2,6,8],[4,7]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,7,8,3,5,6] => [4,2,5,1,6,8,7,3] => [[1,3,6,7],[2,5],[4,8]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,4,7,1,3,5,8,6] => [3,2,5,4,7,8,1,6] => [[1,4,6,8],[2,5,7],[3]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,4,7,1,3,8,5,6] => [3,2,7,4,6,8,1,5] => [[1,4,5,8],[2,6],[3,7]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [3,2,5,4,6,8,7,1] => [[1,4,6,7],[2,5,8],[3]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1,3,5,6,8,7] => [3,2,4,1,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,3,5,8,6,7] => [3,2,4,1,5,7,8,6] => [[1,4,5,6,8],[2,7],[3]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1,3,8,5,6,7] => [3,2,4,1,6,7,8,5] => [[1,4,5,7,8],[2,6],[3]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1,8,3,5,6,7] => [4,2,5,1,6,7,8,3] => [[1,3,6,7,8],[2,5],[4]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,8,1,3,5,6,7] => [3,2,5,4,6,7,8,1] => [[1,4,6,7,8],[2,5],[3]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8] => [3,2,4,1,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,5,6,7,4] => [[1,3,4,6,7],[2,5],[8]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,7,8,6] => [2,1,3,5,4,8,7,6] => [[1,3,4,6],[2,5,7],[8]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,1,3,5,7,4,8,6] => [2,1,3,7,5,8,4,6] => [[1,3,4,6],[2,5,8],[7]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,1,3,5,7,8,4,6] => [2,1,3,6,5,8,7,4] => [[1,3,4,7],[2,5,8],[6]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,1,3,5,4,8,6,7] => [2,1,3,5,4,7,8,6] => [[1,3,4,6,8],[2,5,7]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [2,1,5,8,3,6,7,4] => [[1,3,4,7],[2,5,6],[8]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7] => [2,1,5,6,3,4,8,7] => [[1,3,4,7],[2,5,6,8]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,1,5,3,6,8,4,7] => [2,1,5,7,3,6,8,4] => [[1,3,4,8],[2,5,6],[7]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,1,5,6,3,7,8,4] => [2,1,6,8,5,3,7,4] => [[1,3,4],[2,5,7],[6,8]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,1,5,6,7,3,8,4] => [2,1,7,8,5,6,3,4] => [[1,3,4],[2,5,6],[7,8]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,3,4] => [2,1,4,8,5,6,7,3] => [[1,3,5,6,7],[2,4],[8]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,8,7] => [2,1,4,6,5,3,8,7] => [[1,3,5,7],[2,4,8],[6]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,1,5,6,3,4,7,8] => [2,1,4,6,5,3,7,8] => [[1,3,5,7,8],[2,4],[6]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,1,5,3,7,4,8,6] => [2,1,5,7,3,8,4,6] => [[1,3,4,6],[2,5,7,8]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,1,5,3,7,8,4,6] => [2,1,5,6,3,8,7,4] => [[1,3,4,7],[2,5,6],[8]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6,8] => [2,1,5,6,3,7,4,8] => [[1,3,4,7,8],[2,5,6]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,5,7,3,8,4,6] => [2,1,7,6,5,8,3,4] => [[1,3,4],[2,5,8],[6],[7]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,5,7,8,3,4,6] => [2,1,4,6,5,8,7,3] => [[1,3,5,7],[2,4,8],[6]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,5,3,4,6,8,7] => [2,1,4,5,3,6,8,7] => [[1,3,5,6,7],[2,4,8]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,1,5,3,8,4,6,7] => [2,1,5,6,3,7,8,4] => [[1,3,4,7,8],[2,5,6]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,5,3,4,6,7,8] => [2,1,4,5,3,6,7,8] => [[1,3,5,6,7,8],[2,4]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,1,3,6,7,8,4] => [3,2,5,8,1,6,7,4] => [[1,4,6,7],[2,5],[3,8]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,5,1,3,6,7,4,8] => [3,2,5,7,1,6,4,8] => [[1,4,6,8],[2,5],[3,7]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,5,1,3,6,8,4,7] => [3,2,5,7,1,6,8,4] => [[1,4,6,8],[2,5],[3,7]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,1,3,6,4,7,8] => [3,2,5,6,1,4,7,8] => [[1,4,6,7,8],[2,5],[3]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,5,1,6,3,7,8,4] => [5,2,6,8,1,3,7,4] => [[1,3,4],[2,6,7],[5,8]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,5,1,6,3,7,4,8] => [5,2,6,7,1,3,4,8] => [[1,3,4,8],[2,6,7],[5]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,1,6,7,3,8,4] => [5,2,7,8,1,6,3,4] => [[1,3,4],[2,6,8],[5,7]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,1,6,7,8,3,4] => [5,2,4,8,1,6,7,3] => [[1,3,6,7],[2,4],[5,8]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,5,1,6,3,4,8,7] => [5,2,4,6,1,3,8,7] => [[1,3,6,7],[2,4,8],[5]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,5,6,1,3,7,8,4] => [3,2,6,8,5,1,7,4] => [[1,4,7],[2,5,8],[3,6]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,5,6,1,3,7,4,8] => [3,2,6,7,5,1,4,8] => [[1,4,7,8],[2,5],[3,6]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,5,6,1,7,3,8,4] => [6,2,7,8,5,1,3,4] => [[1,3,4],[2,5,8],[6,7]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,5,6,7,1,3,8,4] => [3,2,7,8,5,6,1,4] => [[1,4,6],[2,5,8],[3,7]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,8,1,3,4] => [3,2,4,8,5,6,7,1] => [[1,4,5,6,7],[2,8],[3]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => [3,2,4,7,5,6,8,1] => [[1,4,5,6,8],[2,7],[3]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,7,8,6] => [3,2,4,5,1,8,7,6] => [[1,4,5,6],[2,7],[3,8]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,7,4,8,6] => [3,2,5,7,1,8,4,6] => [[1,4,6,8],[2,5,7],[3]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,7,8,4,6] => [3,2,5,6,1,8,7,4] => [[1,4,6,7],[2,5],[3,8]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,5,1,7,3,4,8,6] => [5,2,4,7,1,8,3,6] => [[1,3,6,8],[2,4,7],[5]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,5,7,1,3,4,8,6] => [3,2,4,7,5,8,1,6] => [[1,4,5,6],[2,7,8],[3]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,5,7,1,3,8,4,6] => [3,2,7,6,5,8,1,4] => [[1,4,8],[2,5],[3,6],[7]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [3,2,4,6,5,8,7,1] => [[1,4,5,7],[2,6,8],[3]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,5,1,3,8,4,6,7] => [3,2,5,6,1,7,8,4] => [[1,4,6,7,8],[2,5],[3]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,4,6,7,8] => [3,2,4,5,1,6,7,8] => [[1,4,5,6,7,8],[2],[3]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,6,7,5] => [[1,3,4,5,7],[2,6],[8]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [[1,3,4,5,7,8],[2,6]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,1,3,6,7,4,8,5] => [2,1,3,7,8,6,4,5] => [[1,3,4,5],[2,6,8],[7]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,6,7,8,4,5] => [2,1,3,5,8,6,7,4] => [[1,3,4,6,7],[2,5],[8]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,1,3,6,4,5,8,7] => [2,1,3,5,6,4,8,7] => [[1,3,4,6,7],[2,5,8]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,1,3,6,4,8,5,7] => [2,1,3,6,7,4,8,5] => [[1,3,4,5,8],[2,6,7]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [2,1,4,6,8,3,7,5] => [[1,3,5,7],[2,4,6],[8]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,6,3,7,4,8,5] => [2,1,6,7,8,3,4,5] => [[1,3,4,5],[2,6,7,8]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,6,3,7,8,4,5] => [2,1,6,5,8,3,7,4] => [[1,3,4],[2,5,7],[6,8]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,6,7,3,4,8,5] => [2,1,4,7,8,6,3,5] => [[1,3,5,8],[2,4,6],[7]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,1,6,7,3,8,4,5] => [2,1,7,5,8,6,3,4] => [[1,3,4],[2,5,6],[7,8]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,3,4,5] => [2,1,4,5,8,6,7,3] => [[1,3,5,6,7],[2,4],[8]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,8,7] => [2,1,4,5,6,3,8,7] => [[1,3,5,6,7],[2,4,8]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,1,6,3,4,8,5,7] => [2,1,4,6,7,3,8,5] => [[1,3,5,7,8],[2,4,6]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,1,6,3,8,4,5,7] => [2,1,6,5,7,3,8,4] => [[1,3,4,8],[2,5,7],[6]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,6,1,3,7,4,8,5] => [3,2,6,7,8,1,4,5] => [[1,4,5,8],[2,6,7],[3]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,1,3,7,8,4,5] => [3,2,6,5,8,1,7,4] => [[1,4,7],[2,5,8],[3,6]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,6,1,3,7,4,5,8] => [3,2,6,5,7,1,4,8] => [[1,4,7,8],[2,5],[3,6]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,6,1,7,3,4,8,5] => [6,2,4,7,8,1,3,5] => [[1,3,5,8],[2,4,7],[6]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,6,7,1,3,4,8,5] => [3,2,4,7,8,6,1,5] => [[1,4,5,8],[2,6],[3,7]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,6,7,1,3,8,4,5] => [3,2,7,5,8,6,1,4] => [[1,4,6],[2,5,8],[3,7]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => [3,2,4,5,8,6,7,1] => [[1,4,5,6,7],[2,8],[3]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,6,1,3,8,4,5,7] => [3,2,6,5,7,1,8,4] => [[1,4,7,8],[2,5],[3,6]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,6,1,8,3,4,5,7] => [6,2,4,5,7,1,8,3] => [[1,3,5,7,8],[2,4],[6]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [3,2,4,5,7,6,8,1] => [[1,4,5,6,8],[2,7],[3]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,6,1,3,4,5,7,8] => [3,2,4,5,6,1,7,8] => [[1,4,5,6,7,8],[2],[3]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,7,6] => [[1,3,4,5,6],[2,7],[8]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,4,7,5,8,6] => [2,1,3,4,7,8,5,6] => [[1,3,4,5,6],[2,7,8]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,1,7,3,8,4,5,6] => [2,1,7,5,6,8,3,4] => [[1,3,4,8],[2,5,6],[7]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,7,8,3,4,5,6] => [2,1,4,5,6,8,7,3] => [[1,3,5,6,7],[2,4],[8]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6,8] => [2,1,4,5,6,7,3,8] => [[1,3,5,6,7,8],[2,4]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,7,1,3,4,5,8,6] => [3,2,4,5,7,8,1,6] => [[1,4,5,6,8],[2,7],[3]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,7,1,8,3,4,5,6] => [7,2,4,5,6,8,1,3] => [[1,3,5,6,8],[2,4],[7]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [3,2,4,5,6,8,7,1] => [[1,4,5,6,7],[2,8],[3]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6,8] => [3,2,4,5,6,7,1,8] => [[1,4,5,6,7,8],[2],[3]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,3,4,5,8,6,7] => [2,1,3,4,5,7,8,6] => [[1,3,4,5,6,8],[2,7]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,1,3,4,8,5,6,7] => [2,1,3,4,6,7,8,5] => [[1,3,4,5,7,8],[2,6]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => [2,1,3,5,6,7,8,4] => [[1,3,4,6,7,8],[2,5]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [2,1,4,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [3,2,4,5,6,7,8,1] => [[1,4,5,6,7,8],[2],[3]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,2] => [1,8,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3],[8]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,2,8] => [1,7,3,4,5,6,2,8] => [[1,2,4,5,6,8],[3],[7]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,8,2,7] => [1,7,3,4,5,6,8,2] => [[1,2,4,5,6,8],[3],[7]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,2,7,8] => [1,6,3,4,5,2,7,8] => [[1,2,4,5,7,8],[3],[6]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,5,2,7,8,6] => [1,5,3,4,2,8,7,6] => [[1,2,4,6],[3,7],[5,8]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,5,7,2,8,6] => [1,7,3,4,5,8,2,6] => [[1,2,4,5,6],[3,8],[7]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,7,8,2,6] => [1,6,3,4,5,8,7,2] => [[1,2,4,5,7],[3,8],[6]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,5,2,8,6,7] => [1,5,3,4,2,7,8,6] => [[1,2,4,6,8],[3,7],[5]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [1,5,3,4,2,6,7,8] => [[1,2,4,6,7,8],[3],[5]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [[1,2,5,8],[3,6],[4,7]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,6,2,7,8,5] => [1,6,3,4,8,2,7,5] => [[1,2,4,5],[3,7],[6,8]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,6,7,2,8,5] => [1,7,3,4,8,6,2,5] => [[1,2,4,5],[3,6],[7,8]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,8,7] => [1,5,3,4,6,2,8,7] => [[1,2,4,6,7],[3,8],[5]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,4,2,5,7,8,6] => [1,4,3,2,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,4,2,5,7,6,8] => [1,4,3,2,5,7,6,8] => [[1,2,5,6,8],[3,7],[4]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,2,7,5,8,6] => [1,4,3,2,7,8,5,6] => [[1,2,5,6],[3,7,8],[4]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,4,2,7,8,5,6] => [1,4,3,2,6,8,7,5] => [[1,2,5,7],[3,6],[4,8]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,4,2,7,5,6,8] => [1,4,3,2,6,7,5,8] => [[1,2,5,7,8],[3,6],[4]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,4,7,2,5,8,6] => [1,5,3,4,7,8,2,6] => [[1,2,4,6,8],[3,7],[5]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => [1,5,3,4,6,7,2,8] => [[1,2,4,6,7,8],[3],[5]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => [[1,2,5,6,7],[3,8],[4]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,3,4,2,5,8,6,7] => [1,4,3,2,5,7,8,6] => [[1,2,5,6,8],[3,7],[4]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [1,4,3,2,6,7,8,5] => [[1,2,5,7,8],[3,6],[4]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [1,5,3,4,6,7,8,2] => [[1,2,4,6,7,8],[3],[5]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,5,6,4,8,7] => [1,3,2,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,5,6,8,4,7] => [1,3,2,7,5,6,8,4] => [[1,2,4,6,8],[3,5],[7]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,5,6,4,7,8] => [1,3,2,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,7,6] => [[1,2,4,6],[3,5,7],[8]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,7,4,8,6] => [1,3,2,7,5,8,4,6] => [[1,2,4,6],[3,5,8],[7]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,7,8,4,6] => [1,3,2,6,5,8,7,4] => [[1,2,4,7],[3,5,8],[6]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,3,2,5,4,7,8,6] => [[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,5,8,4,6,7] => [1,3,2,6,5,7,8,4] => [[1,2,4,7,8],[3,5],[6]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,5,2,6,7,8,4] => [1,5,3,8,2,6,7,4] => [[1,2,4,7],[3,6],[5,8]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,5,2,6,7,4,8] => [1,5,3,7,2,6,4,8] => [[1,2,4,8],[3,6],[5,7]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,5,2,6,4,7,8] => [1,5,3,6,2,4,7,8] => [[1,2,4,7,8],[3,6],[5]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,5,6,2,7,8,4] => [1,6,3,8,5,2,7,4] => [[1,2,4,7],[3,5],[6,8]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,5,6,2,7,4,8] => [1,6,3,7,5,2,4,8] => [[1,2,4,8],[3,5],[6,7]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,5,6,7,2,8,4] => [1,7,3,8,5,6,2,4] => [[1,2,4,6],[3,5],[7,8]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,8,2,4] => [1,4,3,8,5,6,7,2] => [[1,2,5,6,7],[3,8],[4]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [1,4,3,6,5,2,7,8] => [[1,2,5,7,8],[3,6],[4]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,7,4,8,6] => [1,5,3,7,2,8,4,6] => [[1,2,4,6],[3,7,8],[5]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,7,8,4,6] => [1,5,3,6,2,8,7,4] => [[1,2,4,7],[3,6],[5,8]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,7,2,4,8,6] => [1,4,3,7,5,8,2,6] => [[1,2,5,6],[3,7,8],[4]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,7,2,8,4,6] => [1,7,3,6,5,8,2,4] => [[1,2,4,8],[3,5],[6],[7]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,7,8,2,4,6] => [1,4,3,6,5,8,7,2] => [[1,2,5,7],[3,6,8],[4]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [1,5,3,6,2,7,8,4] => [[1,2,4,7,8],[3,6],[5]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [1,4,3,6,5,7,8,2] => [[1,2,5,7,8],[3,6],[4]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,2,4,6,7,5,8] => [1,3,2,4,7,6,5,8] => [[1,2,4,5,8],[3,6],[7]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,4,6,8,5,7] => [1,3,2,4,7,6,8,5] => [[1,2,4,5,8],[3,6],[7]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [[1,2,4,5,7,8],[3,6]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,2,6,4,7,8,5] => [1,3,2,6,8,4,7,5] => [[1,2,4,5],[3,6,7],[8]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,6,4,7,5,8] => [1,3,2,6,7,4,5,8] => [[1,2,4,5,8],[3,6,7]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,2,6,7,4,5,8] => [1,3,2,5,7,6,4,8] => [[1,2,4,6,8],[3,5],[7]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,4,8,5,7] => [1,3,2,6,7,4,8,5] => [[1,2,4,5,8],[3,6,7]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,2,6,4,5,7,8] => [1,3,2,5,6,4,7,8] => [[1,2,4,6,7,8],[3,5]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,2,7,4,8,5] => [1,6,3,7,8,2,4,5] => [[1,2,4,5],[3,7,8],[6]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,6,7,2,4,8,5] => [1,4,3,7,8,6,2,5] => [[1,2,5,8],[3,6],[4,7]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,6,7,2,8,4,5] => [1,7,3,5,8,6,2,4] => [[1,2,4,6],[3,5],[7,8]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,6,7,8,2,4,5] => [1,4,3,5,8,6,7,2] => [[1,2,5,6,7],[3,8],[4]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,6,7,2,4,5,8] => [1,4,3,5,7,6,2,8] => [[1,2,5,6,8],[3,7],[4]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,6,2,4,8,5,7] => [1,4,3,6,7,2,8,5] => [[1,2,5,7,8],[3,6],[4]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,6,2,8,4,5,7] => [1,6,3,5,7,2,8,4] => [[1,2,4,7,8],[3,5],[6]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,6,2,4,5,7,8] => [1,4,3,5,6,2,7,8] => [[1,2,5,6,7,8],[3],[4]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,7,6] => [[1,2,4,5,6],[3,7],[8]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,3,2,4,7,5,8,6] => [1,3,2,4,7,8,5,6] => [[1,2,4,5,6],[3,7,8]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,4,7,8,5,6] => [1,3,2,4,6,8,7,5] => [[1,2,4,5,7],[3,6],[8]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,3,2,7,4,5,8,6] => [1,3,2,5,7,8,4,6] => [[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,7,4,8,5,6] => [1,3,2,7,6,8,4,5] => [[1,2,4,5],[3,6,8],[7]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,3,2,7,8,4,5,6] => [1,3,2,5,6,8,7,4] => [[1,2,4,6,7],[3,5],[8]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,3,2,7,4,5,6,8] => [1,3,2,5,6,7,4,8] => [[1,2,4,6,7,8],[3,5]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,3,7,2,4,5,8,6] => [1,4,3,5,7,8,2,6] => [[1,2,5,6,8],[3,7],[4]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,3,7,2,4,8,5,6] => [1,4,3,7,6,8,2,5] => [[1,2,5,8],[3,6],[4,7]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [1,7,3,5,6,8,2,4] => [[1,2,4,6,8],[3,5],[7]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,7,8,6] => [[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,3,2,4,8,5,6,7] => [1,3,2,4,6,7,8,5] => [[1,2,4,5,7,8],[3,6]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,3,2,8,4,5,6,7] => [1,3,2,5,6,7,8,4] => [[1,2,4,6,7,8],[3,5]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [1,4,3,5,6,7,8,2] => [[1,2,5,6,7,8],[3],[4]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,2] => [3,8,1,4,5,6,7,2] => [[1,2,5,6,7],[3,4],[8]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,2,8] => [3,7,1,4,5,6,2,8] => [[1,2,5,6,8],[3,4],[7]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,5,6,2,8,7] => [3,6,1,4,5,2,8,7] => [[1,2,5,7],[3,4,8],[6]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,4,5,6,8,2,7] => [3,7,1,4,5,6,8,2] => [[1,2,5,6,8],[3,4],[7]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,4,5,6,2,7,8] => [3,6,1,4,5,2,7,8] => [[1,2,5,7,8],[3,4],[6]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,5,2,7,8,6] => [3,5,1,4,2,8,7,6] => [[1,2,6],[3,4,7],[5,8]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,2,6,7,8] => [3,5,1,4,2,6,7,8] => [[1,2,6,7,8],[3,4],[5]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [3,4,1,2,8,6,7,5] => [[1,2,5,7],[3,4,6],[8]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,4,2,6,7,5,8] => [3,4,1,2,7,6,5,8] => [[1,2,5,8],[3,4,6],[7]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7] => [3,4,1,2,6,5,8,7] => [[1,2,5,7],[3,4,6,8]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,8,5,7] => [3,4,1,2,7,6,8,5] => [[1,2,5,8],[3,4,6],[7]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,1,4,2,6,5,7,8] => [3,4,1,2,6,5,7,8] => [[1,2,5,7,8],[3,4,6]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,1,4,6,2,7,5,8] => [3,6,1,4,7,2,5,8] => [[1,2,5,8],[3,4,7],[6]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,8,7] => [3,5,1,4,6,2,8,7] => [[1,2,6,7],[3,4,8],[5]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,8,5,7] => [3,6,1,4,7,2,8,5] => [[1,2,5,8],[3,4,7],[6]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,4,6,8,2,5,7] => [3,5,1,4,7,6,8,2] => [[1,2,6,8],[3,4,7],[5]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,7,8,6] => [3,4,1,2,5,8,7,6] => [[1,2,5,6],[3,4,7],[8]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,2,5,7,6,8] => [3,4,1,2,5,7,6,8] => [[1,2,5,6,8],[3,4,7]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,7,5,8,6] => [3,4,1,2,7,8,5,6] => [[1,2,5,6],[3,4,7,8]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,4,2,7,8,5,6] => [3,4,1,2,6,8,7,5] => [[1,2,5,7],[3,4,6],[8]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,4,2,7,5,6,8] => [3,4,1,2,6,7,5,8] => [[1,2,5,7,8],[3,4,6]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,4,7,2,8,5,6] => [3,7,1,4,6,8,2,5] => [[1,2,5,8],[3,4,6],[7]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,1,4,7,2,5,6,8] => [3,5,1,4,6,7,2,8] => [[1,2,6,7,8],[3,4],[5]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,2,5,6,8,7] => [3,4,1,2,5,6,8,7] => [[1,2,5,6,7],[3,4,8]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,2,5,8,6,7] => [3,4,1,2,5,7,8,6] => [[1,2,5,6,8],[3,4,7]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,4,2,8,5,6,7] => [3,4,1,2,6,7,8,5] => [[1,2,5,7,8],[3,4,6]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,1,4,8,2,5,6,7] => [3,5,1,4,6,7,8,2] => [[1,2,6,7,8],[3,4],[5]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,2,5,6,7,8] => [3,4,1,2,5,6,7,8] => [[1,2,5,6,7,8],[3,4]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,2] => [4,8,3,1,5,6,7,2] => [[1,2,6,7],[3,5],[4,8]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,5,6,7,2,8] => [4,7,3,1,5,6,2,8] => [[1,2,6,8],[3,5],[4,7]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,4,1,5,6,2,8,7] => [4,6,3,1,5,2,8,7] => [[1,2,7],[3,5,8],[4,6]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,4,1,5,6,2,7,8] => [4,6,3,1,5,2,7,8] => [[1,2,7,8],[3,5],[4,6]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,4,1,5,2,7,8,6] => [4,5,3,1,2,8,7,6] => [[1,2,6],[3,5,7],[4,8]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,7,8,2,6] => [4,6,3,1,5,8,7,2] => [[1,2,7],[3,5,8],[4,6]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,4,1,5,2,6,8,7] => [4,5,3,1,2,6,8,7] => [[1,2,6,7],[3,5,8],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,2] => [5,8,3,4,1,6,7,2] => [[1,2,6,7],[3,4],[5,8]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,5,1,6,7,2,8] => [5,7,3,4,1,6,2,8] => [[1,2,6,8],[3,4],[5,7]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,1,6,2,8,7] => [5,6,3,4,1,2,8,7] => [[1,2,7],[3,4,8],[5,6]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,1,7,8,2] => [6,8,3,4,5,1,7,2] => [[1,2,5,7],[3,4],[6,8]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,6,1,7,2,8] => [6,7,3,4,5,1,2,8] => [[1,2,5,8],[3,4],[6,7]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,1,8,2] => [7,8,3,4,5,6,1,2] => [[1,2,5,6],[3,4],[7,8]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,1,2] => [2,8,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,1,2,8] => [2,7,3,4,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [2,6,3,4,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,5,1,2,7,8,6] => [2,5,3,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,5,7,1,2,8,6] => [2,7,3,4,5,8,1,6] => [[1,3,4,5,6],[2,8],[7]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,5,7,1,8,2,6] => [7,6,3,4,5,8,1,2] => [[1,2,5,8],[3,4],[6],[7]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,5,7,8,1,2,6] => [2,6,3,4,5,8,7,1] => [[1,3,4,5,7],[2,8],[6]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,5,1,8,2,6,7] => [5,6,3,4,1,7,8,2] => [[1,2,7,8],[3,4],[5,6]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [2,6,3,4,5,7,8,1] => [[1,3,4,5,7,8],[2],[6]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [2,5,3,4,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [2,4,3,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,8,5,7] => [2,4,3,1,7,6,8,5] => [[1,3,5,8],[2,6],[4,7]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,6,5,7,8] => [2,4,3,1,6,5,7,8] => [[1,3,5,7,8],[2,6],[4]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,4,1,6,2,7,8,5] => [4,6,3,1,8,2,7,5] => [[1,2,5],[3,6,7],[4,8]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,6,2,7,5,8] => [4,6,3,1,7,2,5,8] => [[1,2,5,8],[3,6,7],[4]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,4,1,6,7,2,8,5] => [4,7,3,1,8,6,2,5] => [[1,2,5],[3,6,8],[4,7]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,4,1,6,7,2,5,8] => [4,5,3,1,7,6,2,8] => [[1,2,6,8],[3,5],[4,7]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,8,5,7] => [4,6,3,1,7,2,8,5] => [[1,2,5,8],[3,6,7],[4]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,4,6,1,2,7,5,8] => [2,6,3,4,7,1,5,8] => [[1,3,4,5,8],[2,7],[6]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,4,6,1,7,2,8,5] => [6,7,3,4,8,1,2,5] => [[1,2,5],[3,4,8],[6,7]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,4,6,1,7,8,2,5] => [6,5,3,4,8,1,7,2] => [[1,2,7],[3,4],[5,8],[6]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,6,7,8,1,2,5] => [2,5,3,4,8,6,7,1] => [[1,3,4,6,7],[2,8],[5]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [2,5,3,4,7,6,8,1] => [[1,3,4,6,8],[2,7],[5]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,4,1,2,5,7,8,6] => [2,4,3,1,5,8,7,6] => [[1,3,5,6],[2,7],[4,8]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,4,1,2,7,5,8,6] => [2,4,3,1,7,8,5,6] => [[1,3,5,6],[2,7,8],[4]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,2,7,8,5,6] => [2,4,3,1,6,8,7,5] => [[1,3,5,7],[2,6],[4,8]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,4,1,7,2,5,8,6] => [4,5,3,1,7,8,2,6] => [[1,2,6,8],[3,5,7],[4]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,4,1,7,2,8,5,6] => [4,7,3,1,6,8,2,5] => [[1,2,5],[3,6,8],[4,7]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,4,1,7,8,2,5,6] => [4,5,3,1,6,8,7,2] => [[1,2,6,7],[3,5],[4,8]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [7,5,3,4,6,8,1,2] => [[1,2,6,8],[3,4],[5],[7]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => [2,5,3,4,6,8,7,1] => [[1,3,4,6,7],[2,8],[5]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1,2,8,5,6,7] => [2,4,3,1,6,7,8,5] => [[1,3,5,7,8],[2,6],[4]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1,8,2,5,6,7] => [4,5,3,1,6,7,8,2] => [[1,2,6,7,8],[3,5],[4]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,8,1,2,5,6,7] => [2,5,3,4,6,7,8,1] => [[1,3,4,6,7,8],[2],[5]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [2,4,3,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,5,6,7,8,4] => [2,3,1,8,5,6,7,4] => [[1,3,4,6,7],[2,5],[8]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,5,6,7,4,8] => [2,3,1,7,5,6,4,8] => [[1,3,4,6,8],[2,5],[7]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,5,6,4,7,8] => [2,3,1,6,5,4,7,8] => [[1,3,4,7,8],[2,5],[6]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,8] => [2,3,1,5,4,7,6,8] => [[1,3,4,6,8],[2,5,7]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,7,4,8,6] => [2,3,1,7,5,8,4,6] => [[1,3,4,6],[2,5,8],[7]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,7,8,4,6] => [2,3,1,6,5,8,7,4] => [[1,3,4,7],[2,5,8],[6]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,5,4,6,7,8] => [2,3,1,5,4,6,7,8] => [[1,3,4,6,7,8],[2,5]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7] => [3,5,1,6,2,4,8,7] => [[1,2,4,7],[3,5,6,8]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,5,2,6,8,4,7] => [3,5,1,7,2,6,8,4] => [[1,2,4,8],[3,5,6],[7]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,4,7,8] => [3,5,1,6,2,4,7,8] => [[1,2,4,7,8],[3,5,6]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,5,6,2,7,8,4] => [3,6,1,8,5,2,7,4] => [[1,2,4],[3,5,7],[6,8]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,5,6,7,2,8,4] => [3,7,1,8,5,6,2,4] => [[1,2,4],[3,5,6],[7,8]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,5,6,7,8,2,4] => [3,4,1,8,5,6,7,2] => [[1,2,5,6,7],[3,4],[8]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,5,6,7,2,4,8] => [3,4,1,7,5,6,2,8] => [[1,2,5,6,8],[3,4],[7]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,5,6,2,8,4,7] => [3,6,1,7,5,2,8,4] => [[1,2,4,8],[3,5,7],[6]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,5,6,8,2,4,7] => [3,4,1,7,5,6,8,2] => [[1,2,5,6,8],[3,4],[7]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,7,8,6] => [3,4,1,5,2,8,7,6] => [[1,2,5,6],[3,4,7],[8]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6,8] => [3,4,1,5,2,7,6,8] => [[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,8,6] => [3,5,1,7,2,8,4,6] => [[1,2,4,6],[3,5,7,8]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,7,8,4,6] => [3,5,1,6,2,8,7,4] => [[1,2,4,7],[3,5,6],[8]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6,8] => [3,5,1,6,2,7,4,8] => [[1,2,4,7,8],[3,5,6]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,7,2,4,8,6] => [3,4,1,7,5,8,2,6] => [[1,2,5,6],[3,4,8],[7]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,7,2,8,4,6] => [3,7,1,6,5,8,2,4] => [[1,2,4],[3,5,8],[6],[7]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,7,8,2,4,6] => [3,4,1,6,5,8,7,2] => [[1,2,5,7],[3,4,8],[6]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,5,2,8,4,6,7] => [3,5,1,6,2,7,8,4] => [[1,2,4,7,8],[3,5,6]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,5,8,2,4,6,7] => [3,4,1,6,5,7,8,2] => [[1,2,5,7,8],[3,4],[6]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,5,2,4,6,7,8] => [3,4,1,5,2,6,7,8] => [[1,2,5,6,7,8],[3,4]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,5,1,2,6,7,8,4] => [2,5,3,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [2,5,3,7,1,6,4,8] => [[1,3,4,8],[2,6],[5,7]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,5,1,2,6,8,4,7] => [2,5,3,7,1,6,8,4] => [[1,3,4,8],[2,6],[5,7]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,5,1,6,2,7,8,4] => [5,6,3,8,1,2,7,4] => [[1,2,4],[3,6,7],[5,8]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,5,1,6,2,7,4,8] => [5,6,3,7,1,2,4,8] => [[1,2,4,8],[3,6,7],[5]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,5,1,6,7,2,8,4] => [5,7,3,8,1,6,2,4] => [[1,2,4],[3,6,8],[5,7]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => [5,4,3,6,1,2,8,7] => [[1,2,7],[3,6,8],[4],[5]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,5,1,6,8,2,4,7] => [5,4,3,7,1,6,8,2] => [[1,2,8],[3,6],[4,7],[5]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,5,1,6,2,4,7,8] => [5,4,3,6,1,2,7,8] => [[1,2,7,8],[3,6],[4],[5]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,5,6,1,2,7,8,4] => [2,6,3,8,5,1,7,4] => [[1,3,4,7],[2,5],[6,8]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,5,6,1,7,2,8,4] => [6,7,3,8,5,1,2,4] => [[1,2,4],[3,5,8],[6,7]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,5,6,1,7,8,2,4] => [6,4,3,8,5,1,7,2] => [[1,2,7],[3,5],[4,8],[6]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,5,6,1,7,2,4,8] => [6,4,3,7,5,1,2,8] => [[1,2,8],[3,5],[4,7],[6]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,5,6,7,1,2,8,4] => [2,7,3,8,5,6,1,4] => [[1,3,4,6],[2,5],[7,8]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,8,1,2,4] => [2,4,3,8,5,6,7,1] => [[1,3,5,6,7],[2,8],[4]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,5,6,1,2,4,8,7] => [2,4,3,6,5,1,8,7] => [[1,3,5,7],[2,6,8],[4]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [6,4,3,7,5,1,8,2] => [[1,2,8],[3,5],[4,7],[6]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [2,4,3,7,5,6,8,1] => [[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,5,6,1,2,4,7,8] => [2,4,3,6,5,1,7,8] => [[1,3,5,7,8],[2,6],[4]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,7,8,6] => [2,4,3,5,1,8,7,6] => [[1,3,5,6],[2,7],[4,8]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,7,8,4,6] => [2,5,3,6,1,8,7,4] => [[1,3,4,7],[2,6],[5,8]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,7,2,4,8,6] => [5,4,3,7,1,8,2,6] => [[1,2,6],[3,7,8],[4],[5]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => [5,7,3,6,1,8,2,4] => [[1,2,4],[3,6,8],[5,7]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,7,8,2,4,6] => [5,4,3,6,1,8,7,2] => [[1,2,7],[3,6],[4,8],[5]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,7,1,2,4,8,6] => [2,4,3,7,5,8,1,6] => [[1,3,5,6],[2,7,8],[4]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,7,1,2,8,4,6] => [2,7,3,6,5,8,1,4] => [[1,3,4,8],[2,5],[6],[7]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,7,1,8,2,4,6] => [7,4,3,6,5,8,1,2] => [[1,2,8],[3,5],[4,6],[7]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [2,4,3,6,5,8,7,1] => [[1,3,5,7],[2,6,8],[4]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6,8] => [2,4,3,6,5,7,1,8] => [[1,3,5,7,8],[2,6],[4]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,5,1,2,4,8,6,7] => [2,4,3,5,1,7,8,6] => [[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,5,1,8,2,4,6,7] => [5,4,3,6,1,7,8,2] => [[1,2,7,8],[3,6],[4],[5]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,5,8,1,2,4,6,7] => [2,4,3,6,5,7,8,1] => [[1,3,5,7,8],[2,6],[4]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,5,1,2,4,6,7,8] => [2,4,3,5,1,6,7,8] => [[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7] => [2,3,1,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [3,1,2,4,6,8,5,7] => [2,3,1,4,7,6,8,5] => [[1,3,4,5,8],[2,6],[7]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [3,1,2,6,4,7,8,5] => [2,3,1,6,8,4,7,5] => [[1,3,4,5],[2,6,7],[8]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,6,7,4,8,5] => [2,3,1,7,8,6,4,5] => [[1,3,4,5],[2,6,8],[7]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [3,1,2,6,8,4,5,7] => [2,3,1,5,7,6,8,4] => [[1,3,4,6,8],[2,5],[7]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,1,2,6,4,5,7,8] => [2,3,1,5,6,4,7,8] => [[1,3,4,6,7,8],[2,5]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,1,6,2,4,7,5,8] => [3,4,1,6,7,2,5,8] => [[1,2,5,7,8],[3,4,6]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [3,1,6,2,7,4,8,5] => [3,6,1,7,8,2,4,5] => [[1,2,4,5],[3,6,7,8]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,1,6,7,2,4,5,8] => [3,4,1,5,7,6,2,8] => [[1,2,5,6,8],[3,4],[7]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,8,7] => [3,4,1,5,6,2,8,7] => [[1,2,5,6,7],[3,4,8]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [3,1,6,2,4,8,5,7] => [3,4,1,6,7,2,8,5] => [[1,2,5,7,8],[3,4,6]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,6,8,2,4,5,7] => [3,4,1,5,7,6,8,2] => [[1,2,5,6,8],[3,4],[7]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,1,6,2,4,5,7,8] => [3,4,1,5,6,2,7,8] => [[1,2,5,6,7,8],[3,4]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,6,1,2,4,7,8,5] => [2,4,3,6,8,1,7,5] => [[1,3,5,7],[2,6],[4,8]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => [2,4,3,6,7,1,5,8] => [[1,3,5,7,8],[2,6],[4]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,6,1,2,7,4,8,5] => [2,6,3,7,8,1,4,5] => [[1,3,4,5],[2,7,8],[6]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [3,6,1,2,7,8,4,5] => [2,6,3,5,8,1,7,4] => [[1,3,4,7],[2,5],[6,8]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,6,1,7,2,4,8,5] => [6,4,3,7,8,1,2,5] => [[1,2,5],[3,7,8],[4],[6]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => [6,7,3,5,8,1,2,4] => [[1,2,4],[3,5,8],[6,7]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [3,6,1,7,8,2,4,5] => [6,4,3,5,8,1,7,2] => [[1,2,7],[3,5],[4,8],[6]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [3,6,7,1,2,4,8,5] => [2,4,3,7,8,6,1,5] => [[1,3,5,8],[2,6],[4,7]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [3,6,7,1,2,8,4,5] => [2,7,3,5,8,6,1,4] => [[1,3,4,6],[2,5],[7,8]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [2,4,3,5,8,6,7,1] => [[1,3,5,6,7],[2,8],[4]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,8,7] => [2,4,3,5,6,1,8,7] => [[1,3,5,6,7],[2,8],[4]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,2,4,5,7,6,8] => [2,3,1,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,4,7,5,8,6] => [2,3,1,4,7,8,5,6] => [[1,3,4,5,6],[2,7,8]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [3,1,2,4,7,5,6,8] => [2,3,1,4,6,7,5,8] => [[1,3,4,5,7,8],[2,6]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,2,7,4,5,8,6] => [2,3,1,5,7,8,4,6] => [[1,3,4,6,8],[2,5,7]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [3,1,2,7,4,8,5,6] => [2,3,1,7,6,8,4,5] => [[1,3,4,5],[2,6,8],[7]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,1,2,7,4,5,6,8] => [2,3,1,5,6,7,4,8] => [[1,3,4,6,7,8],[2,5]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,7,2,4,5,8,6] => [3,4,1,5,7,8,2,6] => [[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [3,1,7,2,4,8,5,6] => [3,4,1,7,6,8,2,5] => [[1,2,5,8],[3,4,6],[7]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [3,1,7,2,8,4,5,6] => [3,7,1,5,6,8,2,4] => [[1,2,4,8],[3,5,6],[7]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,7,8,2,4,5,6] => [3,4,1,5,6,8,7,2] => [[1,2,5,6,7],[3,4],[8]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6,8] => [3,4,1,5,6,7,2,8] => [[1,2,5,6,7,8],[3,4]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,7,1,2,4,5,8,6] => [2,4,3,5,7,8,1,6] => [[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => [2,4,3,5,6,8,7,1] => [[1,3,5,6,7],[2,8],[4]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [2,3,1,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,2,4,5,8,6,7] => [2,3,1,4,5,7,8,6] => [[1,3,4,5,6,8],[2,7]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,2,4,8,5,6,7] => [2,3,1,4,6,7,8,5] => [[1,3,4,5,7,8],[2,6]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,2,8,4,5,6,7] => [2,3,1,5,6,7,8,4] => [[1,3,4,6,7,8],[2,5]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [3,4,1,5,6,7,8,2] => [[1,2,5,6,7,8],[3,4]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [2,4,3,5,6,7,8,1] => [[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,3] => [1,2,8,4,5,6,7,3] => [[1,2,3,5,6,7],[4],[8]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,6,8,3,7] => [1,2,7,4,5,6,8,3] => [[1,2,3,5,6,8],[4],[7]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,5,3,7,8,6] => [1,2,5,4,3,8,7,6] => [[1,2,3,6],[4,7],[5,8]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,7,3,8,6] => [1,2,7,4,5,8,3,6] => [[1,2,3,5,6],[4,8],[7]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,4,5,3,6,8,7] => [1,2,5,4,3,6,8,7] => [[1,2,3,6,7],[4,8],[5]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,4,5,3,8,6,7] => [1,2,5,4,3,7,8,6] => [[1,2,3,6,8],[4,7],[5]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,4,5,8,3,6,7] => [1,2,6,4,5,7,8,3] => [[1,2,3,5,7,8],[4],[6]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [1,2,5,4,3,6,7,8] => [[1,2,3,6,7,8],[4],[5]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [[1,2,3,5,7],[4,6,8]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,8,5,7] => [1,2,4,3,7,6,8,5] => [[1,2,3,5,8],[4,6],[7]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,6,3,7,8,5] => [1,2,6,4,8,3,7,5] => [[1,2,3,5],[4,7],[6,8]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,6,3,7,5,8] => [1,2,6,4,7,3,5,8] => [[1,2,3,5,8],[4,7],[6]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,6,7,3,8,5] => [1,2,7,4,8,6,3,5] => [[1,2,3,5],[4,6],[7,8]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,8,5,7] => [1,2,6,4,7,3,8,5] => [[1,2,3,5,8],[4,7],[6]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,8,3,5,7] => [1,2,5,4,7,6,8,3] => [[1,2,3,6,8],[4,7],[5]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,3,7,5,8,6] => [1,2,4,3,7,8,5,6] => [[1,2,3,5,6],[4,7,8]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,4,3,7,5,6,8] => [1,2,4,3,6,7,5,8] => [[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,7,3,5,8,6] => [1,2,5,4,7,8,3,6] => [[1,2,3,6,8],[4,7],[5]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,4,7,8,3,5,6] => [1,2,5,4,6,8,7,3] => [[1,2,3,6,7],[4,8],[5]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [1,2,5,4,6,7,3,8] => [[1,2,3,6,7,8],[4],[5]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,3,5,8,6,7] => [1,2,4,3,5,7,8,6] => [[1,2,3,5,6,8],[4,7]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [1,2,4,3,6,7,8,5] => [[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [1,2,5,4,6,7,8,3] => [[1,2,3,6,7,8],[4],[5]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,3] => [1,4,8,2,5,6,7,3] => [[1,2,3,6,7],[4,5],[8]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,4,2,5,6,7,3,8] => [1,4,7,2,5,6,3,8] => [[1,2,3,6,8],[4,5],[7]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,4,2,5,6,8,3,7] => [1,4,7,2,5,6,8,3] => [[1,2,3,6,8],[4,5],[7]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,4,2,5,6,3,7,8] => [1,4,6,2,5,3,7,8] => [[1,2,3,7,8],[4,5],[6]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6,8] => [1,4,5,2,3,7,6,8] => [[1,2,3,6,8],[4,5,7]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,4,2,5,7,3,8,6] => [1,4,7,2,5,8,3,6] => [[1,2,3,6],[4,5,8],[7]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3,8,6,7] => [1,4,5,2,3,7,8,6] => [[1,2,3,6,8],[4,5,7]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,4,2,5,3,6,7,8] => [1,4,5,2,3,6,7,8] => [[1,2,3,6,7,8],[4,5]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,5,2,6,7,8,3] => [1,5,8,4,2,6,7,3] => [[1,2,3,7],[4,6],[5,8]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,5,2,6,7,3,8] => [1,5,7,4,2,6,3,8] => [[1,2,3,8],[4,6],[5,7]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,5,2,6,8,3,7] => [1,5,7,4,2,6,8,3] => [[1,2,3,8],[4,6],[5,7]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,5,2,6,3,7,8] => [1,5,6,4,2,3,7,8] => [[1,2,3,7,8],[4,6],[5]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,4,5,6,2,7,8,3] => [1,6,8,4,5,2,7,3] => [[1,2,3,7],[4,5],[6,8]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,4,5,6,2,7,3,8] => [1,6,7,4,5,2,3,8] => [[1,2,3,8],[4,5],[6,7]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,7,2,8,3] => [1,7,8,4,5,6,2,3] => [[1,2,3,6],[4,5],[7,8]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,2,3] => [1,3,8,4,5,6,7,2] => [[1,2,4,5,6,7],[3],[8]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,7,2,3,8] => [1,3,7,4,5,6,2,8] => [[1,2,4,5,6,8],[3],[7]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,4,5,6,2,3,8,7] => [1,3,6,4,5,2,8,7] => [[1,2,4,5,7],[3,8],[6]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,4,5,6,2,8,3,7] => [1,6,7,4,5,2,8,3] => [[1,2,3,8],[4,5],[6,7]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,6,8,2,3,7] => [1,3,7,4,5,6,8,2] => [[1,2,4,5,6,8],[3],[7]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6,8] => [1,3,5,4,2,7,6,8] => [[1,2,4,6,8],[3,7],[5]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,5,2,7,3,8,6] => [1,5,7,4,2,8,3,6] => [[1,2,3,6],[4,7,8],[5]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,4,5,2,7,8,3,6] => [1,5,6,4,2,8,7,3] => [[1,2,3,7],[4,6],[5,8]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => [1,3,7,4,5,8,2,6] => [[1,2,4,5,6],[3,8],[7]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,4,5,2,3,8,6,7] => [1,3,5,4,2,7,8,6] => [[1,2,4,6,8],[3,7],[5]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,4,5,8,2,3,6,7] => [1,3,6,4,5,7,8,2] => [[1,2,4,5,7,8],[3],[6]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,6,7,8,5] => [1,3,4,2,8,6,7,5] => [[1,2,4,5,7],[3,6],[8]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7] => [1,3,4,2,6,5,8,7] => [[1,2,4,5,7],[3,6,8]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,8,5,7] => [1,3,4,2,7,6,8,5] => [[1,2,4,5,8],[3,6],[7]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,6,3,7,8,5] => [1,4,6,2,8,3,7,5] => [[1,2,3,5],[4,6,7],[8]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,6,3,7,5,8] => [1,4,6,2,7,3,5,8] => [[1,2,3,5,8],[4,6,7]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,7,8,3,5] => [1,4,5,2,8,6,7,3] => [[1,2,3,6,7],[4,5],[8]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,8,7] => [1,4,5,2,6,3,8,7] => [[1,2,3,6,7],[4,5,8]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => [1,4,6,2,7,3,8,5] => [[1,2,3,5,8],[4,6,7]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,6,3,5,7,8] => [1,4,5,2,6,3,7,8] => [[1,2,3,6,7,8],[4,5]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,4,6,2,3,7,8,5] => [1,3,6,4,8,2,7,5] => [[1,2,4,5],[3,7],[6,8]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,4,6,2,3,7,5,8] => [1,3,6,4,7,2,5,8] => [[1,2,4,5,8],[3,7],[6]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,4,6,2,7,3,8,5] => [1,6,7,4,8,2,3,5] => [[1,2,3,5],[4,7,8],[6]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,6,2,7,8,3,5] => [1,6,5,4,8,2,7,3] => [[1,2,3],[4,7],[5,8],[6]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,7,3,5,8] => [1,6,5,4,7,2,3,8] => [[1,2,3,8],[4,7],[5],[6]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,4,6,7,2,3,8,5] => [1,3,7,4,8,6,2,5] => [[1,2,4,5],[3,6],[7,8]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,4,6,7,2,8,3,5] => [1,7,5,4,8,6,2,3] => [[1,2,3],[4,6],[5,8],[7]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => [1,3,5,4,7,6,2,8] => [[1,2,4,6,8],[3,7],[5]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,8,5,7] => [1,3,6,4,7,2,8,5] => [[1,2,4,5,8],[3,7],[6]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [1,3,5,4,7,6,8,2] => [[1,2,4,6,8],[3,7],[5]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2,3,5,7,6,8] => [1,3,4,2,5,7,6,8] => [[1,2,4,5,6,8],[3,7]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,4,2,3,7,5,8,6] => [1,3,4,2,7,8,5,6] => [[1,2,4,5,6],[3,7,8]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,3,7,8,5,6] => [1,3,4,2,6,8,7,5] => [[1,2,4,5,7],[3,6],[8]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2,3,7,5,6,8] => [1,3,4,2,6,7,5,8] => [[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,4,2,7,3,5,8,6] => [1,4,5,2,7,8,3,6] => [[1,2,3,6,8],[4,5,7]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,7,3,8,5,6] => [1,4,7,2,6,8,3,5] => [[1,2,3,5],[4,6,8],[7]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => [1,4,5,2,6,8,7,3] => [[1,2,3,6,7],[4,5],[8]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2,7,3,5,6,8] => [1,4,5,2,6,7,3,8] => [[1,2,3,6,7,8],[4,5]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,4,7,2,3,5,8,6] => [1,3,5,4,7,8,2,6] => [[1,2,4,6,8],[3,7],[5]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,7,2,3,8,5,6] => [1,3,7,4,6,8,2,5] => [[1,2,4,5,8],[3,6],[7]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,4,2,3,5,6,8,7] => [1,3,4,2,5,6,8,7] => [[1,2,4,5,6,7],[3,8]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [1,3,4,2,5,7,8,6] => [[1,2,4,5,6,8],[3,7]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,2,3,8,5,6,7] => [1,3,4,2,6,7,8,5] => [[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => [1,4,5,2,6,7,8,3] => [[1,2,3,6,7,8],[4,5]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8] => [1,3,4,2,5,6,7,8] => [[1,2,4,5,6,7,8],[3]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,3] => [2,4,8,1,5,6,7,3] => [[1,3,5,6,7],[2,4],[8]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,5,6,3,8,7] => [2,4,6,1,5,3,8,7] => [[1,3,5,7],[2,4,8],[6]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,5,6,8,3,7] => [2,4,7,1,5,6,8,3] => [[1,3,5,6,8],[2,4],[7]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3,7,8] => [2,4,6,1,5,3,7,8] => [[1,3,5,7,8],[2,4],[6]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,5,3,7,8,6] => [2,4,5,1,3,8,7,6] => [[1,3,5,6],[2,4,7],[8]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6,8] => [2,4,5,1,3,7,6,8] => [[1,3,5,6,8],[2,4,7]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,5,7,8,3,6] => [2,4,6,1,5,8,7,3] => [[1,3,5,7],[2,4,8],[6]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,1,2,5,3,8,6,7] => [2,4,5,1,3,7,8,6] => [[1,3,5,6,8],[2,4,7]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,5,3,6,7,8] => [2,4,5,1,3,6,7,8] => [[1,3,5,6,7,8],[2,4]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [4,5,8,1,2,6,7,3] => [[1,2,3,7],[4,5,6],[8]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,5,2,6,7,3,8] => [4,5,7,1,2,6,3,8] => [[1,2,3,8],[4,5,6],[7]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [4,5,6,1,2,3,8,7] => [[1,2,3,7],[4,5,6,8]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,5,2,6,8,3,7] => [4,5,7,1,2,6,8,3] => [[1,2,3,8],[4,5,6],[7]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,1,5,2,6,3,7,8] => [4,5,6,1,2,3,7,8] => [[1,2,3,7,8],[4,5,6]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,1,5,6,2,7,3,8] => [4,6,7,1,5,2,3,8] => [[1,2,3,8],[4,5,7],[6]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,5,6,7,2,8,3] => [4,7,8,1,5,6,2,3] => [[1,2,3],[4,5,6],[7,8]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,5,6,7,8,2,3] => [4,3,8,1,5,6,7,2] => [[1,2,6,7],[3,5],[4,8]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,5,6,2,3,8,7] => [4,3,6,1,5,2,8,7] => [[1,2,7],[3,5,8],[4,6]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [4,1,5,6,8,2,3,7] => [4,3,7,1,5,6,8,2] => [[1,2,6,8],[3,5],[4,7]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,1,5,6,2,3,7,8] => [4,3,6,1,5,2,7,8] => [[1,2,7,8],[3,5],[4,6]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => [4,3,5,1,2,8,7,6] => [[1,2,6],[3,5,7],[4,8]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6,8] => [4,3,5,1,2,7,6,8] => [[1,2,6,8],[3,5,7],[4]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,5,2,7,3,8,6] => [4,5,7,1,2,8,3,6] => [[1,2,3,6],[4,5,7,8]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => [4,5,6,1,2,8,7,3] => [[1,2,3,7],[4,5,6],[8]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6,8] => [4,5,6,1,2,7,3,8] => [[1,2,3,7,8],[4,5,6]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,5,7,2,3,8,6] => [4,3,7,1,5,8,2,6] => [[1,2,6],[3,5,8],[4,7]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,1,5,7,8,2,3,6] => [4,3,6,1,5,8,7,2] => [[1,2,7],[3,5,8],[4,6]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6,8] => [4,3,6,1,5,7,2,8] => [[1,2,7,8],[3,5],[4,6]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,1,5,2,8,3,6,7] => [4,5,6,1,2,7,8,3] => [[1,2,3,7,8],[4,5,6]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,1,5,2,3,6,7,8] => [4,3,5,1,2,6,7,8] => [[1,2,6,7,8],[3,5],[4]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [2,5,7,4,1,6,3,8] => [[1,3,6,8],[2,4],[5,7]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => [2,5,6,4,1,3,8,7] => [[1,3,6,7],[2,4,8],[5]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [4,5,1,2,6,8,3,7] => [2,5,7,4,1,6,8,3] => [[1,3,6,8],[2,4],[5,7]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,5,1,6,2,7,8,3] => [5,6,8,4,1,2,7,3] => [[1,2,3],[4,6,7],[5,8]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,5,1,6,2,7,3,8] => [5,6,7,4,1,2,3,8] => [[1,2,3,8],[4,6,7],[5]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,5,1,6,7,2,8,3] => [5,7,8,4,1,6,2,3] => [[1,2,3],[4,6,8],[5,7]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [4,5,1,6,7,2,3,8] => [5,3,7,4,1,6,2,8] => [[1,2,6,8],[3,4],[5,7]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [4,5,1,6,2,3,8,7] => [5,3,6,4,1,2,8,7] => [[1,2,7],[3,4,8],[5,6]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [4,5,1,6,2,8,3,7] => [5,6,7,4,1,2,8,3] => [[1,2,3,8],[4,6,7],[5]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,1,6,2,3,7,8] => [5,3,6,4,1,2,7,8] => [[1,2,7,8],[3,4],[5,6]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,6,1,2,7,8,3] => [2,6,8,4,5,1,7,3] => [[1,3,5,7],[2,4],[6,8]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,6,1,2,7,3,8] => [2,6,7,4,5,1,3,8] => [[1,3,5,8],[2,4],[6,7]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,1,7,2,8,3] => [6,7,8,4,5,1,2,3] => [[1,2,3],[4,5,8],[6,7]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,6,1,7,8,2,3] => [6,3,8,4,5,1,7,2] => [[1,2,5,7],[3,4],[6,8]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,1,8,2,3] => [7,3,8,4,5,6,1,2] => [[1,2,5,6],[3,4],[7,8]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,1,2,3] => [2,3,8,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => [2,3,6,4,5,1,8,7] => [[1,3,4,5,7],[2,8],[6]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,6,1,2,8,3,7] => [2,6,7,4,5,1,8,3] => [[1,3,5,8],[2,4],[6,7]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [6,3,7,4,5,1,8,2] => [[1,2,5,8],[3,4],[6,7]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [2,3,7,4,5,6,8,1] => [[1,3,4,5,6,8],[2],[7]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [2,3,6,4,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,7,8,6] => [2,3,5,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,5,1,2,7,3,8,6] => [2,5,7,4,1,8,3,6] => [[1,3,6,8],[2,4,7],[5]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6,8] => [2,5,6,4,1,7,3,8] => [[1,3,6,7,8],[2,4],[5]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [4,5,1,7,8,2,3,6] => [5,3,6,4,1,8,7,2] => [[1,2,7],[3,4,8],[5,6]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6,8] => [5,3,6,4,1,7,2,8] => [[1,2,7,8],[3,4],[5,6]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => [2,7,6,4,5,8,1,3] => [[1,3,5,8],[2,4],[6],[7]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [2,3,6,4,5,8,7,1] => [[1,3,4,5,7],[2,8],[6]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,5,1,2,3,6,8,7] => [2,3,5,4,1,6,8,7] => [[1,3,4,6,7],[2,8],[5]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,5,1,2,8,3,6,7] => [2,5,6,4,1,7,8,3] => [[1,3,6,7,8],[2,4],[5]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [2,3,6,4,5,7,8,1] => [[1,3,4,5,7,8],[2],[6]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [2,3,5,4,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => [2,3,4,1,8,6,7,5] => [[1,3,4,5,7],[2,6],[8]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,6,7,5,8] => [2,3,4,1,7,6,5,8] => [[1,3,4,5,8],[2,6],[7]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => [2,3,4,1,6,5,8,7] => [[1,3,4,5,7],[2,6,8]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,8,5,7] => [2,3,4,1,7,6,8,5] => [[1,3,4,5,8],[2,6],[7]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,6,5,7,8] => [2,3,4,1,6,5,7,8] => [[1,3,4,5,7,8],[2,6]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,6,3,7,8,5] => [2,4,6,1,8,3,7,5] => [[1,3,5,7],[2,4,6],[8]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,6,7,3,5,8] => [2,4,5,1,7,6,3,8] => [[1,3,5,6,8],[2,4],[7]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,8,7] => [2,4,5,1,6,3,8,7] => [[1,3,5,6,7],[2,4,8]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,8,5,7] => [2,4,6,1,7,3,8,5] => [[1,3,5,7,8],[2,4,6]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,6,3,5,7,8] => [2,4,5,1,6,3,7,8] => [[1,3,5,6,7,8],[2,4]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [4,3,6,1,8,2,7,5] => [[1,2,5],[3,6,7],[4,8]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,6,2,3,7,5,8] => [4,3,6,1,7,2,5,8] => [[1,2,5,8],[3,6,7],[4]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => [4,6,7,1,8,2,3,5] => [[1,2,3,5],[4,6,7,8]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,6,7,8,2,3,5] => [4,3,5,1,8,6,7,2] => [[1,2,6,7],[3,5],[4,8]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,8,7] => [4,3,5,1,6,2,8,7] => [[1,2,6,7],[3,5,8],[4]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,8,5,7] => [4,3,6,1,7,2,8,5] => [[1,2,5,8],[3,6,7],[4]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,8,2,3,5,7] => [4,3,5,1,7,6,8,2] => [[1,2,6,8],[3,5],[4,7]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,6,2,3,5,7,8] => [4,3,5,1,6,2,7,8] => [[1,2,6,7,8],[3,5],[4]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [2,3,6,4,7,1,5,8] => [[1,3,4,5,8],[2,7],[6]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [4,6,1,2,7,3,8,5] => [2,6,7,4,8,1,3,5] => [[1,3,5,8],[2,4,7],[6]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [4,6,1,2,7,8,3,5] => [2,6,5,4,8,1,7,3] => [[1,3,7],[2,4],[5,8],[6]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [4,6,1,2,7,3,5,8] => [2,6,5,4,7,1,3,8] => [[1,3,7,8],[2,4],[5],[6]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [4,6,1,7,2,3,8,5] => [6,3,7,4,8,1,2,5] => [[1,2,5],[3,4,8],[6,7]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [4,6,1,7,2,8,3,5] => [6,7,5,4,8,1,2,3] => [[1,2,3],[4,7,8],[5],[6]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [4,6,1,7,8,2,3,5] => [6,3,5,4,8,1,7,2] => [[1,2,7],[3,4],[5,8],[6]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,6,1,7,2,3,5,8] => [6,3,5,4,7,1,2,8] => [[1,2,7,8],[3,4],[5],[6]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [7,3,5,4,8,6,1,2] => [[1,2,6],[3,4],[5,8],[7]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [2,3,5,4,8,6,7,1] => [[1,3,4,6,7],[2,8],[5]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,8,3,5,7] => [2,6,5,4,7,1,8,3] => [[1,3,7,8],[2,4],[5],[6]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,8,2,3,5,7] => [6,3,5,4,7,1,8,2] => [[1,2,7,8],[3,4],[5],[6]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,8,1,2,3,5,7] => [2,3,5,4,7,6,8,1] => [[1,3,4,6,8],[2,7],[5]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => [2,3,4,1,5,8,7,6] => [[1,3,4,5,6],[2,7],[8]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,7,6,8] => [2,3,4,1,5,7,6,8] => [[1,3,4,5,6,8],[2,7]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,3,7,5,8,6] => [2,3,4,1,7,8,5,6] => [[1,3,4,5,6],[2,7,8]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,3,7,8,5,6] => [2,3,4,1,6,8,7,5] => [[1,3,4,5,7],[2,6],[8]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,3,7,5,6,8] => [2,3,4,1,6,7,5,8] => [[1,3,4,5,7,8],[2,6]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,7,3,5,8,6] => [2,4,5,1,7,8,3,6] => [[1,3,5,6,8],[2,4,7]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [4,1,2,7,3,8,5,6] => [2,4,7,1,6,8,3,5] => [[1,3,5,8],[2,4,6],[7]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [4,1,2,7,8,3,5,6] => [2,4,5,1,6,8,7,3] => [[1,3,5,6,7],[2,4],[8]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,7,2,3,5,8,6] => [4,3,5,1,7,8,2,6] => [[1,2,6,8],[3,5,7],[4]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [4,1,7,2,3,8,5,6] => [4,3,7,1,6,8,2,5] => [[1,2,5],[3,6,8],[4,7]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [4,1,7,2,8,3,5,6] => [4,7,5,1,6,8,2,3] => [[1,2,3,8],[4,5,6],[7]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,1,7,8,2,3,5,6] => [4,3,5,1,6,8,7,2] => [[1,2,6,7],[3,5],[4,8]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,7,1,8,2,3,5,6] => [7,3,5,4,6,8,1,2] => [[1,2,6,8],[3,4],[5],[7]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6,8] => [2,3,5,4,6,7,1,8] => [[1,3,4,6,7,8],[2],[5]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [2,3,4,1,5,6,8,7] => [[1,3,4,5,6,7],[2,8]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [4,1,2,3,5,8,6,7] => [2,3,4,1,5,7,8,6] => [[1,3,4,5,6,8],[2,7]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => [2,3,4,1,6,7,8,5] => [[1,3,4,5,7,8],[2,6]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,8,3,5,6,7] => [2,4,5,1,6,7,8,3] => [[1,3,5,6,7,8],[2,4]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [4,3,5,1,6,7,8,2] => [[1,2,6,7,8],[3,5],[4]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [2,3,5,4,6,7,8,1] => [[1,3,4,6,7,8],[2],[5]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [2,3,4,1,5,6,7,8] => [[1,3,4,5,6,7,8],[2]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => [[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,4,8] => [1,2,3,7,5,6,4,8] => [[1,2,3,4,6,8],[5],[7]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,2,3,5,6,4,8,7] => [1,2,3,6,5,4,8,7] => [[1,2,3,4,7],[5,8],[6]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,8,4,7] => [1,2,3,7,5,6,8,4] => [[1,2,3,4,6,8],[5],[7]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,5,6,4,7,8] => [1,2,3,6,5,4,7,8] => [[1,2,3,4,7,8],[5],[6]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,7,6] => [[1,2,3,4,6],[5,7],[8]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [[1,2,3,4,6,8],[5,7]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,2,3,5,7,4,8,6] => [1,2,3,7,5,8,4,6] => [[1,2,3,4,6],[5,8],[7]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,2,3,5,7,8,4,6] => [1,2,3,6,5,8,7,4] => [[1,2,3,4,7],[5,8],[6]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6,8] => [1,2,3,6,5,7,4,8] => [[1,2,3,4,7,8],[5],[6]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [[1,2,3,4,6,7],[5,8]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,7,8,6] => [[1,2,3,4,6,8],[5,7]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,5,8,4,6,7] => [1,2,3,6,5,7,8,4] => [[1,2,3,4,7,8],[5],[6]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [[1,2,3,4,6,7,8],[5]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,4] => [1,2,5,8,3,6,7,4] => [[1,2,3,4,7],[5,6],[8]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,2,5,3,6,7,4,8] => [1,2,5,7,3,6,4,8] => [[1,2,3,4,8],[5,6],[7]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,2,5,3,6,4,8,7] => [1,2,5,6,3,4,8,7] => [[1,2,3,4,7],[5,6,8]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,2,5,3,6,8,4,7] => [1,2,5,7,3,6,8,4] => [[1,2,3,4,8],[5,6],[7]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,2,5,3,6,4,7,8] => [1,2,5,6,3,4,7,8] => [[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,2,5,6,3,7,8,4] => [1,2,6,8,5,3,7,4] => [[1,2,3,4],[5,7],[6,8]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,2,5,6,3,7,4,8] => [1,2,6,7,5,3,4,8] => [[1,2,3,4,8],[5,7],[6]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,2,5,6,7,3,8,4] => [1,2,7,8,5,6,3,4] => [[1,2,3,4],[5,6],[7,8]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,6,7,8,3,4] => [1,2,4,8,5,6,7,3] => [[1,2,3,5,6,7],[4],[8]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,2,5,6,3,8,4,7] => [1,2,6,7,5,3,8,4] => [[1,2,3,4,8],[5,7],[6]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,2,5,6,8,3,4,7] => [1,2,4,7,5,6,8,3] => [[1,2,3,5,6,8],[4],[7]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [1,2,4,6,5,3,7,8] => [[1,2,3,5,7,8],[4],[6]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,7,8,6] => [1,2,4,5,3,8,7,6] => [[1,2,3,5,6],[4,7],[8]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6,8] => [1,2,4,5,3,7,6,8] => [[1,2,3,5,6,8],[4,7]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,2,5,3,7,4,8,6] => [1,2,5,7,3,8,4,6] => [[1,2,3,4,6],[5,7,8]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,2,5,3,7,8,4,6] => [1,2,5,6,3,8,7,4] => [[1,2,3,4,7],[5,6],[8]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6,8] => [1,2,5,6,3,7,4,8] => [[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,2,5,7,3,8,4,6] => [1,2,7,6,5,8,3,4] => [[1,2,3,4],[5,8],[6],[7]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4,8,6,7] => [1,2,4,5,3,7,8,6] => [[1,2,3,5,6,8],[4,7]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [1,2,5,6,3,7,8,4] => [[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,5,2,3,6,7,8,4] => [1,3,5,8,2,6,7,4] => [[1,2,4,6,7],[3,5],[8]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,5,2,3,6,7,4,8] => [1,3,5,7,2,6,4,8] => [[1,2,4,6,8],[3,5],[7]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,5,2,3,6,4,8,7] => [1,3,5,6,2,4,8,7] => [[1,2,4,6,7],[3,5,8]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,2,3,6,4,7,8] => [1,3,5,6,2,4,7,8] => [[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,5,2,6,3,7,8,4] => [1,5,6,8,2,3,7,4] => [[1,2,3,4],[5,6,7],[8]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2,6,3,7,4,8] => [1,5,6,7,2,3,4,8] => [[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,5,2,6,7,3,8,4] => [1,5,7,8,2,6,3,4] => [[1,2,3,4],[5,6,8],[7]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,7,8,3,4] => [1,5,4,8,2,6,7,3] => [[1,2,3,7],[4,6],[5,8]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,2,6,7,3,4,8] => [1,5,4,7,2,6,3,8] => [[1,2,3,8],[4,6],[5,7]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,3,8,4,7] => [1,5,6,7,2,3,8,4] => [[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,2,6,8,3,4,7] => [1,5,4,7,2,6,8,3] => [[1,2,3,8],[4,6],[5,7]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,2,6,3,4,7,8] => [1,5,4,6,2,3,7,8] => [[1,2,3,7,8],[4,6],[5]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,5,6,2,3,7,8,4] => [1,3,6,8,5,2,7,4] => [[1,2,4,7],[3,5],[6,8]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,5,6,2,3,7,4,8] => [1,3,6,7,5,2,4,8] => [[1,2,4,7,8],[3,5],[6]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,5,6,2,7,3,8,4] => [1,6,7,8,5,2,3,4] => [[1,2,3,4],[5,7,8],[6]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,5,6,2,7,8,3,4] => [1,6,4,8,5,2,7,3] => [[1,2,3,7],[4,5],[6,8]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,5,6,2,7,3,4,8] => [1,6,4,7,5,2,3,8] => [[1,2,3,8],[4,5],[6,7]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,5,6,7,2,3,8,4] => [1,3,7,8,5,6,2,4] => [[1,2,4,6],[3,5],[7,8]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,6,7,2,8,3,4] => [1,7,4,8,5,6,2,3] => [[1,2,3,6],[4,5],[7,8]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,6,7,8,2,3,4] => [1,3,4,8,5,6,7,2] => [[1,2,4,5,6,7],[3],[8]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,6,2,3,8,4,7] => [1,3,6,7,5,2,8,4] => [[1,2,4,7,8],[3,5],[6]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,7,8,6] => [1,3,4,5,2,8,7,6] => [[1,2,4,5,6],[3,7],[8]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => [1,3,4,5,2,7,6,8] => [[1,2,4,5,6,8],[3,7]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,7,4,8,6] => [1,3,5,7,2,8,4,6] => [[1,2,4,6,8],[3,5,7]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6,8] => [1,3,5,6,2,7,4,8] => [[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,5,2,7,3,4,8,6] => [1,5,4,7,2,8,3,6] => [[1,2,3,6],[4,7,8],[5]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,7,3,8,4,6] => [1,5,7,6,2,8,3,4] => [[1,2,3,4],[5,6,8],[7]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6,8] => [1,5,4,6,2,7,3,8] => [[1,2,3,7,8],[4,6],[5]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,5,7,2,3,4,8,6] => [1,3,4,7,5,8,2,6] => [[1,2,4,5,6],[3,8],[7]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,7,2,3,8,4,6] => [1,3,7,6,5,8,2,4] => [[1,2,4,8],[3,5],[6],[7]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [1,7,4,6,5,8,2,3] => [[1,2,3,8],[4,5],[6],[7]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [1,3,4,5,2,7,8,6] => [[1,2,4,5,6,8],[3,7]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => [1,5,4,6,2,7,8,3] => [[1,2,3,7,8],[4,6],[5]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [1,3,4,6,5,7,8,2] => [[1,2,4,5,7,8],[3],[6]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8] => [1,3,4,5,2,6,7,8] => [[1,2,4,5,6,7,8],[3]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,4] => [2,3,5,8,1,6,7,4] => [[1,3,4,6,7],[2,5],[8]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,6,4,7,8] => [2,3,5,6,1,4,7,8] => [[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,2,6,3,7,8,4] => [2,5,6,8,1,3,7,4] => [[1,3,4,7],[2,5,6],[8]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,7,3,8,4] => [2,5,7,8,1,6,3,4] => [[1,3,4,8],[2,5,6],[7]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,1,2,6,3,8,4,7] => [2,5,6,7,1,3,8,4] => [[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,2,6,3,4,7,8] => [2,5,4,6,1,3,7,8] => [[1,3,6,7,8],[2,4],[5]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => [5,3,6,8,1,2,7,4] => [[1,2,4],[3,6,7],[5,8]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,6,2,7,3,8,4] => [5,6,7,8,1,2,3,4] => [[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [5,1,6,2,7,8,3,4] => [5,6,4,8,1,2,7,3] => [[1,2,3],[4,6,7],[5,8]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,6,7,2,3,8,4] => [5,3,7,8,1,6,2,4] => [[1,2,4],[3,6,8],[5,7]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [5,1,6,7,2,8,3,4] => [5,7,4,8,1,6,2,3] => [[1,2,3],[4,6,8],[5,7]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,1,6,7,8,2,3,4] => [5,3,4,8,1,6,7,2] => [[1,2,6,7],[3,4],[5,8]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [5,1,6,2,3,8,4,7] => [5,3,6,7,1,2,8,4] => [[1,2,4,8],[3,6,7],[5]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,1,6,2,8,3,4,7] => [5,6,4,7,1,2,8,3] => [[1,2,3,8],[4,6,7],[5]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,6,1,2,3,7,8,4] => [2,3,6,8,5,1,7,4] => [[1,3,4,7],[2,5],[6,8]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1,2,7,3,8,4] => [2,6,7,8,5,1,3,4] => [[1,3,4,8],[2,5,7],[6]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [5,6,1,2,7,8,3,4] => [2,6,4,8,5,1,7,3] => [[1,3,5,7],[2,4],[6,8]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,6,1,7,2,3,8,4] => [6,3,7,8,5,1,2,4] => [[1,2,4],[3,5,8],[6,7]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [5,6,1,7,2,8,3,4] => [6,7,4,8,5,1,2,3] => [[1,2,3],[4,5,8],[6,7]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,6,1,7,8,2,3,4] => [6,3,4,8,5,1,7,2] => [[1,2,5,7],[3,4],[6,8]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,6,7,1,2,3,8,4] => [2,3,7,8,5,6,1,4] => [[1,3,4,6],[2,5],[7,8]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [5,6,7,1,2,8,3,4] => [2,7,4,8,5,6,1,3] => [[1,3,5,6],[2,4],[7,8]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [7,3,4,8,5,6,1,2] => [[1,2,5,6],[3,4],[7,8]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [2,3,4,8,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => [2,3,4,7,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [5,6,1,2,3,8,4,7] => [2,3,6,7,5,1,8,4] => [[1,3,4,7,8],[2,5],[6]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => [2,3,4,7,5,6,8,1] => [[1,3,4,5,6,8],[2],[7]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,6,1,2,3,4,7,8] => [2,3,4,6,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,7,8,6] => [2,3,4,5,1,8,7,6] => [[1,3,4,5,6],[2,7],[8]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6,8] => [2,3,4,5,1,7,6,8] => [[1,3,4,5,6,8],[2,7]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,7,3,4,8,6] => [2,5,4,7,1,8,3,6] => [[1,3,6,8],[2,4,7],[5]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6,8] => [2,5,4,6,1,7,3,8] => [[1,3,6,7,8],[2,4],[5]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => [5,7,4,6,1,8,2,3] => [[1,2,3],[4,6,8],[5,7]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,7,1,2,3,4,8,6] => [2,3,4,7,5,8,1,6] => [[1,3,4,5,6],[2,8],[7]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [5,7,1,2,3,8,4,6] => [2,3,7,6,5,8,1,4] => [[1,3,4,8],[2,5],[6],[7]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,7,1,2,8,3,4,6] => [2,7,4,6,5,8,1,3] => [[1,3,5,8],[2,4],[6],[7]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [2,3,4,6,5,8,7,1] => [[1,3,4,5,7],[2,8],[6]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6,8] => [2,3,4,6,5,7,1,8] => [[1,3,4,5,7,8],[2],[6]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [2,3,4,5,1,6,8,7] => [[1,3,4,5,6,7],[2,8]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,1,2,3,4,8,6,7] => [2,3,4,5,1,7,8,6] => [[1,3,4,5,6,8],[2,7]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,8,4,6,7] => [2,3,5,6,1,7,8,4] => [[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,1,2,8,3,4,6,7] => [2,5,4,6,1,7,8,3] => [[1,3,6,7,8],[2,4],[5]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [2,3,4,6,5,7,8,1] => [[1,3,4,5,7,8],[2],[6]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => [2,3,4,5,1,6,7,8] => [[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => [[1,2,3,4,5,7],[6],[8]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,6,5,8] => [[1,2,3,4,5,8],[6],[7]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [[1,2,3,4,5,7],[6,8]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,6,8,5,7] => [1,2,3,4,7,6,8,5] => [[1,2,3,4,5,8],[6],[7]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,6,4,7,8,5] => [1,2,3,6,8,4,7,5] => [[1,2,3,4,5],[6,7],[8]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,6,4,7,5,8] => [1,2,3,6,7,4,5,8] => [[1,2,3,4,5,8],[6,7]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,2,3,6,7,4,8,5] => [1,2,3,7,8,6,4,5] => [[1,2,3,4,5],[6,8],[7]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,2,3,6,7,8,4,5] => [1,2,3,5,8,6,7,4] => [[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,2,3,6,7,4,5,8] => [1,2,3,5,7,6,4,8] => [[1,2,3,4,6,8],[5],[7]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,2,3,6,4,5,8,7] => [1,2,3,5,6,4,8,7] => [[1,2,3,4,6,7],[5,8]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,2,3,6,4,8,5,7] => [1,2,3,6,7,4,8,5] => [[1,2,3,4,5,8],[6,7]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,2,3,6,8,4,5,7] => [1,2,3,5,7,6,8,4] => [[1,2,3,4,6,8],[5],[7]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [1,2,3,5,6,4,7,8] => [[1,2,3,4,6,7,8],[5]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,2,6,3,4,7,8,5] => [1,2,4,6,8,3,7,5] => [[1,2,3,5,7],[4,6],[8]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,2,6,3,7,4,8,5] => [1,2,6,7,8,3,4,5] => [[1,2,3,4,5],[6,7,8]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,2,6,3,7,8,4,5] => [1,2,6,5,8,3,7,4] => [[1,2,3,4],[5,7],[6,8]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,2,6,7,3,4,8,5] => [1,2,4,7,8,6,3,5] => [[1,2,3,5,8],[4,6],[7]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,7,8,3,4,5] => [1,2,4,5,8,6,7,3] => [[1,2,3,5,6,7],[4],[8]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,8,7] => [1,2,4,5,6,3,8,7] => [[1,2,3,5,6,7],[4,8]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => [1,2,6,5,7,3,8,4] => [[1,2,3,4,8],[5,7],[6]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,3,4,5,7,8] => [1,2,4,5,6,3,7,8] => [[1,2,3,5,6,7,8],[4]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => [1,3,4,6,7,2,5,8] => [[1,2,4,5,7,8],[3,6]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,6,2,3,7,4,8,5] => [1,3,6,7,8,2,4,5] => [[1,2,4,5,8],[3,6,7]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,2,3,7,4,5,8] => [1,3,6,5,7,2,4,8] => [[1,2,4,7,8],[3,5],[6]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,6,2,7,3,4,8,5] => [1,6,4,7,8,2,3,5] => [[1,2,3,5],[4,7,8],[6]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,7,3,8,4,5] => [1,6,7,5,8,2,3,4] => [[1,2,3,4],[5,7,8],[6]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,6,2,7,3,4,5,8] => [1,6,4,5,7,2,3,8] => [[1,2,3,7,8],[4,5],[6]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,7,2,3,8,4,5] => [1,3,7,5,8,6,2,4] => [[1,2,4,6],[3,5],[7,8]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [1,3,4,5,8,6,7,2] => [[1,2,4,5,6,7],[3],[8]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,6,7,2,3,4,5,8] => [1,3,4,5,7,6,2,8] => [[1,2,4,5,6,8],[3],[7]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,8,7] => [1,3,4,5,6,2,8,7] => [[1,2,4,5,6,7],[3,8]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [1,3,4,6,7,2,8,5] => [[1,2,4,5,7,8],[3,6]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,6,2,8,3,4,5,7] => [1,6,4,5,7,2,8,3] => [[1,2,3,7,8],[4,5],[6]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [1,3,4,5,7,6,8,2] => [[1,2,4,5,6,8],[3],[7]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,6,2,3,4,5,7,8] => [1,3,4,5,6,2,7,8] => [[1,2,4,5,6,7,8],[3]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => [2,3,4,6,8,1,7,5] => [[1,3,4,5,7],[2,6],[8]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,7,5,8] => [2,3,4,6,7,1,5,8] => [[1,3,4,5,7,8],[2,6]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,3,7,4,8,5] => [2,3,6,7,8,1,4,5] => [[1,3,4,5,8],[2,6,7]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,1,2,7,3,8,4,5] => [2,6,7,5,8,1,3,4] => [[1,3,4,8],[2,5,7],[6]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [6,1,2,7,3,4,5,8] => [2,6,4,5,7,1,3,8] => [[1,3,5,7,8],[2,4],[6]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,1,7,2,8,3,4,5] => [6,7,4,5,8,1,2,3] => [[1,2,3],[4,5,8],[6,7]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [6,1,7,8,2,3,4,5] => [6,3,4,5,8,1,7,2] => [[1,2,5,7],[3,4],[6,8]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [6,1,7,2,3,4,5,8] => [6,3,4,5,7,1,2,8] => [[1,2,5,7,8],[3,4],[6]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => [2,3,4,7,8,6,1,5] => [[1,3,4,5,8],[2,6],[7]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,7,1,2,3,8,4,5] => [2,3,7,5,8,6,1,4] => [[1,3,4,6],[2,5],[7,8]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [6,7,1,8,2,3,4,5] => [7,3,4,5,8,6,1,2] => [[1,2,5,6],[3,4],[7,8]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [2,3,4,5,8,6,7,1] => [[1,3,4,5,6,7],[2],[8]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5,8] => [2,3,4,5,7,6,1,8] => [[1,3,4,5,6,8],[2],[7]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [2,3,4,5,6,1,8,7] => [[1,3,4,5,6,7],[2,8]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [6,1,2,8,3,4,5,7] => [2,6,4,5,7,1,8,3] => [[1,3,5,7,8],[2,4],[6]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [6,3,4,5,7,1,8,2] => [[1,2,5,7,8],[3,4],[6]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [2,3,4,5,7,6,8,1] => [[1,3,4,5,6,8],[2],[7]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => [2,3,4,5,6,1,7,8] => [[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => [[1,2,3,4,5,6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [[1,2,3,4,5,6,8],[7]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => [1,2,3,4,7,8,5,6] => [[1,2,3,4,5,6],[7,8]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,7,8,5,6] => [1,2,3,4,6,8,7,5] => [[1,2,3,4,5,7],[6],[8]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,7,5,6,8] => [1,2,3,4,6,7,5,8] => [[1,2,3,4,5,7,8],[6]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => [1,2,3,5,7,8,4,6] => [[1,2,3,4,6,8],[5,7]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => [1,2,3,7,6,8,4,5] => [[1,2,3,4,5],[6,8],[7]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,3,7,8,4,5,6] => [1,2,3,5,6,8,7,4] => [[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [1,2,3,5,6,7,4,8] => [[1,2,3,4,6,7,8],[5]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => [1,2,4,5,7,8,3,6] => [[1,2,3,5,6,8],[4,7]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [1,2,7,5,6,8,3,4] => [[1,2,3,4,8],[5,6],[7]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [1,2,4,5,6,8,7,3] => [[1,2,3,5,6,7],[4],[8]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6,8] => [1,2,4,5,6,7,3,8] => [[1,2,3,5,6,7,8],[4]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => [1,3,4,5,7,8,2,6] => [[1,2,4,5,6,8],[3,7]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [1,3,4,7,6,8,2,5] => [[1,2,4,5,8],[3,6],[7]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,7,2,3,8,4,5,6] => [1,3,7,5,6,8,2,4] => [[1,2,4,6,8],[3,5],[7]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,7,2,8,3,4,5,6] => [1,7,4,5,6,8,2,3] => [[1,2,3,6,8],[4,5],[7]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [1,3,4,5,6,8,7,2] => [[1,2,4,5,6,7],[3],[8]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8] => [1,3,4,5,6,7,2,8] => [[1,2,4,5,6,7,8],[3]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [2,3,4,5,7,8,1,6] => [[1,3,4,5,6,8],[2,7]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => [2,3,4,7,6,8,1,5] => [[1,3,4,5,8],[2,6],[7]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,1,2,3,8,4,5,6] => [2,3,7,5,6,8,1,4] => [[1,3,4,6,8],[2,5],[7]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [7,1,2,8,3,4,5,6] => [2,7,4,5,6,8,1,3] => [[1,3,5,6,8],[2,4],[7]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [7,3,4,5,6,8,1,2] => [[1,2,5,6,8],[3,4],[7]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [2,3,4,5,6,8,7,1] => [[1,3,4,5,6,7],[2],[8]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => [2,3,4,5,6,7,1,8] => [[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,8],[7]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,3,4,8,5,6,7] => [1,2,3,4,6,7,8,5] => [[1,2,3,4,5,7,8],[6]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => [[1,2,3,4,6,7,8],[5]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [1,2,4,5,6,7,8,3] => [[1,2,3,5,6,7,8],[4]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [1,3,4,5,6,7,8,2] => [[1,2,4,5,6,7,8],[3]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [[1,2,3,4,5,6,7,8],[9]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [[1,2,3,4,5,6,7,8,9],[10]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [2,3,4,5,6,8,9,1,7] => [[1,3,4,5,6,7,9],[2,8]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => [3,2,4,5,6,7,8,9,1] => [[1,4,5,6,7,8,9],[2],[3]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [[1,2,3,4,5,6,7,8,9,10],[11]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => [2,3,4,5,6,7,9,10,1,8] => [[1,3,4,5,6,7,8,10],[2,9]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => [1,3,4,5,6,8,9,2,7] => [[1,2,4,5,6,7,9],[3,8]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => [2,3,4,5,6,7,1,9,8] => [[1,3,4,5,6,7,8],[2,9]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => [2,1,4,5,6,7,8,9,3] => [[1,3,5,6,7,8,9],[2,4]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7,9] => [3,2,4,5,6,7,8,1,9] => [[1,4,5,6,7,8,9],[2],[3]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => [3,2,4,5,6,7,8,9,10,1] => [[1,4,5,6,7,8,9,10],[2],[3]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,11,9] => [2,3,4,5,6,7,8,10,11,1,9] => [[1,3,4,5,6,7,8,9,11],[2,10]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,10,9] => [2,3,4,5,6,7,8,1,10,9] => [[1,3,4,5,6,7,8,9],[2,10]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,1,10,3,4,5,6,7,8,9] => [2,1,4,5,6,7,8,9,10,3] => [[1,3,5,6,7,8,9,10],[2,4]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,11,1,3,4,5,6,7,8,9,10] => [3,2,4,5,6,7,8,9,10,11,1] => [[1,4,5,6,7,8,9,10,11],[2],[3]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,11,10] => [2,3,4,5,6,7,8,9,1,11,10] => [[1,3,4,5,6,7,8,9,10],[2,11]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,9,8] => [1,3,4,5,6,7,2,9,8] => [[1,2,4,5,6,7,8],[3,9]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7,9] => [2,1,4,5,6,7,8,3,9] => [[1,3,5,6,7,8,9],[2,4]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,9,10,1,3,4,5,6,7,8] => [3,2,4,5,6,7,8,10,9,1] => [[1,4,5,6,7,8,9],[2,10],[3]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,8,6,9,7] => [1,2,3,4,5,8,9,6,7] => [[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,9,8] => [2,3,1,4,5,6,7,9,8] => [[1,3,4,5,6,7,8],[2,9]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [[1,2,3,4,5,6,7,9],[8]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,9,7,8] => [2,1,3,4,5,6,8,9,7] => [[1,3,4,5,6,7,9],[2,8]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => [[1,2,3,4,5,6,7],[8],[9]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [7,1,2,3,4,8,5,9,6] => [2,3,4,7,8,9,1,5,6] => [[1,3,4,5,6,9],[2,7,8]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => [[1,3,4,5,6,7,8],[2,9]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,9,2,4,5,6,7,8] => [1,4,3,5,6,7,8,9,2] => [[1,2,5,6,7,8,9],[3],[4]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,5,6,9,7,10,8] => [1,2,3,4,5,6,9,10,7,8] => [[1,2,3,4,5,6,7,8],[9,10]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [[1,2,3,4,5,6,7,8,10],[9]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,8,9,6] => [2,3,4,5,7,9,1,8,6] => [[1,3,4,5,6,8],[2,7],[9]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,7,10,8,9] => [2,1,3,4,5,6,7,9,10,8] => [[1,3,4,5,6,7,8,10],[2,9]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7,9] => [2,3,4,5,6,1,8,7,9] => [[1,3,4,5,6,7,9],[2,8]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,9,1,4,5,6,7,8] => [4,2,3,5,6,7,8,9,1] => [[1,3,5,6,7,8,9],[2],[4]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8,9,10] => [3,2,4,1,5,6,7,8,9,10] => [[1,4,5,6,7,8,9,10],[2],[3]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,9,8] => [[1,2,3,4,5,6,7,8],[9],[10]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1,2,3,4,5,9,6,10,7] => [2,3,4,5,8,9,10,1,6,7] => [[1,3,4,5,6,7,10],[2,8,9]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => [[1,3,4,5,6,7,8,9],[2,10]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,8,9,7] => [2,3,4,5,6,1,9,8,7] => [[1,3,4,5,6,7],[2,8],[9]]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,3,1,9,4,5,6,7,8] => [3,2,1,5,6,7,8,9,4] => [[1,4,6,7,8,9],[2,5],[3]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [[1,4,5,6,7,8,9,10],[2],[3]]
[] => [] => [] => []
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,1,2] => [2,9,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2],[9]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,8,1,2,9] => [2,8,3,4,5,6,7,1,9] => [[1,3,4,5,6,7,9],[2],[8]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9] => [[1,3,5,6,7,8,9],[2],[4]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [3,1,2,4,5,6,9,7,8] => [2,3,1,4,5,6,8,9,7] => [[1,3,4,5,6,7,9],[2,8]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3,1,2,9,4,5,6,7,8] => [2,3,1,5,6,7,8,9,4] => [[1,3,4,6,7,8,9],[2,5]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,9,2,4,5,6,7,8] => [3,4,1,5,6,7,8,9,2] => [[1,2,5,6,7,8,9],[3,4]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,9,1,2,4,5,6,7,8] => [2,4,3,5,6,7,8,9,1] => [[1,3,5,6,7,8,9],[2],[4]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,8,9,2,3] => [1,3,9,4,5,6,7,8,2] => [[1,2,4,5,6,7,8],[3],[9]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,1,2,3] => [2,3,9,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2],[9]]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => [2,3,6,4,5,1,7,8,9] => [[1,3,4,5,7,8,9],[2],[6]]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8,9] => [2,3,5,4,1,6,7,8,9] => [[1,3,4,6,7,8,9],[2],[5]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,1,2,3,9,5,6,7,8] => [2,3,4,1,6,7,8,9,5] => [[1,3,4,5,7,8,9],[2,6]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8,9] => [1,3,4,5,2,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [2,3,4,9,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2],[9]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [2,3,4,8,5,6,7,1,9] => [[1,3,4,5,6,7,9],[2],[8]]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,6,1,2,3,4,7,8,9] => [2,3,4,6,5,1,7,8,9] => [[1,3,4,5,7,8,9],[2],[6]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5,1,2,3,4,9,6,7,8] => [2,3,4,5,1,7,8,9,6] => [[1,3,4,5,6,8,9],[2,7]]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [5,9,1,2,3,4,6,7,8] => [2,3,4,6,5,7,8,9,1] => [[1,3,4,5,7,8,9],[2],[6]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]]
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,6,3,4,5,7,8,9] => [1,2,4,5,6,3,7,8,9] => [[1,2,3,5,6,7,8,9],[4]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [2,3,4,5,9,6,7,8,1] => [[1,3,4,5,6,7,8],[2],[9]]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [6,7,9,1,2,3,4,5,8] => [2,3,4,5,8,6,7,9,1] => [[1,3,4,5,6,7,9],[2],[8]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7,9] => [2,3,4,5,7,6,8,1,9] => [[1,3,4,5,6,8,9],[2],[7]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,9,7,8] => [2,3,4,5,6,1,8,9,7] => [[1,3,4,5,6,7,9],[2,8]]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [6,9,1,2,3,4,5,7,8] => [2,3,4,5,7,6,8,9,1] => [[1,3,4,5,6,8,9],[2],[7]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [2,3,4,5,6,1,7,8,9] => [[1,3,4,5,6,7,8,9],[2]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,7,9,2,3,4,5,6,8] => [1,3,4,5,6,8,7,9,2] => [[1,2,4,5,6,7,9],[3],[8]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8,9] => [1,3,4,5,6,7,2,8,9] => [[1,2,4,5,6,7,8,9],[3]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [7,1,8,2,3,4,5,6,9] => [7,3,4,5,6,8,1,2,9] => [[1,2,5,6,8,9],[3,4],[7]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => [2,3,4,5,6,9,7,8,1] => [[1,3,4,5,6,7,8],[2],[9]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6,9] => [2,3,4,5,6,8,7,1,9] => [[1,3,4,5,6,7,9],[2],[8]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,9,6,8] => [2,3,4,5,7,8,1,9,6] => [[1,3,4,5,6,8,9],[2,7]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [7,9,1,2,3,4,5,6,8] => [2,3,4,5,6,8,7,9,1] => [[1,3,4,5,6,7,9],[2],[8]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9] => [2,3,4,5,6,7,1,8,9] => [[1,3,4,5,6,7,8,9],[2]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,5,8,9,6,7] => [1,2,3,4,5,7,9,8,6] => [[1,2,3,4,5,6,8],[7],[9]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,5,8,6,7,9] => [1,2,3,4,5,7,8,6,9] => [[1,2,3,4,5,6,8,9],[7]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [1,2,3,4,8,9,5,6,7] => [1,2,3,4,6,7,9,8,5] => [[1,2,3,4,5,7,8],[6],[9]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7,9] => [1,2,3,5,6,7,8,4,9] => [[1,2,3,4,6,7,8,9],[5]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,8,2,9,3,4,5,6,7] => [1,8,4,5,6,7,9,2,3] => [[1,2,3,6,7,9],[4,5],[8]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7] => [1,3,4,5,6,7,9,8,2] => [[1,2,4,5,6,7,8],[3],[9]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7,9] => [1,3,4,5,6,7,8,2,9] => [[1,2,4,5,6,7,8,9],[3]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [8,1,2,3,9,4,5,6,7] => [2,3,8,5,6,7,9,1,4] => [[1,3,4,6,7,9],[2,5],[8]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => [2,3,4,5,6,7,9,8,1] => [[1,3,4,5,6,7,8],[2],[9]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9] => [2,3,4,5,6,7,8,1,9] => [[1,3,4,5,6,7,8,9],[2]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,8,9,7] => [[1,2,3,4,5,6,7,9],[8]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,9,6,7,8] => [1,2,3,4,5,7,8,9,6] => [[1,2,3,4,5,6,8,9],[7]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [1,2,3,4,6,7,8,9,5] => [[1,2,3,4,5,7,8,9],[6]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [1,2,3,5,6,7,8,9,4] => [[1,2,3,4,6,7,8,9],[5]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,9,3,4,5,6,7,8] => [1,2,4,5,6,7,8,9,3] => [[1,2,3,5,6,7,8,9],[4]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => [1,3,4,5,6,7,8,9,2] => [[1,2,4,5,6,7,8,9],[3]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9] => [[1,3,4,5,6,7,9],[2],[8]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,9,1,8] => [8,2,3,4,5,6,7,9,1] => [[1,3,4,5,6,7,9],[2],[8]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,8,9,1,7] => [7,2,3,4,5,6,9,8,1] => [[1,3,4,5,6,8],[2,9],[7]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,7,8,9,1,6] => [6,2,3,4,5,9,7,8,1] => [[1,3,4,5,7,8],[2,9],[6]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,9,1,5] => [5,2,3,4,9,6,7,8,1] => [[1,3,4,6,7,8],[2,9],[5]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,9,1,4] => [4,2,3,9,5,6,7,8,1] => [[1,3,5,6,7,8],[2,9],[4]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,9,1,3] => [3,2,9,4,5,6,7,8,1] => [[1,4,5,6,7,8],[2,9],[3]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10] => [[1,3,4,5,6,7,8,10],[2],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9] => [[1,3,4,5,6,8,9],[2],[7]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,10,1,9] => [9,2,3,4,5,6,7,8,10,1] => [[1,3,4,5,6,7,8,10],[2],[9]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,6,1,9,7,8] => [6,2,3,4,5,1,8,9,7] => [[1,3,4,5,7,9],[2,8],[6]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,7,9,10,1,8] => [8,2,3,4,5,6,7,10,9,1] => [[1,3,4,5,6,7,9],[2,10],[8]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,5,1,8,9,6,7] => [5,2,3,4,1,7,9,8,6] => [[1,3,4,6,8],[2,7],[5,9]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,8,9,10,1,7] => [7,2,3,4,5,6,10,8,9,1] => [[1,3,4,5,6,8,9],[2,10],[7]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,1,7,8,9,5,6] => [4,2,3,1,6,9,7,8,5] => [[1,3,5,7,8],[2,6],[4,9]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,7,8,9,10,1,6] => [6,2,3,4,5,10,7,8,9,1] => [[1,3,4,5,7,8,9],[2,10],[6]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,7,8,9,4,5] => [3,2,1,5,9,6,7,8,4] => [[1,4,6,7,8],[2,5],[3,9]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,9,10,1,5] => [5,2,3,4,10,6,7,8,9,1] => [[1,3,4,6,7,8,9],[2,10],[5]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,9,3,4] => [2,1,4,9,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4],[9]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,9,10,1,4] => [4,2,3,10,5,6,7,8,9,1] => [[1,3,5,6,7,8,9],[2,10],[4]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,8,9,10,1,3] => [3,2,10,4,5,6,7,8,9,1] => [[1,4,5,6,7,8,9],[2,10],[3]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,9,10,1,2] => [2,10,3,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9,10],[2],[11]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,9,11,1,10] => [10,2,3,4,5,6,7,8,9,11,1] => [[1,3,4,5,6,7,8,9,11],[2],[10]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => [[1,3,4,5,7,8,9],[2],[6]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [[1,3,4,6,7,8,9],[2],[5]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [[1,3,5,6,7,8,9],[2],[4]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,10,1,6,7,8,9] => [6,2,3,4,5,7,8,9,10,1] => [[1,3,4,5,7,8,9,10],[2],[6]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,5,6,1,2,3,9,10,7,8] => [2,3,6,4,5,1,8,10,9,7] => [[1,3,4,5,7,9],[2,8],[6,10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8] => [7,2,3,4,5,6,1,9,8] => [[1,3,4,5,6,8],[2,9],[7]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8] => [3,2,1,5,4,7,6,9,8] => [[1,4,6,8],[2,5,7,9],[3]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,4,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4],[9]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [[1,3,5,7,9],[2,4,6,8]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [[1,3,5,6,7,8,9],[2,4]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => [[1,3,4,5,6,7,9],[2,8]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,2] => [1,9,3,4,5,6,7,8,2] => [[1,2,4,5,6,7,8],[3],[9]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3],[4]]
[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] => [1,3,2,5,4,7,6,9,8] => [[1,2,4,6,8],[3,5,7,9]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => [[1,2,4,6,7,8,9],[3,5]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,3,2,4,5,6,8,9,7] => [1,3,2,4,5,6,9,8,7] => [[1,2,4,5,6,7],[3,8],[9]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => [[1,2,4,5,6,7,8],[3,9]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,4,5,6,7,8,3] => [[1,2,3,5,6,7,8],[4],[9]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => [[1,2,3,5,7,9],[4,6,8]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [[1,2,3,5,6,7,8,9],[4]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,5,6,7,8,4] => [[1,2,3,4,6,7,8],[5],[9]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => [[1,2,3,4,6,8],[5,7,9]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [[1,2,3,4,6,7,8,9],[5]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,6,7,8,5] => [[1,2,3,4,5,7,8],[6],[9]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [[1,2,3,4,5,7,8,9],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,7,8,6] => [[1,2,3,4,5,6,8],[7],[9]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => [[1,2,3,4,5,6,8],[7,9]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => [[1,2,3,4,5,6,8,9],[7]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,1,5,4,7,6,9,8,10] => [[1,4,6,8,10],[2,5,7,9],[3]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,3,4,5,6,7,8,9,2] => [[1,2,4,5,6,7,8,9],[3],[10]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,4,5,6,7,8,9,3] => [[1,2,3,5,6,7,8,9],[4],[10]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,5,6,7,8,9,4] => [[1,2,3,4,6,7,8,9],[5],[10]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,6,7,8,9,5] => [[1,2,3,4,5,7,8,9],[6],[10]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,7,8,9,6] => [[1,2,3,4,5,6,8,9],[7],[10]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,8,9,7] => [[1,2,3,4,5,6,7,9],[8],[10]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [[1,2,3,4,5,6,7,9,10],[8]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,2] => [3,9,1,4,5,6,7,8,2] => [[1,2,5,6,7,8],[3,4],[9]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,6,1,7,8,9,2] => [6,9,3,4,5,1,7,8,2] => [[1,2,5,7,8],[3,4],[6,9]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,1,8,9,2] => [7,9,3,4,5,6,1,8,2] => [[1,2,5,6,8],[3,4],[7,9]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,1,9,2] => [8,9,3,4,5,6,7,1,2] => [[1,2,5,6,7],[3,4],[8,9]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => [3,10,1,4,5,6,7,8,9,2] => [[1,2,5,6,7,8,9],[3,4],[10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,7,8,1,9,10,2] => [8,10,3,4,5,6,7,1,9,2] => [[1,2,5,6,7,9],[3,4],[8,10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,1,10,2] => [9,10,3,4,5,6,7,8,1,2] => [[1,2,5,6,7,8],[3,4],[9,10]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,7,9,2,8] => [1,8,3,4,5,6,7,9,2] => [[1,2,4,5,6,7,9],[3],[8]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8,10] => [2,3,4,5,6,7,8,9,1,10] => [[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,10,2] => [[1,2,4,5,6,7,8,9,10],[3]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [2,3,4,5,6,7,8,9,10,1,11] => [[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [2,3,4,5,6,7,9,8,1,10] => [[1,3,4,5,6,7,8,10],[2],[9]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [1,3,4,5,6,7,8,10,9,2] => [[1,2,4,5,6,7,8,9],[3],[10]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => [1,3,4,5,6,7,8,9,10,11,2] => [[1,2,4,5,6,7,8,9,10,11],[3]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,8,2,9] => [3,8,1,4,5,6,7,2,9] => [[1,2,5,6,7,9],[3,4],[8]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,10,8,9] => [1,2,3,4,5,6,7,9,10,8] => [[1,2,3,4,5,6,7,8,10],[9]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => [1,2,3,4,5,6,7,8,10,11,9] => [[1,2,3,4,5,6,7,8,9,11],[10]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,4,7,5,8,9,6] => [1,2,3,4,7,9,5,8,6] => [[1,2,3,4,5,6],[7,8],[9]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,3,6,4,7,8,9,5] => [1,2,3,6,9,4,7,8,5] => [[1,2,3,4,5,8],[6,7],[9]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,9,4] => [1,2,5,9,3,6,7,8,4] => [[1,2,3,4,7,8],[5,6],[9]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,9,3] => [1,4,9,2,5,6,7,8,3] => [[1,2,3,6,7,8],[4,5],[9]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [2,3,4,5,6,7,8,1,9,10] => [[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => [2,3,4,5,6,7,8,9,10,11,1] => [[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,2,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3,4]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => [3,2,4,5,6,10,7,8,9,1] => [[1,4,5,6,7,8,9],[2,10],[3]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,1,4,8,9,2,5,6,7] => [3,5,1,4,6,7,9,8,2] => [[1,2,6,7,8],[3,4,9],[5]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [2,3,4,10,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2],[10]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,7,6,8,9] => [2,3,4,5,1,7,6,8,9] => [[1,3,4,5,6,8,9],[2,7]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => [1,2,3,6,5,7,8,9,4] => [[1,2,3,4,7,8,9],[5],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,5,7,9,6,8] => [1,2,3,4,5,8,7,9,6] => [[1,2,3,4,5,6,9],[7],[8]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [1,2,3,4,5,6,8,9,10,7] => [[1,2,3,4,5,6,7,9,10],[8]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,4,6,9,5,7,8] => [1,2,3,4,7,6,8,9,5] => [[1,2,3,4,5,8,9],[6],[7]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [1,2,3,4,5,7,8,9,10,6] => [[1,2,3,4,5,6,8,9,10],[7]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [1,2,3,4,6,7,8,9,10,5] => [[1,2,3,4,5,7,8,9,10],[6]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,4,9,3,5,6,7,8] => [1,2,5,4,6,7,8,9,3] => [[1,2,3,6,7,8,9],[4],[5]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [1,2,3,5,6,7,8,9,10,4] => [[1,2,3,4,6,7,8,9,10],[5]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [1,2,4,5,6,7,8,9,10,3] => [[1,2,3,5,6,7,8,9,10],[4]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [1,2,3,4,7,5,8,6,9] => [1,2,3,4,7,8,5,6,9] => [[1,2,3,4,5,6,9],[7,8]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => [2,3,1,5,4,7,6,9,8] => [[1,3,4,6,8],[2,5,7,9]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,2,4,7,6,9,8] => [3,4,1,5,2,7,6,9,8] => [[1,2,5,6,8],[3,4,7,9]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7,9] => [3,5,1,6,2,4,8,7,9] => [[1,2,4,7,9],[3,5,6,8]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7,9] => [3,4,1,2,6,5,8,7,9] => [[1,2,5,7,9],[3,4,6,8]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,9,8,10] => [2,3,1,5,4,7,6,9,8,10] => [[1,3,4,6,8,10],[2,5,7,9]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,7,4,9,6,10,8] => [3,5,1,7,2,9,4,10,6,8] => [[1,2,4,6,8],[3,5,7,9,10]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,8,6,10,9] => [3,5,1,7,2,8,4,6,10,9] => [[1,2,4,6,9],[3,5,7,8,10]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,6,4,8,7,10,9] => [3,5,1,6,2,4,8,7,10,9] => [[1,2,4,7,9],[3,5,6,8,10]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [3,4,1,2,6,5,8,7,10,9] => [[1,2,5,7,9],[3,4,6,8,10]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [2,4,3,1,5,6,7,8,9,10] => [[1,3,5,6,7,8,9,10],[2],[4]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [2,3,10,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2],[10]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8,10] => [1,3,4,5,6,7,8,9,2,10] => [[1,2,4,5,6,7,8,9,10],[3]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [1,2,3,8,4,5,6,7,9,10] => [1,2,3,5,6,7,8,4,9,10] => [[1,2,3,4,6,7,8,9,10],[5]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => [3,2,5,4,7,6,9,8,10,1] => [[1,4,6,8,10],[2,5,7,9],[3]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [6,7,8,9,10,1,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9,10]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,4,6,8,10,12,1,3,5,7,9,11] => [3,2,5,4,7,6,9,8,11,10,12,1] => [[1,4,6,8,10,12],[2,5,7,9,11],[3]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1,8,2,9,3,10,4,11,5,12,6] => [7,8,9,10,11,12,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [[1,2,3,4,5,6,7,8,9,10,11]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [2,3,1,4,5,6,7,8,9,10,11] => [[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,10,7,9] => [2,3,4,5,6,8,9,1,10,7] => [[1,3,4,5,6,7,9,10],[2,8]]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,10,2,4,5,6,7,8,9] => [3,4,1,5,6,7,8,9,10,2] => [[1,2,5,6,7,8,9,10],[3,4]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,11,2] => [3,11,1,4,5,6,7,8,9,10,2] => [[1,2,5,6,7,8,9,10],[3,4],[11]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => [[1,2,3,4,5,6,7,8,9,11],[10]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [2,3,4,5,10,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2],[10]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [9,1,10,2,3,4,5,6,7,8] => [9,3,4,5,6,7,8,10,1,2] => [[1,2,5,6,7,8,10],[3,4],[9]]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [3,7,8,9,10,1,2,4,5,6] => [2,4,3,5,6,10,7,8,9,1] => [[1,3,5,6,7,8,9],[2,10],[4]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,10,1,4,5,6,7,8,9] => [4,2,3,5,6,7,8,9,10,1] => [[1,3,5,6,7,8,9,10],[2],[4]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,2,3,4,7,8,9,5] => [2,3,4,6,9,1,7,8,5] => [[1,3,4,5,7,8],[2,6],[9]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,4,5,8,6,7,9,10] => [1,2,3,4,5,7,8,6,9,10] => [[1,2,3,4,5,6,8,9,10],[7]]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [5,10,1,2,3,4,6,7,8,9] => [2,3,4,6,5,7,8,9,10,1] => [[1,3,4,5,7,8,9,10],[2],[6]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,10,9,1] => [[1,3,4,5,6,7,8,9],[2],[10]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,11,10,1] => [[1,3,4,5,6,7,8,9,10],[2],[11]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,8,1,9,7] => [8,2,3,4,5,6,9,1,7] => [[1,3,4,5,6,7],[2,9],[8]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,7,9,1,10,8] => [9,2,3,4,5,6,7,10,1,8] => [[1,3,4,5,6,7,8],[2,10],[9]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [2,3,4,5,6,10,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2],[10]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [2,3,4,5,6,7,10,8,9,1] => [[1,3,4,5,6,7,8,9],[2],[10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,8,9,10,1,11,2] => [10,11,3,4,5,6,7,8,9,1,2] => [[1,2,5,6,7,8,9],[3,4],[10,11]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7,9] => [2,3,4,1,6,5,8,7,9] => [[1,3,4,5,7,9],[2,6,8]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,8,1,9,3] => [8,2,9,4,5,6,7,1,3] => [[1,3,5,6,7],[2,4],[8,9]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [2,3,4,8,5,6,7,1,9,10] => [[1,3,4,5,6,7,9,10],[2],[8]]
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [2,3,6,4,5,1,7,8,9,10] => [[1,3,4,5,7,8,9,10],[2],[6]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,5,6,9,7,8,10] => [1,2,3,4,5,6,8,9,7,10] => [[1,2,3,4,5,6,7,9,10],[8]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8,9,10] => [1,3,4,2,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3,1,2,10,4,5,6,7,8,9] => [2,3,1,5,6,7,8,9,10,4] => [[1,3,4,6,7,8,9,10],[2,5]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,10,6,7,8,9] => [2,3,4,5,1,7,8,9,10,6] => [[1,3,4,5,6,8,9,10],[2,7]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,7,8,9,10,1,2,3,4,6] => [2,3,4,6,5,10,7,8,9,1] => [[1,3,4,5,7,8,9],[2,10],[6]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,7,8,9,10,1,2,3,5,6] => [2,3,5,4,6,10,7,8,9,1] => [[1,3,4,6,7,8,9],[2,10],[5]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,10,1,11,9] => [10,2,3,4,5,6,7,8,11,1,9] => [[1,3,4,5,6,7,8,9],[2,11],[10]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,7,8,10,1,2,3,4,9] => [2,3,4,9,5,6,7,8,10,1] => [[1,3,4,5,6,7,8,10],[2],[9]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,10,9] => [[1,2,3,4,5,6,7,8,9],[10],[11]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,7,8,9,1,10,3] => [9,2,10,4,5,6,7,8,1,3] => [[1,3,5,6,7,8],[2,4],[9,10]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,9,8] => [1,4,5,2,3,7,6,9,8] => [[1,2,3,6,8],[4,5,7,9]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,3,6,5,8,7,9] => [1,3,4,2,6,5,8,7,9] => [[1,2,4,5,7,9],[3,6,8]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7,10,9] => [1,3,4,2,6,5,8,7,10,9] => [[1,2,4,5,7,9],[3,6,8,10]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7,9] => [3,2,4,1,6,5,8,7,9] => [[1,4,5,7,9],[2,6,8],[3]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [2,1,7,8,9,10,3,4,5,6] => [2,1,4,5,6,10,7,8,9,3] => [[1,3,5,6,7,8,9],[2,4],[10]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [3,4,1,2,8,9,10,5,6,7] => [2,4,3,1,6,7,10,8,9,5] => [[1,3,5,7,8,9],[2,6],[4,10]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,6,7,8,1,2,3,4,10,9] => [2,3,4,8,5,6,7,1,10,9] => [[1,3,4,5,6,7,9],[2,10],[8]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,2,3,4,5,6,9,10,7] => [2,3,4,5,6,8,10,1,9,7] => [[1,3,4,5,6,7,9],[2,8],[10]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,5,6,9,10,7,8] => [1,2,3,4,5,6,8,10,9,7] => [[1,2,3,4,5,6,7,9],[8],[10]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,7,6,10,8,9] => [1,3,2,5,4,7,6,9,10,8] => [[1,2,4,6,8,10],[3,5,7,9]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => [4,2,6,1,8,3,9,5,10,7] => [[1,3,5,7,10],[2,6,8,9],[4]]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,4,6,8,10,1,2,5,7,9] => [2,5,3,4,7,6,9,8,10,1] => [[1,3,4,6,8,10],[2,7,9],[5]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,7,6,9,8,12,10,11] => [1,3,2,5,4,7,6,9,8,11,12,10] => [[1,2,4,6,8,10,12],[3,5,7,9,11]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [1,12,2,3,4,5,6,7,8,9,10,11] => [1,3,4,5,6,7,8,9,10,11,12,2] => [[1,2,4,5,6,7,8,9,10,11,12],[3]]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [2,3,4,5,6,7,8,9,10,11,12,1] => [[1,3,4,5,6,7,8,9,10,11,12],[2]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => [4,2,5,1,3,7,6,9,8,10] => [[1,3,6,8,10],[2,5,7,9],[4]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [2,1,7,3,8,4,9,5,10,6] => [2,1,7,8,9,10,3,4,5,6] => [[1,3,4,5,6],[2,7,8,9,10]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,4,6,5,3,8,10,9,7,12,11] => [[1,3,5,7,9,11],[2,4,8,12],[6,10]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [2,1,8,3,9,4,10,5,11,6,12,7] => [2,1,8,9,10,11,12,3,4,5,6,7] => [[1,3,4,5,6,7],[2,8,9,10,11,12]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,8,5,7,9] => [4,2,6,1,7,3,8,5,9] => [[1,3,5,8,9],[2,6,7],[4]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7,10,9] => [2,1,5,6,3,4,8,7,10,9] => [[1,3,4,7,9],[2,5,6,8,10]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [3,1,4,2,9,5,10,6,11,7,12,8] => [3,4,1,2,9,10,11,12,5,6,7,8] => [[1,2,5,6,7,8],[3,4,9,10,11,12]]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,5,6,9,10,1,2,3,7,8] => [2,3,7,4,5,6,8,10,9,1] => [[1,3,4,5,6,8,9],[2,10],[7]]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,5,8,9,10,1,2,3,6,7] => [2,3,6,4,5,7,10,8,9,1] => [[1,3,4,5,7,8,9],[2,10],[6]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,1,6,3,5,8,7,9] => [4,2,5,1,6,3,8,7,9] => [[1,3,6,7,9],[2,5,8],[4]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6,9,8] => [4,2,5,1,3,7,6,9,8] => [[1,3,6,8],[2,5,7,9],[4]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,8,7,10,9] => [3,2,4,1,6,5,8,7,10,9] => [[1,4,5,7,9],[2,6,8,10],[3]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,8,3,9,5,10,7] => [4,6,8,1,9,2,10,3,5,7] => [[1,2,3,5,7],[4,6,8,9,10]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[1,3,5,7,9,11],[2,4,6,8,10,12]]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,6,8,9,10,1,3,4,5,7] => [3,2,4,5,7,6,10,8,9,1] => [[1,4,5,6,8,9],[2,7,10],[3]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,8,9,10,11,12,1,3,4,5,6,7] => [3,2,4,5,6,7,12,8,9,10,11,1] => [[1,4,5,6,7,8,9,10,11],[2,12],[3]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,6,2,7,3,8,4,9,5] => [1,6,7,8,9,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,6,2,7,3,8,4,9] => [5,6,7,8,1,2,3,4,9] => [[1,2,3,4,9],[5,6,7,8]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,7,2,8,3,9,4,10,6] => [5,7,8,9,1,10,2,3,4,6] => [[1,2,3,4,6],[5,7,8,9,10]]
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
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.
searching the database
Sorry, this map was not found in the database.