Processing math: 100%

Identifier
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Images
[1,0] => [1] => [1] => [[1]]
[1,0,1,0] => [1,2] => [1,2] => [[1,2]]
[1,1,0,0] => [2,1] => [2,1] => [[1],[2]]
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [[1,2,3]]
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [[1,2],[3]]
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [[1,3],[2]]
[1,1,0,1,0,0] => [2,3,1] => [3,2,1] => [[1],[2],[3]]
[1,1,1,0,0,0] => [3,2,1] => [2,3,1] => [[1,2],[3]]
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [[1,2,3,4]]
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => [[1,2,3],[4]]
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => [[1,2,4],[3]]
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,3,2] => [[1,2],[3],[4]]
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,3,4,2] => [[1,2,3],[4]]
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [[1,3,4],[2]]
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [[1,3],[2,4]]
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,2,1,4] => [[1,4],[2],[3]]
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,2,3,1] => [[1,3],[2],[4]]
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [3,2,4,1] => [[1,3],[2],[4]]
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,3,1,4] => [[1,2,4],[3]]
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [4,3,2,1] => [[1],[2],[3],[4]]
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [2,4,3,1] => [[1,2],[3],[4]]
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [2,3,4,1] => [[1,2,3],[4]]
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [[1,2,3,4,5]]
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [[1,2,3,4],[5]]
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => [[1,2,3,5],[4]]
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,4,3] => [[1,2,3],[4],[5]]
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,4,5,3] => [[1,2,3,4],[5]]
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => [[1,2,4,5],[3]]
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [[1,2,4],[3,5]]
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,3,2,5] => [[1,2,5],[3],[4]]
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,3,4,2] => [[1,2,4],[3],[5]]
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,4,3,5,2] => [[1,2,4],[3],[5]]
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,3,4,2,5] => [[1,2,3,5],[4]]
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,5,4,3,2] => [[1,2],[3],[4],[5]]
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [1,3,5,4,2] => [[1,2,3],[4],[5]]
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,3,4,5,2] => [[1,2,3,4],[5]]
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [[1,3,4,5],[2]]
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => [[1,3,4],[2,5]]
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => [[1,3,5],[2,4]]
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,4,3] => [[1,3],[2,4],[5]]
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,1,4,5,3] => [[1,3,4],[2,5]]
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,2,1,4,5] => [[1,4,5],[2],[3]]
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2,1,5,4] => [[1,4],[2,5],[3]]
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,2,3,1,5] => [[1,3,5],[2],[4]]
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => [[1,3,4],[2],[5]]
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [4,2,3,5,1] => [[1,3,4],[2],[5]]
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,2,4,1,5] => [[1,3,5],[2],[4]]
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [5,2,4,3,1] => [[1,3],[2],[4],[5]]
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [3,2,5,4,1] => [[1,3],[2,4],[5]]
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [3,2,4,5,1] => [[1,3,4],[2],[5]]
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [2,3,1,4,5] => [[1,2,4,5],[3]]
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,3,1,5,4] => [[1,2,4],[3,5]]
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [4,3,2,1,5] => [[1,5],[2],[3],[4]]
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [5,3,2,4,1] => [[1,4],[2],[3],[5]]
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [4,3,2,5,1] => [[1,4],[2],[3],[5]]
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [2,4,3,1,5] => [[1,2,5],[3],[4]]
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]]
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [2,5,3,4,1] => [[1,2,4],[3],[5]]
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [2,4,3,5,1] => [[1,2,4],[3],[5]]
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [2,3,4,1,5] => [[1,2,3,5],[4]]
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [5,3,4,2,1] => [[1,3],[2],[4],[5]]
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [2,5,4,3,1] => [[1,2],[3],[4],[5]]
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [2,3,5,4,1] => [[1,2,3],[4],[5]]
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [2,3,4,5,1] => [[1,2,3,4],[5]]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [[1,2,3,4],[5],[6]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [[1,2,3,4,5],[6]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [[1,2,3,5],[4,6]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [[1,2,3,6],[4],[5]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [[1,2,3,5],[4],[6]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,5,4,6,3] => [[1,2,3,5],[4],[6]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [[1,2,3,4,6],[5]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,6,5,4,3] => [[1,2,3],[4],[5],[6]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [1,2,4,6,5,3] => [[1,2,3,4],[5],[6]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,4,5,6,3] => [[1,2,3,4,5],[6]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [[1,2,4,5],[3,6]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [[1,2,4,6],[3,5]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [[1,2,4],[3,5],[6]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [[1,2,4,5],[3,6]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [[1,2,5,6],[3],[4]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [[1,2,5],[3,6],[4]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [[1,2,4,6],[3],[5]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [[1,2,4,5],[3],[6]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,5,3,4,6,2] => [[1,2,4,5],[3],[6]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,4,3,5,2,6] => [[1,2,4,6],[3],[5]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,6,3,5,4,2] => [[1,2,4],[3],[5],[6]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [1,4,3,6,5,2] => [[1,2,4],[3,5],[6]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,4,3,5,6,2] => [[1,2,4,5],[3],[6]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [[1,2,3,5,6],[4]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [[1,2,3,5],[4,6]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,5,4,3,2,6] => [[1,2,6],[3],[4],[5]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,6,4,3,5,2] => [[1,2,5],[3],[4],[6]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,5,4,3,6,2] => [[1,2,5],[3],[4],[6]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [1,3,5,4,2,6] => [[1,2,3,6],[4],[5]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [1,3,6,4,5,2] => [[1,2,3,5],[4],[6]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [1,3,5,4,6,2] => [[1,2,3,5],[4],[6]]
>>> Load all 1935 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,3,4,5,2,6] => [[1,2,3,4,6],[5]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,6,4,5,3,2] => [[1,2,4],[3],[5],[6]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [1,3,6,5,4,2] => [[1,2,3],[4],[5],[6]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [1,3,4,6,5,2] => [[1,2,3,4],[5],[6]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,3,4,5,6,2] => [[1,2,3,4,5],[6]]
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [[1,3,4,5],[2,6]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [[1,3,4,6],[2,5]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [[1,3,4],[2,5],[6]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [[1,3,4,5],[2,6]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [[1,3,6],[2,4],[5]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [[1,3,5],[2,4],[6]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,5,4,6,3] => [[1,3,5],[2,4],[6]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [[1,3,4,6],[2,5]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [2,1,4,6,5,3] => [[1,3,4],[2,5],[6]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,4,5,6,3] => [[1,3,4,5],[2,6]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [[1,4,5,6],[2],[3]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [[1,4,5],[2,6],[3]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [[1,4,6],[2,5],[3]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1,5,6,4] => [[1,4,5],[2,6],[3]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [[1,3,5,6],[2],[4]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [[1,3,5],[2,6],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [[1,3,4,6],[2],[5]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [[1,3,4,5],[2],[6]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [5,2,3,4,6,1] => [[1,3,4,5],[2],[6]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [4,2,3,5,1,6] => [[1,3,4,6],[2],[5]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [6,2,3,5,4,1] => [[1,3,4],[2],[5],[6]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [4,2,3,6,5,1] => [[1,3,4],[2,5],[6]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [4,2,3,5,6,1] => [[1,3,4,5],[2],[6]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,2,4,1,5,6] => [[1,3,5,6],[2],[4]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,2,4,1,6,5] => [[1,3,5],[2,6],[4]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [5,2,4,3,1,6] => [[1,3,6],[2],[4],[5]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [6,2,4,3,5,1] => [[1,3,5],[2],[4],[6]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [5,2,4,3,6,1] => [[1,3,5],[2],[4],[6]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [3,2,5,4,1,6] => [[1,3,6],[2,4],[5]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [6,2,5,4,3,1] => [[1,3],[2],[4],[5],[6]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [3,2,6,4,5,1] => [[1,3,5],[2,4],[6]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [3,2,5,4,6,1] => [[1,3,5],[2,4],[6]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [3,2,4,5,1,6] => [[1,3,4,6],[2],[5]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [6,2,4,5,3,1] => [[1,3,4],[2],[5],[6]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [3,2,6,5,4,1] => [[1,3],[2,4],[5],[6]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [3,2,4,6,5,1] => [[1,3,4],[2,5],[6]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [3,2,4,5,6,1] => [[1,3,4,5],[2],[6]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [[1,2,4,5,6],[3]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [[1,2,4,5],[3,6]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [[1,2,4,6],[3,5]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [2,3,1,6,5,4] => [[1,2,4],[3,5],[6]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [[1,2,4,5],[3,6]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [5,3,2,4,1,6] => [[1,4,6],[2],[3],[5]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [6,3,2,4,5,1] => [[1,4,5],[2],[3],[6]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [5,3,2,4,6,1] => [[1,4,5],[2],[3],[6]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [4,3,2,5,1,6] => [[1,4,6],[2],[3],[5]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [6,3,2,5,4,1] => [[1,4],[2,5],[3],[6]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [4,3,2,6,5,1] => [[1,4],[2,5],[3],[6]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [4,3,2,5,6,1] => [[1,4,5],[2],[3],[6]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [2,4,3,1,5,6] => [[1,2,5,6],[3],[4]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [2,4,3,1,6,5] => [[1,2,5],[3,6],[4]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [6,4,3,2,5,1] => [[1,5],[2],[3],[4],[6]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [5,4,3,2,6,1] => [[1,5],[2],[3],[4],[6]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [2,5,3,4,1,6] => [[1,2,4,6],[3],[5]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [6,5,3,4,2,1] => [[1,4],[2],[3],[5],[6]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [2,6,3,4,5,1] => [[1,2,4,5],[3],[6]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [2,5,3,4,6,1] => [[1,2,4,5],[3],[6]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [2,4,3,5,1,6] => [[1,2,4,6],[3],[5]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [6,4,3,5,2,1] => [[1,4],[2],[3],[5],[6]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [2,6,3,5,4,1] => [[1,2,4],[3],[5],[6]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [2,4,3,6,5,1] => [[1,2,4],[3,5],[6]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [2,4,3,5,6,1] => [[1,2,4,5],[3],[6]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [2,3,4,1,5,6] => [[1,2,3,5,6],[4]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [2,3,4,1,6,5] => [[1,2,3,5],[4,6]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [5,3,4,2,1,6] => [[1,3,6],[2],[4],[5]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [6,3,4,2,5,1] => [[1,3,5],[2],[4],[6]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [5,3,4,2,6,1] => [[1,3,5],[2],[4],[6]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [2,5,4,3,1,6] => [[1,2,6],[3],[4],[5]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [2,6,4,3,5,1] => [[1,2,5],[3],[4],[6]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [2,5,4,3,6,1] => [[1,2,5],[3],[4],[6]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [2,3,5,4,1,6] => [[1,2,3,6],[4],[5]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [6,3,5,4,2,1] => [[1,3],[2],[4],[5],[6]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [2,3,6,4,5,1] => [[1,2,3,5],[4],[6]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [2,3,5,4,6,1] => [[1,2,3,5],[4],[6]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [2,3,4,5,1,6] => [[1,2,3,4,6],[5]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [6,3,4,5,2,1] => [[1,3,4],[2],[5],[6]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [2,6,4,5,3,1] => [[1,2,4],[3],[5],[6]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [2,3,6,5,4,1] => [[1,2,3],[4],[5],[6]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [2,3,4,6,5,1] => [[1,2,3,4],[5],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => [[1,2,3,4,5],[6]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [[1,2,3,4,5],[6],[7]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [[1,2,3,4,6],[5,7]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [[1,2,3,4,7],[5],[6]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [[1,2,3,4,6],[5],[7]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,6,5,7,4] => [[1,2,3,4,6],[5],[7]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => [[1,2,3,4,5,7],[6]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,2,3,7,6,5,4] => [[1,2,3,4],[5],[6],[7]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [1,2,3,5,7,6,4] => [[1,2,3,4,5],[6],[7]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,2,3,5,6,7,4] => [[1,2,3,4,5,6],[7]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [[1,2,3,5,7],[4,6]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [[1,2,3,5],[4,6],[7]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,2,4,3,6,7,5] => [[1,2,3,5,6],[4,7]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [[1,2,3,6,7],[4],[5]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [[1,2,3,6],[4,7],[5]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [[1,2,3,5,7],[4],[6]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [[1,2,3,5,6],[4],[7]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,6,4,5,7,3] => [[1,2,3,5,6],[4],[7]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,5,4,6,3,7] => [[1,2,3,5,7],[4],[6]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,2,7,4,6,5,3] => [[1,2,3,5],[4],[6],[7]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [1,2,5,4,7,6,3] => [[1,2,3,5],[4,6],[7]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,2,5,4,6,7,3] => [[1,2,3,5,6],[4],[7]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => [[1,2,3,4,6,7],[5]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,2,4,5,3,7,6] => [[1,2,3,4,6],[5,7]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,2,6,5,4,3,7] => [[1,2,3,7],[4],[5],[6]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,2,7,5,4,6,3] => [[1,2,3,6],[4],[5],[7]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,2,6,5,4,7,3] => [[1,2,3,6],[4],[5],[7]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [1,2,4,6,5,3,7] => [[1,2,3,4,7],[5],[6]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [1,2,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [1,2,4,7,5,6,3] => [[1,2,3,4,6],[5],[7]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [1,2,4,6,5,7,3] => [[1,2,3,4,6],[5],[7]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,2,4,5,6,3,7] => [[1,2,3,4,5,7],[6]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,2,7,5,6,4,3] => [[1,2,3,5],[4],[6],[7]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [1,2,4,7,6,5,3] => [[1,2,3,4],[5],[6],[7]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [1,2,4,5,7,6,3] => [[1,2,3,4,5],[6],[7]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,2,4,5,6,7,3] => [[1,2,3,4,5,6],[7]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [[1,2,4,5,7],[3,6]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [[1,2,4,5],[3,6],[7]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,3,2,4,6,7,5] => [[1,2,4,5,6],[3,7]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [[1,2,4,6,7],[3,5]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [[1,2,4,6],[3,5,7]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [[1,2,4,7],[3,5],[6]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [[1,2,4,6],[3,5],[7]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,3,2,6,5,7,4] => [[1,2,4,6],[3,5],[7]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,3,2,5,6,4,7] => [[1,2,4,5,7],[3,6]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,3,2,7,6,5,4] => [[1,2,4],[3,5],[6],[7]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [1,3,2,5,7,6,4] => [[1,2,4,5],[3,6],[7]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,3,2,5,6,7,4] => [[1,2,4,5,6],[3,7]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [[1,2,5,6,7],[3],[4]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [[1,2,5,6],[3,7],[4]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [[1,2,5,7],[3,6],[4]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [[1,2,5],[3,6],[4,7]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,4,3,2,6,7,5] => [[1,2,5,6],[3,7],[4]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [[1,2,4,6,7],[3],[5]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [[1,2,4,6],[3,7],[5]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [[1,2,4,5,7],[3],[6]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [[1,2,4,5,6],[3],[7]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,6,3,4,5,7,2] => [[1,2,4,5,6],[3],[7]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,5,3,4,6,2,7] => [[1,2,4,5,7],[3],[6]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,7,3,4,6,5,2] => [[1,2,4,5],[3],[6],[7]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [1,5,3,4,7,6,2] => [[1,2,4,5],[3,6],[7]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,5,3,4,6,7,2] => [[1,2,4,5,6],[3],[7]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,4,3,5,2,6,7] => [[1,2,4,6,7],[3],[5]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,4,3,5,2,7,6] => [[1,2,4,6],[3,7],[5]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [1,6,3,5,4,2,7] => [[1,2,4,7],[3],[5],[6]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,7,3,5,4,6,2] => [[1,2,4,6],[3],[5],[7]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,6,3,5,4,7,2] => [[1,2,4,6],[3],[5],[7]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [1,4,3,6,5,2,7] => [[1,2,4,7],[3,5],[6]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [1,7,3,6,5,4,2] => [[1,2,4],[3],[5],[6],[7]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [1,4,3,7,5,6,2] => [[1,2,4,6],[3,5],[7]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [1,4,3,6,5,7,2] => [[1,2,4,6],[3,5],[7]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [1,4,3,5,6,2,7] => [[1,2,4,5,7],[3],[6]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,7,3,5,6,4,2] => [[1,2,4,5],[3],[6],[7]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [1,4,3,7,6,5,2] => [[1,2,4],[3,5],[6],[7]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [1,4,3,5,7,6,2] => [[1,2,4,5],[3,6],[7]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,4,3,5,6,7,2] => [[1,2,4,5,6],[3],[7]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => [[1,2,3,5,6,7],[4]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,3,4,2,5,7,6] => [[1,2,3,5,6],[4,7]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,3,4,2,6,5,7] => [[1,2,3,5,7],[4,6]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,3,4,2,7,6,5] => [[1,2,3,5],[4,6],[7]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,3,4,2,6,7,5] => [[1,2,3,5,6],[4,7]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [1,5,4,3,2,6,7] => [[1,2,6,7],[3],[4],[5]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [1,5,4,3,2,7,6] => [[1,2,6],[3,7],[4],[5]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [1,6,4,3,5,2,7] => [[1,2,5,7],[3],[4],[6]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,7,4,3,5,6,2] => [[1,2,5,6],[3],[4],[7]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [1,6,4,3,5,7,2] => [[1,2,5,6],[3],[4],[7]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [1,5,4,3,6,2,7] => [[1,2,5,7],[3],[4],[6]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,7,4,3,6,5,2] => [[1,2,5],[3,6],[4],[7]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [1,5,4,3,7,6,2] => [[1,2,5],[3,6],[4],[7]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [1,5,4,3,6,7,2] => [[1,2,5,6],[3],[4],[7]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [1,3,5,4,2,6,7] => [[1,2,3,6,7],[4],[5]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [1,3,5,4,2,7,6] => [[1,2,3,6],[4,7],[5]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [1,6,5,4,3,2,7] => [[1,2,7],[3],[4],[5],[6]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [1,7,5,4,3,6,2] => [[1,2,6],[3],[4],[5],[7]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [1,6,5,4,3,7,2] => [[1,2,6],[3],[4],[5],[7]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [1,3,6,4,5,2,7] => [[1,2,3,5,7],[4],[6]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [1,7,6,4,5,3,2] => [[1,2,5],[3],[4],[6],[7]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [1,3,7,4,5,6,2] => [[1,2,3,5,6],[4],[7]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [1,3,6,4,5,7,2] => [[1,2,3,5,6],[4],[7]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [1,3,5,4,6,2,7] => [[1,2,3,5,7],[4],[6]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [1,7,5,4,6,3,2] => [[1,2,5],[3],[4],[6],[7]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [1,3,7,4,6,5,2] => [[1,2,3,5],[4],[6],[7]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [1,3,5,4,7,6,2] => [[1,2,3,5],[4,6],[7]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [1,3,5,4,6,7,2] => [[1,2,3,5,6],[4],[7]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [1,3,4,5,2,6,7] => [[1,2,3,4,6,7],[5]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [1,3,4,5,2,7,6] => [[1,2,3,4,6],[5,7]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,6,4,5,3,2,7] => [[1,2,4,7],[3],[5],[6]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,7,4,5,3,6,2] => [[1,2,4,6],[3],[5],[7]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,6,4,5,3,7,2] => [[1,2,4,6],[3],[5],[7]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [1,3,6,5,4,2,7] => [[1,2,3,7],[4],[5],[6]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [1,3,7,5,4,6,2] => [[1,2,3,6],[4],[5],[7]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [1,3,6,5,4,7,2] => [[1,2,3,6],[4],[5],[7]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [1,3,4,6,5,2,7] => [[1,2,3,4,7],[5],[6]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [1,7,4,6,5,3,2] => [[1,2,4],[3],[5],[6],[7]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [1,3,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [1,3,4,7,5,6,2] => [[1,2,3,4,6],[5],[7]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [1,3,4,6,5,7,2] => [[1,2,3,4,6],[5],[7]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [1,3,4,5,6,2,7] => [[1,2,3,4,5,7],[6]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,7,4,5,6,3,2] => [[1,2,4,5],[3],[6],[7]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [1,3,7,5,6,4,2] => [[1,2,3,5],[4],[6],[7]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [1,3,4,7,6,5,2] => [[1,2,3,4],[5],[6],[7]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [1,3,4,5,7,6,2] => [[1,2,3,4,5],[6],[7]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,3,4,5,6,7,2] => [[1,2,3,4,5,6],[7]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [[1,3,4,5,7],[2,6]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [[1,3,4,5],[2,6],[7]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [2,1,3,4,6,7,5] => [[1,3,4,5,6],[2,7]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [[1,3,4,6,7],[2,5]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [[1,3,4,6],[2,5,7]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [[1,3,4,7],[2,5],[6]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [[1,3,4,6],[2,5],[7]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [2,1,3,6,5,7,4] => [[1,3,4,6],[2,5],[7]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [2,1,3,5,6,4,7] => [[1,3,4,5,7],[2,6]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [2,1,3,7,6,5,4] => [[1,3,4],[2,5],[6],[7]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [2,1,3,5,7,6,4] => [[1,3,4,5],[2,6],[7]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [2,1,3,5,6,7,4] => [[1,3,4,5,6],[2,7]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [[1,3,5,6,7],[2,4]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [[1,3,5,6],[2,4,7]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [[1,3,5,7],[2,4,6]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [[1,3,5],[2,4,6],[7]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [2,1,4,3,6,7,5] => [[1,3,5,6],[2,4,7]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [[1,3,6,7],[2,4],[5]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [[1,3,6],[2,4,7],[5]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [[1,3,5,7],[2,4],[6]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [[1,3,5,6],[2,4],[7]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [2,1,6,4,5,7,3] => [[1,3,5,6],[2,4],[7]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [2,1,5,4,6,3,7] => [[1,3,5,7],[2,4],[6]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [2,1,7,4,6,5,3] => [[1,3,5],[2,4],[6],[7]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [2,1,5,4,7,6,3] => [[1,3,5],[2,4,6],[7]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [2,1,5,4,6,7,3] => [[1,3,5,6],[2,4],[7]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [2,1,4,5,3,6,7] => [[1,3,4,6,7],[2,5]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [2,1,4,5,3,7,6] => [[1,3,4,6],[2,5,7]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [2,1,6,5,4,3,7] => [[1,3,7],[2,4],[5],[6]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [2,1,7,5,4,6,3] => [[1,3,6],[2,4],[5],[7]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [2,1,6,5,4,7,3] => [[1,3,6],[2,4],[5],[7]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [2,1,4,6,5,3,7] => [[1,3,4,7],[2,5],[6]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [2,1,4,7,5,6,3] => [[1,3,4,6],[2,5],[7]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [2,1,4,6,5,7,3] => [[1,3,4,6],[2,5],[7]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [2,1,4,5,6,3,7] => [[1,3,4,5,7],[2,6]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [2,1,7,5,6,4,3] => [[1,3,5],[2,4],[6],[7]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [2,1,4,7,6,5,3] => [[1,3,4],[2,5],[6],[7]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [2,1,4,5,7,6,3] => [[1,3,4,5],[2,6],[7]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,1,4,5,6,7,3] => [[1,3,4,5,6],[2,7]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [[1,4,5,6],[2,7],[3]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [[1,4,5,7],[2,6],[3]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [[1,4,5],[2,6],[3,7]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [3,2,1,4,6,7,5] => [[1,4,5,6],[2,7],[3]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [[1,4,6,7],[2,5],[3]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [[1,4,6],[2,5,7],[3]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [[1,4,7],[2,5],[3,6]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [[1,4,6],[2,5],[3,7]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [3,2,1,6,5,7,4] => [[1,4,6],[2,5],[3,7]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [3,2,1,5,6,4,7] => [[1,4,5,7],[2,6],[3]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [3,2,1,5,7,6,4] => [[1,4,5],[2,6],[3,7]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [3,2,1,5,6,7,4] => [[1,4,5,6],[2,7],[3]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [[1,3,5,6,7],[2],[4]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [[1,3,5,6],[2,7],[4]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [[1,3,5,7],[2,6],[4]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [[1,3,5],[2,6],[4,7]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [4,2,3,1,6,7,5] => [[1,3,5,6],[2,7],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [[1,3,4,6,7],[2],[5]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [[1,3,4,6],[2,7],[5]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [[1,3,4,5,7],[2],[6]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [6,2,3,4,5,7,1] => [[1,3,4,5,6],[2],[7]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [5,2,3,4,6,1,7] => [[1,3,4,5,7],[2],[6]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [7,2,3,4,6,5,1] => [[1,3,4,5],[2],[6],[7]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [5,2,3,4,7,6,1] => [[1,3,4,5],[2,6],[7]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [5,2,3,4,6,7,1] => [[1,3,4,5,6],[2],[7]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [4,2,3,5,1,6,7] => [[1,3,4,6,7],[2],[5]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [4,2,3,5,1,7,6] => [[1,3,4,6],[2,7],[5]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [6,2,3,5,4,1,7] => [[1,3,4,7],[2],[5],[6]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [7,2,3,5,4,6,1] => [[1,3,4,6],[2],[5],[7]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [6,2,3,5,4,7,1] => [[1,3,4,6],[2],[5],[7]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [4,2,3,6,5,1,7] => [[1,3,4,7],[2,5],[6]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [7,2,3,6,5,4,1] => [[1,3,4],[2],[5],[6],[7]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [4,2,3,7,5,6,1] => [[1,3,4,6],[2,5],[7]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [4,2,3,6,5,7,1] => [[1,3,4,6],[2,5],[7]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [4,2,3,5,6,1,7] => [[1,3,4,5,7],[2],[6]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [7,2,3,5,6,4,1] => [[1,3,4,5],[2],[6],[7]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [4,2,3,7,6,5,1] => [[1,3,4],[2,5],[6],[7]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [4,2,3,5,7,6,1] => [[1,3,4,5],[2,6],[7]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [4,2,3,5,6,7,1] => [[1,3,4,5,6],[2],[7]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [3,2,4,1,5,6,7] => [[1,3,5,6,7],[2],[4]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [3,2,4,1,5,7,6] => [[1,3,5,6],[2,7],[4]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [3,2,4,1,6,5,7] => [[1,3,5,7],[2,6],[4]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [3,2,4,1,7,6,5] => [[1,3,5],[2,6],[4,7]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,2,4,1,6,7,5] => [[1,3,5,6],[2,7],[4]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [5,2,4,3,1,6,7] => [[1,3,6,7],[2],[4],[5]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [5,2,4,3,1,7,6] => [[1,3,6],[2,7],[4],[5]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [6,2,4,3,5,1,7] => [[1,3,5,7],[2],[4],[6]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [7,2,4,3,5,6,1] => [[1,3,5,6],[2],[4],[7]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [6,2,4,3,5,7,1] => [[1,3,5,6],[2],[4],[7]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [5,2,4,3,6,1,7] => [[1,3,5,7],[2],[4],[6]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [7,2,4,3,6,5,1] => [[1,3,5],[2,6],[4],[7]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [5,2,4,3,7,6,1] => [[1,3,5],[2,6],[4],[7]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [5,2,4,3,6,7,1] => [[1,3,5,6],[2],[4],[7]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [3,2,5,4,1,6,7] => [[1,3,6,7],[2,4],[5]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [3,2,5,4,1,7,6] => [[1,3,6],[2,4,7],[5]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [6,2,5,4,3,1,7] => [[1,3,7],[2],[4],[5],[6]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [7,2,5,4,3,6,1] => [[1,3,6],[2],[4],[5],[7]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [6,2,5,4,3,7,1] => [[1,3,6],[2],[4],[5],[7]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [3,2,6,4,5,1,7] => [[1,3,5,7],[2,4],[6]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [7,2,6,4,5,3,1] => [[1,3,5],[2],[4],[6],[7]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [3,2,7,4,5,6,1] => [[1,3,5,6],[2,4],[7]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [3,2,6,4,5,7,1] => [[1,3,5,6],[2,4],[7]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [3,2,5,4,6,1,7] => [[1,3,5,7],[2,4],[6]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [7,2,5,4,6,3,1] => [[1,3,5],[2],[4],[6],[7]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [3,2,7,4,6,5,1] => [[1,3,5],[2,4],[6],[7]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [3,2,5,4,7,6,1] => [[1,3,5],[2,4,6],[7]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [3,2,5,4,6,7,1] => [[1,3,5,6],[2,4],[7]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [3,2,4,5,1,6,7] => [[1,3,4,6,7],[2],[5]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [3,2,4,5,1,7,6] => [[1,3,4,6],[2,7],[5]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [6,2,4,5,3,1,7] => [[1,3,4,7],[2],[5],[6]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [7,2,4,5,3,6,1] => [[1,3,4,6],[2],[5],[7]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [6,2,4,5,3,7,1] => [[1,3,4,6],[2],[5],[7]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [3,2,6,5,4,1,7] => [[1,3,7],[2,4],[5],[6]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [7,2,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [3,2,7,5,4,6,1] => [[1,3,6],[2,4],[5],[7]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [3,2,6,5,4,7,1] => [[1,3,6],[2,4],[5],[7]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [3,2,4,6,5,1,7] => [[1,3,4,7],[2,5],[6]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [7,2,4,6,5,3,1] => [[1,3,4],[2],[5],[6],[7]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [3,2,4,7,5,6,1] => [[1,3,4,6],[2,5],[7]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [3,2,4,6,5,7,1] => [[1,3,4,6],[2,5],[7]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [3,2,4,5,6,1,7] => [[1,3,4,5,7],[2],[6]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [7,2,4,5,6,3,1] => [[1,3,4,5],[2],[6],[7]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [3,2,7,5,6,4,1] => [[1,3,5],[2,4],[6],[7]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [3,2,4,7,6,5,1] => [[1,3,4],[2,5],[6],[7]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [3,2,4,5,7,6,1] => [[1,3,4,5],[2,6],[7]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [3,2,4,5,6,7,1] => [[1,3,4,5,6],[2],[7]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => [[1,2,4,5,6,7],[3]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [2,3,1,4,5,7,6] => [[1,2,4,5,6],[3,7]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [2,3,1,4,6,5,7] => [[1,2,4,5,7],[3,6]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [2,3,1,4,7,6,5] => [[1,2,4,5],[3,6],[7]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [2,3,1,4,6,7,5] => [[1,2,4,5,6],[3,7]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [2,3,1,5,4,6,7] => [[1,2,4,6,7],[3,5]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [2,3,1,5,4,7,6] => [[1,2,4,6],[3,5,7]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [2,3,1,6,5,4,7] => [[1,2,4,7],[3,5],[6]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [2,3,1,7,5,6,4] => [[1,2,4,6],[3,5],[7]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [2,3,1,6,5,7,4] => [[1,2,4,6],[3,5],[7]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [2,3,1,5,6,4,7] => [[1,2,4,5,7],[3,6]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [2,3,1,7,6,5,4] => [[1,2,4],[3,5],[6],[7]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [2,3,1,5,7,6,4] => [[1,2,4,5],[3,6],[7]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [2,3,1,5,6,7,4] => [[1,2,4,5,6],[3,7]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [4,3,2,1,5,6,7] => [[1,5,6,7],[2],[3],[4]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [4,3,2,1,5,7,6] => [[1,5,6],[2,7],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [4,3,2,1,6,5,7] => [[1,5,7],[2,6],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [4,3,2,1,6,7,5] => [[1,5,6],[2,7],[3],[4]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [5,3,2,4,1,6,7] => [[1,4,6,7],[2],[3],[5]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [5,3,2,4,1,7,6] => [[1,4,6],[2,7],[3],[5]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [6,3,2,4,5,1,7] => [[1,4,5,7],[2],[3],[6]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [7,3,2,4,5,6,1] => [[1,4,5,6],[2],[3],[7]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [6,3,2,4,5,7,1] => [[1,4,5,6],[2],[3],[7]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [5,3,2,4,6,1,7] => [[1,4,5,7],[2],[3],[6]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [7,3,2,4,6,5,1] => [[1,4,5],[2,6],[3],[7]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [5,3,2,4,7,6,1] => [[1,4,5],[2,6],[3],[7]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [5,3,2,4,6,7,1] => [[1,4,5,6],[2],[3],[7]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [4,3,2,5,1,6,7] => [[1,4,6,7],[2],[3],[5]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [4,3,2,5,1,7,6] => [[1,4,6],[2,7],[3],[5]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [6,3,2,5,4,1,7] => [[1,4,7],[2,5],[3],[6]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [7,3,2,5,4,6,1] => [[1,4,6],[2,5],[3],[7]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [6,3,2,5,4,7,1] => [[1,4,6],[2,5],[3],[7]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [4,3,2,6,5,1,7] => [[1,4,7],[2,5],[3],[6]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [7,3,2,6,5,4,1] => [[1,4],[2,5],[3],[6],[7]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [4,3,2,7,5,6,1] => [[1,4,6],[2,5],[3],[7]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [4,3,2,6,5,7,1] => [[1,4,6],[2,5],[3],[7]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [4,3,2,5,6,1,7] => [[1,4,5,7],[2],[3],[6]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [7,3,2,5,6,4,1] => [[1,4,5],[2,6],[3],[7]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [4,3,2,7,6,5,1] => [[1,4],[2,5],[3,6],[7]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [4,3,2,5,7,6,1] => [[1,4,5],[2,6],[3],[7]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [4,3,2,5,6,7,1] => [[1,4,5,6],[2],[3],[7]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [2,4,3,1,5,6,7] => [[1,2,5,6,7],[3],[4]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [2,4,3,1,5,7,6] => [[1,2,5,6],[3,7],[4]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [2,4,3,1,6,5,7] => [[1,2,5,7],[3,6],[4]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [2,4,3,1,7,6,5] => [[1,2,5],[3,6],[4,7]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [2,4,3,1,6,7,5] => [[1,2,5,6],[3,7],[4]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [5,4,3,2,1,7,6] => [[1,6],[2,7],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [6,4,3,2,5,1,7] => [[1,5,7],[2],[3],[4],[6]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [7,4,3,2,5,6,1] => [[1,5,6],[2],[3],[4],[7]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [6,4,3,2,5,7,1] => [[1,5,6],[2],[3],[4],[7]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [5,4,3,2,6,1,7] => [[1,5,7],[2],[3],[4],[6]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [7,4,3,2,6,5,1] => [[1,5],[2,6],[3],[4],[7]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [5,4,3,2,7,6,1] => [[1,5],[2,6],[3],[4],[7]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [5,4,3,2,6,7,1] => [[1,5,6],[2],[3],[4],[7]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [2,5,3,4,1,6,7] => [[1,2,4,6,7],[3],[5]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [2,5,3,4,1,7,6] => [[1,2,4,6],[3,7],[5]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [6,5,3,4,2,1,7] => [[1,4,7],[2],[3],[5],[6]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [7,5,3,4,2,6,1] => [[1,4,6],[2],[3],[5],[7]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [6,5,3,4,2,7,1] => [[1,4,6],[2],[3],[5],[7]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [2,6,3,4,5,1,7] => [[1,2,4,5,7],[3],[6]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [7,6,3,4,5,2,1] => [[1,4,5],[2],[3],[6],[7]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [2,7,3,4,5,6,1] => [[1,2,4,5,6],[3],[7]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [2,6,3,4,5,7,1] => [[1,2,4,5,6],[3],[7]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [2,5,3,4,6,1,7] => [[1,2,4,5,7],[3],[6]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [7,5,3,4,6,2,1] => [[1,4,5],[2],[3],[6],[7]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [2,7,3,4,6,5,1] => [[1,2,4,5],[3],[6],[7]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [2,5,3,4,7,6,1] => [[1,2,4,5],[3,6],[7]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [2,5,3,4,6,7,1] => [[1,2,4,5,6],[3],[7]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [2,4,3,5,1,6,7] => [[1,2,4,6,7],[3],[5]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [2,4,3,5,1,7,6] => [[1,2,4,6],[3,7],[5]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [6,4,3,5,2,1,7] => [[1,4,7],[2],[3],[5],[6]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [7,4,3,5,2,6,1] => [[1,4,6],[2],[3],[5],[7]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [6,4,3,5,2,7,1] => [[1,4,6],[2],[3],[5],[7]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [2,6,3,5,4,1,7] => [[1,2,4,7],[3],[5],[6]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [7,6,3,5,4,2,1] => [[1,4],[2],[3],[5],[6],[7]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [2,7,3,5,4,6,1] => [[1,2,4,6],[3],[5],[7]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [2,6,3,5,4,7,1] => [[1,2,4,6],[3],[5],[7]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [2,4,3,6,5,1,7] => [[1,2,4,7],[3,5],[6]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [7,4,3,6,5,2,1] => [[1,4],[2,5],[3],[6],[7]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [2,7,3,6,5,4,1] => [[1,2,4],[3],[5],[6],[7]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [2,4,3,7,5,6,1] => [[1,2,4,6],[3,5],[7]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [2,4,3,6,5,7,1] => [[1,2,4,6],[3,5],[7]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [2,4,3,5,6,1,7] => [[1,2,4,5,7],[3],[6]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [7,4,3,5,6,2,1] => [[1,4,5],[2],[3],[6],[7]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [2,7,3,5,6,4,1] => [[1,2,4,5],[3],[6],[7]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [2,4,3,7,6,5,1] => [[1,2,4],[3,5],[6],[7]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [2,4,3,5,7,6,1] => [[1,2,4,5],[3,6],[7]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [2,4,3,5,6,7,1] => [[1,2,4,5,6],[3],[7]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [2,3,4,1,5,6,7] => [[1,2,3,5,6,7],[4]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [2,3,4,1,5,7,6] => [[1,2,3,5,6],[4,7]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [2,3,4,1,6,5,7] => [[1,2,3,5,7],[4,6]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [2,3,4,1,7,6,5] => [[1,2,3,5],[4,6],[7]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [2,3,4,1,6,7,5] => [[1,2,3,5,6],[4,7]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [5,3,4,2,1,6,7] => [[1,3,6,7],[2],[4],[5]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [5,3,4,2,1,7,6] => [[1,3,6],[2,7],[4],[5]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [6,3,4,2,5,1,7] => [[1,3,5,7],[2],[4],[6]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [7,3,4,2,5,6,1] => [[1,3,5,6],[2],[4],[7]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [6,3,4,2,5,7,1] => [[1,3,5,6],[2],[4],[7]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [5,3,4,2,6,1,7] => [[1,3,5,7],[2],[4],[6]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [7,3,4,2,6,5,1] => [[1,3,5],[2,6],[4],[7]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [5,3,4,2,7,6,1] => [[1,3,5],[2,6],[4],[7]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [5,3,4,2,6,7,1] => [[1,3,5,6],[2],[4],[7]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [2,5,4,3,1,6,7] => [[1,2,6,7],[3],[4],[5]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [2,5,4,3,1,7,6] => [[1,2,6],[3,7],[4],[5]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [7,5,4,3,2,6,1] => [[1,6],[2],[3],[4],[5],[7]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [6,5,4,3,2,7,1] => [[1,6],[2],[3],[4],[5],[7]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [2,6,4,3,5,1,7] => [[1,2,5,7],[3],[4],[6]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [7,6,4,3,5,2,1] => [[1,5],[2],[3],[4],[6],[7]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [2,7,4,3,5,6,1] => [[1,2,5,6],[3],[4],[7]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [2,6,4,3,5,7,1] => [[1,2,5,6],[3],[4],[7]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [2,5,4,3,6,1,7] => [[1,2,5,7],[3],[4],[6]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [7,5,4,3,6,2,1] => [[1,5],[2],[3],[4],[6],[7]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [2,7,4,3,6,5,1] => [[1,2,5],[3,6],[4],[7]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [2,5,4,3,7,6,1] => [[1,2,5],[3,6],[4],[7]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [2,5,4,3,6,7,1] => [[1,2,5,6],[3],[4],[7]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [2,3,5,4,1,6,7] => [[1,2,3,6,7],[4],[5]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [2,3,5,4,1,7,6] => [[1,2,3,6],[4,7],[5]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [6,3,5,4,2,1,7] => [[1,3,7],[2],[4],[5],[6]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [7,3,5,4,2,6,1] => [[1,3,6],[2],[4],[5],[7]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [6,3,5,4,2,7,1] => [[1,3,6],[2],[4],[5],[7]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [2,6,5,4,3,1,7] => [[1,2,7],[3],[4],[5],[6]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [2,7,5,4,3,6,1] => [[1,2,6],[3],[4],[5],[7]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [2,6,5,4,3,7,1] => [[1,2,6],[3],[4],[5],[7]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [2,3,6,4,5,1,7] => [[1,2,3,5,7],[4],[6]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [7,3,6,4,5,2,1] => [[1,3,5],[2],[4],[6],[7]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [2,7,6,4,5,3,1] => [[1,2,5],[3],[4],[6],[7]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [2,3,7,4,5,6,1] => [[1,2,3,5,6],[4],[7]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [2,3,6,4,5,7,1] => [[1,2,3,5,6],[4],[7]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [2,3,5,4,6,1,7] => [[1,2,3,5,7],[4],[6]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [7,3,5,4,6,2,1] => [[1,3,5],[2],[4],[6],[7]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [2,7,5,4,6,3,1] => [[1,2,5],[3],[4],[6],[7]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [2,3,7,4,6,5,1] => [[1,2,3,5],[4],[6],[7]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [2,3,5,4,7,6,1] => [[1,2,3,5],[4,6],[7]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [2,3,5,4,6,7,1] => [[1,2,3,5,6],[4],[7]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [2,3,4,5,1,6,7] => [[1,2,3,4,6,7],[5]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [2,3,4,5,1,7,6] => [[1,2,3,4,6],[5,7]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [6,3,4,5,2,1,7] => [[1,3,4,7],[2],[5],[6]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [7,3,4,5,2,6,1] => [[1,3,4,6],[2],[5],[7]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [6,3,4,5,2,7,1] => [[1,3,4,6],[2],[5],[7]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [2,6,4,5,3,1,7] => [[1,2,4,7],[3],[5],[6]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [7,6,4,5,3,2,1] => [[1,4],[2],[3],[5],[6],[7]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [2,7,4,5,3,6,1] => [[1,2,4,6],[3],[5],[7]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [2,6,4,5,3,7,1] => [[1,2,4,6],[3],[5],[7]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [2,3,6,5,4,1,7] => [[1,2,3,7],[4],[5],[6]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [7,3,6,5,4,2,1] => [[1,3],[2],[4],[5],[6],[7]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [2,3,7,5,4,6,1] => [[1,2,3,6],[4],[5],[7]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [2,3,6,5,4,7,1] => [[1,2,3,6],[4],[5],[7]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [2,3,4,6,5,1,7] => [[1,2,3,4,7],[5],[6]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [7,3,4,6,5,2,1] => [[1,3,4],[2],[5],[6],[7]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [2,7,4,6,5,3,1] => [[1,2,4],[3],[5],[6],[7]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [2,3,7,6,5,4,1] => [[1,2,3],[4],[5],[6],[7]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [2,3,4,7,5,6,1] => [[1,2,3,4,6],[5],[7]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [2,3,4,6,5,7,1] => [[1,2,3,4,6],[5],[7]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [2,3,4,5,6,1,7] => [[1,2,3,4,5,7],[6]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [7,3,4,5,6,2,1] => [[1,3,4,5],[2],[6],[7]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [2,7,4,5,6,3,1] => [[1,2,4,5],[3],[6],[7]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [2,3,7,5,6,4,1] => [[1,2,3,5],[4],[6],[7]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [2,3,4,7,6,5,1] => [[1,2,3,4],[5],[6],[7]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [2,3,4,5,7,6,1] => [[1,2,3,4,5],[6],[7]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [2,3,4,5,6,7,1] => [[1,2,3,4,5,6],[7]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [[1,2,3,4,5,6,8],[7]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => [[1,2,3,4,5,6],[7],[8]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [[1,2,3,4,5,7],[6,8]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,6,5,8] => [[1,2,3,4,5,8],[6],[7]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => [[1,2,3,4,5,7],[6],[8]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [1,2,3,4,7,6,8,5] => [[1,2,3,4,5,7],[6],[8]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [1,2,3,4,6,7,5,8] => [[1,2,3,4,5,6,8],[7]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [1,2,3,4,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [1,2,3,4,6,8,7,5] => [[1,2,3,4,5,6],[7],[8]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [1,2,3,4,6,7,8,5] => [[1,2,3,4,5,6,7],[8]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [[1,2,3,4,6,7,8],[5]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [[1,2,3,4,6,8],[5,7]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,7,6] => [[1,2,3,4,6],[5,7],[8]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [1,2,3,5,4,7,8,6] => [[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [1,2,3,6,5,4,7,8] => [[1,2,3,4,7,8],[5],[6]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [1,2,3,6,5,4,8,7] => [[1,2,3,4,7],[5,8],[6]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [1,2,3,7,5,6,4,8] => [[1,2,3,4,6,8],[5],[7]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => [[1,2,3,4,6,7],[5],[8]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [1,2,3,7,5,6,8,4] => [[1,2,3,4,6,7],[5],[8]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [1,2,3,6,5,7,4,8] => [[1,2,3,4,6,8],[5],[7]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [1,2,3,8,5,7,6,4] => [[1,2,3,4,6],[5],[7],[8]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [1,2,3,6,5,8,7,4] => [[1,2,3,4,6],[5,7],[8]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [1,2,3,6,5,7,8,4] => [[1,2,3,4,6,7],[5],[8]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [1,2,3,5,6,4,7,8] => [[1,2,3,4,5,7,8],[6]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [1,2,3,5,6,4,8,7] => [[1,2,3,4,5,7],[6,8]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [1,2,3,7,6,5,4,8] => [[1,2,3,4,8],[5],[6],[7]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [1,2,3,8,6,5,7,4] => [[1,2,3,4,7],[5],[6],[8]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [1,2,3,7,6,5,8,4] => [[1,2,3,4,7],[5],[6],[8]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => [1,2,3,5,7,6,4,8] => [[1,2,3,4,5,8],[6],[7]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [1,2,3,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [1,2,3,5,8,6,7,4] => [[1,2,3,4,5,7],[6],[8]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [1,2,3,5,7,6,8,4] => [[1,2,3,4,5,7],[6],[8]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [1,2,3,5,6,7,4,8] => [[1,2,3,4,5,6,8],[7]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [1,2,3,8,6,7,5,4] => [[1,2,3,4,6],[5],[7],[8]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [1,2,3,5,8,7,6,4] => [[1,2,3,4,5],[6],[7],[8]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [1,2,3,5,6,8,7,4] => [[1,2,3,4,5,6],[7],[8]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [1,2,3,5,6,7,8,4] => [[1,2,3,4,5,6,7],[8]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [1,2,4,3,5,7,8,6] => [[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [[1,2,3,5,7],[4,6,8]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [1,2,4,3,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,6,5,8] => [1,2,4,3,6,7,5,8] => [[1,2,3,5,6,8],[4,7]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [1,2,4,3,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [1,2,4,3,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [1,2,4,3,6,7,8,5] => [[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [1,2,5,4,3,6,7,8] => [[1,2,3,6,7,8],[4],[5]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6,8,7] => [1,2,5,4,3,6,8,7] => [[1,2,3,6,7],[4,8],[5]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [1,2,5,4,3,8,7,6] => [[1,2,3,6],[4,7],[5,8]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [1,2,5,4,3,7,8,6] => [[1,2,3,6,7],[4,8],[5]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [1,2,6,4,5,3,7,8] => [[1,2,3,5,7,8],[4],[6]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [1,2,8,4,5,6,7,3] => [[1,2,3,5,6,7],[4],[8]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [1,2,7,4,5,6,8,3] => [[1,2,3,5,6,7],[4],[8]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [1,2,6,4,5,7,8,3] => [[1,2,3,5,6,7],[4],[8]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,6,7,5,8,3] => [1,2,8,4,7,6,5,3] => [[1,2,3,5],[4],[6],[7],[8]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [1,2,5,4,8,6,7,3] => [[1,2,3,5,7],[4,6],[8]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [1,2,5,4,7,6,8,3] => [[1,2,3,5,7],[4,6],[8]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,6,5,3,8] => [1,2,5,4,6,7,3,8] => [[1,2,3,5,6,8],[4],[7]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [1,2,8,4,6,7,5,3] => [[1,2,3,5,6],[4],[7],[8]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,7,6,8,5,3] => [1,2,5,4,8,7,6,3] => [[1,2,3,5],[4,6],[7],[8]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => [1,2,5,4,6,8,7,3] => [[1,2,3,5,6],[4,7],[8]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [1,2,5,4,6,7,8,3] => [[1,2,3,5,6,7],[4],[8]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,4,3,7,6,8] => [1,2,4,5,3,7,6,8] => [[1,2,3,4,6,8],[5,7]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [1,2,4,5,3,8,7,6] => [[1,2,3,4,6],[5,7],[8]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [1,2,4,5,3,7,8,6] => [[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,5,4,6,3,7,8] => [1,2,6,5,4,3,7,8] => [[1,2,3,7,8],[4],[5],[6]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [1,2,7,5,4,6,3,8] => [[1,2,3,6,8],[4],[5],[7]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [1,2,8,5,4,6,7,3] => [[1,2,3,6,7],[4],[5],[8]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [1,2,7,5,4,6,8,3] => [[1,2,3,6,7],[4],[5],[8]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [1,2,8,5,4,7,6,3] => [[1,2,3,6],[4,7],[5],[8]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,7,8,6,3] => [1,2,6,5,4,8,7,3] => [[1,2,3,6],[4,7],[5],[8]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [1,2,6,5,4,7,8,3] => [[1,2,3,6,7],[4],[5],[8]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,4,3,7,8] => [1,2,4,6,5,3,7,8] => [[1,2,3,4,7,8],[5],[6]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,4,7,3,8] => [1,2,7,6,5,4,3,8] => [[1,2,3,8],[4],[5],[6],[7]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [1,2,8,6,5,4,7,3] => [[1,2,3,7],[4],[5],[6],[8]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,5,6,4,8,7,3] => [1,2,7,6,5,4,8,3] => [[1,2,3,7],[4],[5],[6],[8]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [1,2,8,7,5,6,4,3] => [[1,2,3,6],[4],[5],[7],[8]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [1,2,4,8,5,6,7,3] => [[1,2,3,4,6,7],[5],[8]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [1,2,4,7,5,6,8,3] => [[1,2,3,4,6,7],[5],[8]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,6,4,8,3] => [1,2,8,6,5,7,4,3] => [[1,2,3,6],[4],[5],[7],[8]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [1,2,4,5,6,3,7,8] => [[1,2,3,4,5,7,8],[6]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,5,4,3,8,7] => [1,2,4,5,6,3,8,7] => [[1,2,3,4,5,7],[6,8]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [1,2,8,5,6,4,7,3] => [[1,2,3,5,7],[4],[6],[8]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,6,5,7,4,8,3] => [1,2,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,5,7,8,4,3] => [1,2,4,8,6,5,7,3] => [[1,2,3,4,7],[5],[6],[8]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => [1,2,4,7,6,5,8,3] => [[1,2,3,4,7],[5],[6],[8]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,6,7,5,8,4,3] => [1,2,4,8,7,6,5,3] => [[1,2,3,4],[5],[6],[7],[8]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [1,2,4,5,8,6,7,3] => [[1,2,3,4,5,7],[6],[8]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [1,2,4,5,6,7,3,8] => [[1,2,3,4,5,6,8],[7]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [1,2,8,5,6,7,4,3] => [[1,2,3,5,6],[4],[7],[8]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [1,2,4,5,8,7,6,3] => [[1,2,3,4,5],[6],[7],[8]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [1,2,4,5,6,8,7,3] => [[1,2,3,4,5,6],[7],[8]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [1,2,4,5,6,7,8,3] => [[1,2,3,4,5,6,7],[8]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,7,6] => [[1,2,4,5,6],[3,7],[8]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [1,3,2,4,5,7,8,6] => [[1,2,4,5,6,7],[3,8]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [[1,2,4,5,7,8],[3,6]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,2,4,6,7,5,8] => [1,3,2,4,7,6,5,8] => [[1,2,4,5,8],[3,6],[7]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,6,7,5] => [[1,2,4,5,7],[3,6],[8]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [1,3,2,4,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [1,3,2,4,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,7,8,6,5] => [1,3,2,4,6,8,7,5] => [[1,2,4,5,6],[3,7],[8]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [1,3,2,4,6,7,8,5] => [[1,2,4,5,6,7],[3,8]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,7,6] => [[1,2,4,6],[3,5,7],[8]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [1,3,2,5,4,7,8,6] => [[1,2,4,6,7],[3,5,8]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [1,3,2,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [1,3,2,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [1,3,2,7,5,6,8,4] => [[1,2,4,6,7],[3,5],[8]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [1,3,2,6,5,7,4,8] => [[1,2,4,6,8],[3,5],[7]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [1,3,2,8,5,7,6,4] => [[1,2,4,6],[3,5],[7],[8]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [1,3,2,6,5,8,7,4] => [[1,2,4,6],[3,5,7],[8]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [1,3,2,6,5,7,8,4] => [[1,2,4,6,7],[3,5],[8]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [1,3,2,5,6,4,7,8] => [[1,2,4,5,7,8],[3,6]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [1,3,2,5,6,4,8,7] => [[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [1,3,2,7,6,5,4,8] => [[1,2,4,8],[3,5],[6],[7]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [1,3,2,8,6,5,7,4] => [[1,2,4,7],[3,5],[6],[8]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [1,3,2,7,6,5,8,4] => [[1,2,4,7],[3,5],[6],[8]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,5,4,8] => [1,3,2,5,7,6,4,8] => [[1,2,4,5,8],[3,6],[7]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [1,3,2,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [1,3,2,5,6,7,4,8] => [[1,2,4,5,6,8],[3,7]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [1,3,2,8,6,7,5,4] => [[1,2,4,6],[3,5],[7],[8]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => [1,3,2,5,8,7,6,4] => [[1,2,4,5],[3,6],[7],[8]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,7,8,6,5,4] => [1,3,2,5,6,8,7,4] => [[1,2,4,5,6],[3,7],[8]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [1,3,2,5,6,7,8,4] => [[1,2,4,5,6,7],[3,8]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => [[1,2,5,6,7],[3,8],[4]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [1,4,3,2,5,7,6,8] => [[1,2,5,6,8],[3,7],[4]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [1,4,3,2,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [1,4,3,2,5,7,8,6] => [[1,2,5,6,7],[3,8],[4]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [[1,2,5,8],[3,6],[4,7]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [1,4,3,2,7,6,8,5] => [[1,2,5,7],[3,6],[4,8]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,4,2,7,6,5,8] => [1,4,3,2,6,7,5,8] => [[1,2,5,6,8],[3,7],[4]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [1,4,3,2,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => [1,4,3,2,6,8,7,5] => [[1,2,5,6],[3,7],[4,8]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [1,4,3,2,6,7,8,5] => [[1,2,5,6,7],[3,8],[4]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [1,5,3,4,2,6,7,8] => [[1,2,4,6,7,8],[3],[5]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [1,5,3,4,2,8,7,6] => [[1,2,4,6],[3,7],[5,8]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [1,5,3,4,2,7,8,6] => [[1,2,4,6,7],[3,8],[5]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [1,6,3,4,5,2,7,8] => [[1,2,4,5,7,8],[3],[6]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [1,7,3,4,5,6,2,8] => [[1,2,4,5,6,8],[3],[7]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [1,8,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3],[8]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [1,7,3,4,5,6,8,2] => [[1,2,4,5,6,7],[3],[8]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [1,6,3,4,5,8,7,2] => [[1,2,4,5,6],[3,7],[8]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,5,2,8,7] => [1,5,3,4,6,2,8,7] => [[1,2,4,5,7],[3,8],[6]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [1,5,3,4,8,6,7,2] => [[1,2,4,5,7],[3,6],[8]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [1,8,3,4,6,7,5,2] => [[1,2,4,5,6],[3],[7],[8]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [1,5,3,4,6,7,8,2] => [[1,2,4,5,6,7],[3],[8]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [1,4,3,5,2,7,6,8] => [[1,2,4,6,8],[3,7],[5]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,4,6,2,7,8] => [1,6,3,5,4,2,7,8] => [[1,2,4,7,8],[3],[5],[6]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,4,6,7,2,8] => [1,7,3,5,4,6,2,8] => [[1,2,4,6,8],[3],[5],[7]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [1,8,3,5,4,6,7,2] => [[1,2,4,6,7],[3],[5],[8]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,4,7,8,6,2] => [1,6,3,5,4,8,7,2] => [[1,2,4,6],[3,7],[5],[8]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => [1,4,3,6,5,2,7,8] => [[1,2,4,7,8],[3,5],[6]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,4,7,2,8] => [1,7,3,6,5,4,2,8] => [[1,2,4,8],[3],[5],[6],[7]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,5,6,4,7,8,2] => [1,8,3,6,5,4,7,2] => [[1,2,4,7],[3],[5],[6],[8]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,5,6,4,8,7,2] => [1,7,3,6,5,4,8,2] => [[1,2,4,7],[3],[5],[6],[8]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,4,8,2] => [1,8,3,7,5,6,4,2] => [[1,2,4,6],[3],[5],[7],[8]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [1,4,3,8,5,6,7,2] => [[1,2,4,6,7],[3,5],[8]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [1,4,3,6,5,7,2,8] => [[1,2,4,6,8],[3,5],[7]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,6,8,4,2] => [1,4,3,8,5,7,6,2] => [[1,2,4,6],[3,5],[7],[8]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [1,4,3,6,5,8,7,2] => [[1,2,4,6],[3,5,7],[8]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [1,4,3,6,5,7,8,2] => [[1,2,4,6,7],[3,5],[8]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,5,4,2,7,8] => [1,4,3,5,6,2,7,8] => [[1,2,4,5,7,8],[3],[6]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => [1,8,3,7,6,5,4,2] => [[1,2,4],[3],[5],[6],[7],[8]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [1,4,3,8,6,5,7,2] => [[1,2,4,7],[3,5],[6],[8]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,5,4,2,8] => [1,4,3,5,7,6,2,8] => [[1,2,4,5,8],[3,6],[7]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [1,4,3,8,7,6,5,2] => [[1,2,4],[3,5],[6],[7],[8]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [1,4,3,5,8,6,7,2] => [[1,2,4,5,7],[3,6],[8]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,7,6,5,8,4,2] => [1,4,3,8,6,7,5,2] => [[1,2,4,6],[3,5],[7],[8]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,7,6,8,5,4,2] => [1,4,3,5,8,7,6,2] => [[1,2,4,5],[3,6],[7],[8]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [1,4,3,5,6,7,8,2] => [[1,2,4,5,6,7],[3],[8]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [1,3,4,2,5,6,7,8] => [[1,2,3,5,6,7,8],[4]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [1,3,4,2,5,6,8,7] => [[1,2,3,5,6,7],[4,8]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [1,3,4,2,5,7,6,8] => [[1,2,3,5,6,8],[4,7]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [1,3,4,2,5,7,8,6] => [[1,2,3,5,6,7],[4,8]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,3,2,6,5,8,7] => [1,3,4,2,6,5,8,7] => [[1,2,3,5,7],[4,6,8]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [1,3,4,2,8,6,7,5] => [[1,2,3,5,7],[4,6],[8]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [1,3,4,2,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [1,3,4,2,6,7,5,8] => [[1,2,3,5,6,8],[4,7]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [1,3,4,2,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,7,8,6,5] => [1,3,4,2,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [1,3,4,2,6,7,8,5] => [[1,2,3,5,6,7],[4,8]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [1,5,4,3,2,6,7,8] => [[1,2,6,7,8],[3],[4],[5]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [1,5,4,3,2,7,6,8] => [[1,2,6,8],[3,7],[4],[5]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3,5,2,7,8,6] => [1,5,4,3,2,8,7,6] => [[1,2,6],[3,7],[4,8],[5]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => [1,5,4,3,2,7,8,6] => [[1,2,6,7],[3,8],[4],[5]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [1,6,4,3,5,2,7,8] => [[1,2,5,7,8],[3],[4],[6]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [1,8,4,3,5,6,7,2] => [[1,2,5,6,7],[3],[4],[8]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,3,5,7,6,8,2] => [1,8,4,3,5,7,6,2] => [[1,2,5,6],[3,7],[4],[8]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,7,8,6,2] => [1,6,4,3,5,8,7,2] => [[1,2,5,6],[3,7],[4],[8]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [1,5,4,3,6,2,7,8] => [[1,2,5,7,8],[3],[4],[6]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [1,8,4,3,6,5,7,2] => [[1,2,5,7],[3,6],[4],[8]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [1,7,4,3,6,5,8,2] => [[1,2,5,7],[3,6],[4],[8]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,3,7,6,5,2,8] => [1,5,4,3,6,7,2,8] => [[1,2,5,6,8],[3],[4],[7]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [1,5,4,3,8,7,6,2] => [[1,2,5],[3,6],[4,7],[8]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [1,5,4,3,6,8,7,2] => [[1,2,5,6],[3,7],[4],[8]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [1,5,4,3,6,7,8,2] => [[1,2,5,6,7],[3],[4],[8]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,5,3,2,6,8,7] => [1,3,5,4,2,6,8,7] => [[1,2,3,6,7],[4,8],[5]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,3,2,7,6,8] => [1,3,5,4,2,7,6,8] => [[1,2,3,6,8],[4,7],[5]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => [1,3,5,4,2,7,8,6] => [[1,2,3,6,7],[4,8],[5]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,3,6,2,7,8] => [1,6,5,4,3,2,7,8] => [[1,2,7,8],[3],[4],[5],[6]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,3,6,7,2,8] => [1,7,5,4,3,6,2,8] => [[1,2,6,8],[3],[4],[5],[7]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [1,8,5,4,3,6,7,2] => [[1,2,6,7],[3],[4],[5],[8]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,3,6,8,7,2] => [1,7,5,4,3,6,8,2] => [[1,2,6,7],[3],[4],[5],[8]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,3,7,8,6,2] => [1,6,5,4,3,8,7,2] => [[1,2,6],[3,7],[4],[5],[8]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,4,5,6,3,2,8,7] => [1,3,6,4,5,2,8,7] => [[1,2,3,5,7],[4,8],[6]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,3,7,2,8] => [1,7,6,4,5,3,2,8] => [[1,2,5,8],[3],[4],[6],[7]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,5,6,3,7,8,2] => [1,8,6,4,5,3,7,2] => [[1,2,5,7],[3],[4],[6],[8]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [1,3,7,4,5,6,2,8] => [[1,2,3,5,6,8],[4],[7]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [1,8,7,4,5,6,3,2] => [[1,2,5,6],[3],[4],[7],[8]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [1,3,8,4,5,6,7,2] => [[1,2,3,5,6,7],[4],[8]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,4,5,7,6,3,2,8] => [1,3,6,4,5,7,2,8] => [[1,2,3,5,6,8],[4],[7]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,5,7,6,3,8,2] => [1,8,6,4,5,7,3,2] => [[1,2,5,6],[3],[4],[7],[8]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,4,5,7,8,6,3,2] => [1,3,6,4,5,8,7,2] => [[1,2,3,5,6],[4,7],[8]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,7,6,3,2] => [1,3,6,4,5,7,8,2] => [[1,2,3,5,6,7],[4],[8]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,6,5,3,7,8,2] => [1,8,5,4,6,3,7,2] => [[1,2,5,7],[3],[4],[6],[8]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,5,3,2,8] => [1,3,5,4,7,6,2,8] => [[1,2,3,5,8],[4,6],[7]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,5,3,8,2] => [1,8,5,4,7,6,3,2] => [[1,2,5],[3,6],[4],[7],[8]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [1,3,5,4,7,6,8,2] => [[1,2,3,5,7],[4,6],[8]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,7,6,5,3,8,2] => [1,8,5,4,6,7,3,2] => [[1,2,5,6],[3],[4],[7],[8]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,4,7,6,8,5,3,2] => [1,3,5,4,8,7,6,2] => [[1,2,3,5],[4,6],[7],[8]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [1,3,4,5,2,6,7,8] => [[1,2,3,4,6,7,8],[5]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [1,3,4,5,2,7,6,8] => [[1,2,3,4,6,8],[5,7]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [1,3,4,5,2,8,7,6] => [[1,2,3,4,6],[5,7],[8]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [1,3,4,5,2,7,8,6] => [[1,2,3,4,6,7],[5,8]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [1,6,4,5,3,2,7,8] => [[1,2,4,7,8],[3],[5],[6]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [1,8,4,5,3,6,7,2] => [[1,2,4,6,7],[3],[5],[8]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [1,7,4,5,3,6,8,2] => [[1,2,4,6,7],[3],[5],[8]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,4,3,7,8,6,2] => [1,6,4,5,3,8,7,2] => [[1,2,4,6],[3,7],[5],[8]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,4,6,3,2,8,7] => [1,3,6,5,4,2,8,7] => [[1,2,3,7],[4,8],[5],[6]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => [1,7,6,5,4,3,2,8] => [[1,2,8],[3],[4],[5],[6],[7]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => [1,8,6,5,4,3,7,2] => [[1,2,7],[3],[4],[5],[6],[8]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,4,6,3,8,7,2] => [1,7,6,5,4,3,8,2] => [[1,2,7],[3],[4],[5],[6],[8]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [1,8,7,5,4,6,3,2] => [[1,2,6],[3],[4],[5],[7],[8]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [1,3,8,5,4,6,7,2] => [[1,2,3,6,7],[4],[5],[8]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,4,7,6,3,2,8] => [1,3,6,5,4,7,2,8] => [[1,2,3,6,8],[4],[5],[7]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,4,7,6,3,8,2] => [1,8,6,5,4,7,3,2] => [[1,2,6],[3],[4],[5],[7],[8]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,4,7,6,8,3,2] => [1,3,8,5,4,7,6,2] => [[1,2,3,6],[4,7],[5],[8]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,4,7,8,6,3,2] => [1,3,6,5,4,8,7,2] => [[1,2,3,6],[4,7],[5],[8]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,5,6,4,3,7,2,8] => [1,7,4,6,5,3,2,8] => [[1,2,4,8],[3],[5],[6],[7]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,4,7,3,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,5,6,7,4,8,3,2] => [1,3,8,7,5,6,4,2] => [[1,2,3,6],[4],[5],[7],[8]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [1,3,4,8,5,6,7,2] => [[1,2,3,4,6,7],[5],[8]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,7,6,4,3,8,2] => [1,8,4,6,5,7,3,2] => [[1,2,4,6],[3],[5],[7],[8]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [1,3,4,6,5,7,8,2] => [[1,2,3,4,6,7],[5],[8]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [1,3,4,5,6,2,7,8] => [[1,2,3,4,5,7,8],[6]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [1,3,4,5,6,2,8,7] => [[1,2,3,4,5,7],[6,8]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [1,8,4,5,6,3,7,2] => [[1,2,4,5,7],[3],[6],[8]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [1,7,4,5,6,3,8,2] => [[1,2,4,5,7],[3],[6],[8]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [1,8,4,7,6,5,3,2] => [[1,2,4],[3],[5],[6],[7],[8]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,5,7,4,8,3,2] => [1,3,8,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7],[8]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,5,8,7,4,3,2] => [1,3,4,7,6,5,8,2] => [[1,2,3,4,7],[5],[6],[8]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => [1,3,4,5,7,6,2,8] => [[1,2,3,4,5,8],[6],[7]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,6,7,5,4,8,3,2] => [1,3,8,5,7,6,4,2] => [[1,2,3,5],[4],[6],[7],[8]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [1,3,4,8,7,6,5,2] => [[1,2,3,4],[5],[6],[7],[8]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [1,3,4,5,8,6,7,2] => [[1,2,3,4,5,7],[6],[8]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [1,3,4,5,7,6,8,2] => [[1,2,3,4,5,7],[6],[8]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [1,3,4,5,6,7,2,8] => [[1,2,3,4,5,6,8],[7]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [1,8,4,5,6,7,3,2] => [[1,2,4,5,6],[3],[7],[8]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [1,3,8,5,6,7,4,2] => [[1,2,3,5,6],[4],[7],[8]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [1,3,4,5,8,7,6,2] => [[1,2,3,4,5],[6],[7],[8]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [1,3,4,5,6,8,7,2] => [[1,2,3,4,5,6],[7],[8]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,2] => [[1,2,3,4,5,6,7],[8]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,7,6] => [[1,3,4,5,6],[2,7],[8]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [2,1,3,4,5,7,8,6] => [[1,3,4,5,6,7],[2,8]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [[1,3,4,5,7,8],[2,6]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,6,7,5] => [[1,3,4,5,7],[2,6],[8]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,4,6,8,7,5] => [2,1,3,4,7,6,8,5] => [[1,3,4,5,7],[2,6],[8]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [2,1,3,4,8,7,6,5] => [[1,3,4,5],[2,6],[7],[8]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [2,1,3,4,6,7,8,5] => [[1,3,4,5,6,7],[2,8]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [2,1,3,5,4,6,8,7] => [[1,3,4,6,7],[2,5,8]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [2,1,3,5,4,8,7,6] => [[1,3,4,6],[2,5,7],[8]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [2,1,3,5,4,7,8,6] => [[1,3,4,6,7],[2,5,8]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,5,6,7,4] => [[1,3,4,6,7],[2,5],[8]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => [2,1,3,8,5,7,6,4] => [[1,3,4,6],[2,5],[7],[8]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,7,8,6,4] => [2,1,3,6,5,8,7,4] => [[1,3,4,6],[2,5,7],[8]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [2,1,3,5,6,4,8,7] => [[1,3,4,5,7],[2,6,8]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,6,5,7,8,4] => [2,1,3,8,6,5,7,4] => [[1,3,4,7],[2,5],[6],[8]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,6,7,5,8,4] => [2,1,3,8,7,6,5,4] => [[1,3,4],[2,5],[6],[7],[8]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,5,4] => [2,1,3,5,8,6,7,4] => [[1,3,4,5,7],[2,6],[8]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,7,6,5,8,4] => [2,1,3,8,6,7,5,4] => [[1,3,4,6],[2,5],[7],[8]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [2,1,3,5,6,7,8,4] => [[1,3,4,5,6,7],[2,8]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [[1,3,5,6,7],[2,4,8]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,7,6] => [[1,3,5,6],[2,4,7],[8]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [2,1,4,3,5,7,8,6] => [[1,3,5,6,7],[2,4,8]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [[1,3,5,7,8],[2,4,6]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [[1,3,5,7],[2,4,6],[8]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [2,1,4,3,7,6,8,5] => [[1,3,5,7],[2,4,6],[8]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [2,1,4,3,6,8,7,5] => [[1,3,5,6],[2,4,7],[8]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [2,1,4,3,6,7,8,5] => [[1,3,5,6,7],[2,4,8]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [2,1,5,4,3,6,7,8] => [[1,3,6,7,8],[2,4],[5]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3,7,8,6] => [2,1,5,4,3,8,7,6] => [[1,3,6],[2,4,7],[5,8]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [[1,3,5,7],[2,4,8],[6]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,1,8,4,5,6,7,3] => [[1,3,5,6,7],[2,4],[8]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,6,8,3] => [2,1,8,4,5,7,6,3] => [[1,3,5,6],[2,4],[7],[8]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [2,1,6,4,5,8,7,3] => [[1,3,5,6],[2,4,7],[8]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [2,1,6,4,5,7,8,3] => [[1,3,5,6,7],[2,4],[8]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [2,1,5,4,6,3,8,7] => [[1,3,5,7],[2,4,8],[6]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,5,7,8,3] => [2,1,8,4,6,5,7,3] => [[1,3,5,7],[2,4],[6],[8]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [2,1,7,4,6,5,8,3] => [[1,3,5,7],[2,4],[6],[8]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => [2,1,8,4,7,6,5,3] => [[1,3,5],[2,4],[6],[7],[8]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,5,3] => [2,1,5,4,8,6,7,3] => [[1,3,5,7],[2,4,6],[8]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [2,1,5,4,7,6,8,3] => [[1,3,5,7],[2,4,6],[8]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [2,1,8,4,6,7,5,3] => [[1,3,5,6],[2,4],[7],[8]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,7,6,8,5,3] => [2,1,5,4,8,7,6,3] => [[1,3,5],[2,4,6],[7],[8]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => [2,1,5,4,6,8,7,3] => [[1,3,5,6],[2,4,7],[8]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [2,1,5,4,6,7,8,3] => [[1,3,5,6,7],[2,4],[8]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [2,1,4,5,3,6,7,8] => [[1,3,4,6,7,8],[2,5]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [2,1,4,5,3,6,8,7] => [[1,3,4,6,7],[2,5,8]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,5,4,3,7,8,6] => [2,1,4,5,3,8,7,6] => [[1,3,4,6],[2,5,7],[8]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [2,1,6,5,4,3,8,7] => [[1,3,7],[2,4,8],[5],[6]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [2,1,8,5,4,6,7,3] => [[1,3,6,7],[2,4],[5],[8]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [2,1,8,5,4,7,6,3] => [[1,3,6],[2,4,7],[5],[8]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => [2,1,6,5,4,8,7,3] => [[1,3,6],[2,4,7],[5],[8]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,4,3,7,8] => [2,1,4,6,5,3,7,8] => [[1,3,4,7,8],[2,5],[6]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [2,1,4,6,5,3,8,7] => [[1,3,4,7],[2,5,8],[6]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,5,6,4,7,3,8] => [2,1,7,6,5,4,3,8] => [[1,3,8],[2,4],[5],[6],[7]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => [2,1,8,6,5,4,7,3] => [[1,3,7],[2,4],[5],[6],[8]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [2,1,7,6,5,4,8,3] => [[1,3,7],[2,4],[5],[6],[8]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => [2,1,8,7,5,6,4,3] => [[1,3,6],[2,4],[5],[7],[8]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [2,1,4,8,5,6,7,3] => [[1,3,4,6,7],[2,5],[8]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => [2,1,8,6,5,7,4,3] => [[1,3,6],[2,4],[5],[7],[8]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [2,1,4,8,5,7,6,3] => [[1,3,4,6],[2,5],[7],[8]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [2,1,4,6,5,8,7,3] => [[1,3,4,6],[2,5,7],[8]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [2,1,4,5,6,3,8,7] => [[1,3,4,5,7],[2,6,8]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,5,4,7,8,3] => [2,1,8,5,6,4,7,3] => [[1,3,5,7],[2,4],[6],[8]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [2,1,7,5,6,4,8,3] => [[1,3,5,7],[2,4],[6],[8]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [2,1,4,8,6,5,7,3] => [[1,3,4,7],[2,5],[6],[8]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [2,1,4,7,6,5,8,3] => [[1,3,4,7],[2,5],[6],[8]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,5,4,8,3] => [2,1,8,5,7,6,4,3] => [[1,3,5],[2,4],[6],[7],[8]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [2,1,4,8,7,6,5,3] => [[1,3,4],[2,5],[6],[7],[8]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [2,1,4,5,8,6,7,3] => [[1,3,4,5,7],[2,6],[8]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [2,1,4,5,6,7,3,8] => [[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [2,1,8,5,6,7,4,3] => [[1,3,5,6],[2,4],[7],[8]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [2,1,4,8,6,7,5,3] => [[1,3,4,6],[2,5],[7],[8]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [2,1,4,5,8,7,6,3] => [[1,3,4,5],[2,6],[7],[8]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,6,5,4,3] => [2,1,4,5,6,8,7,3] => [[1,3,4,5,6],[2,7],[8]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3] => [[1,3,4,5,6,7],[2,8]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,7,6] => [3,2,1,4,5,7,8,6] => [[1,4,5,6,7],[2,8],[3]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => [[1,4,5,7],[2,6],[3,8]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,3,1,4,6,8,7,5] => [3,2,1,4,7,6,8,5] => [[1,4,5,7],[2,6],[3,8]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [3,2,1,4,8,7,6,5] => [[1,4,5],[2,6],[3,7],[8]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => [3,2,1,4,6,8,7,5] => [[1,4,5,6],[2,7],[3,8]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [3,2,1,4,6,7,8,5] => [[1,4,5,6,7],[2,8],[3]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [3,2,1,5,4,6,7,8] => [[1,4,6,7,8],[2,5],[3]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [[1,4,6,8],[2,5,7],[3]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [3,2,1,6,5,4,7,8] => [[1,4,7,8],[2,5],[3,6]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,6,4,8,7] => [3,2,1,6,5,4,8,7] => [[1,4,7],[2,5,8],[3,6]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [[1,4,6,7],[2,5],[3,8]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,7,4] => [3,2,1,7,5,6,8,4] => [[1,4,6,7],[2,5],[3,8]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [3,2,1,8,5,7,6,4] => [[1,4,6],[2,5],[3,7],[8]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => [3,2,1,6,5,8,7,4] => [[1,4,6],[2,5,7],[3,8]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,3,1,5,8,7,6,4] => [3,2,1,6,5,7,8,4] => [[1,4,6,7],[2,5],[3,8]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [3,2,1,5,6,4,7,8] => [[1,4,5,7,8],[2,6],[3]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [3,2,1,7,6,5,4,8] => [[1,4,8],[2,5],[3,6],[7]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,5,7,8,4] => [3,2,1,8,6,5,7,4] => [[1,4,7],[2,5],[3,6],[8]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [3,2,1,7,6,5,8,4] => [[1,4,7],[2,5],[3,6],[8]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,6,7,5,4,8] => [3,2,1,5,7,6,4,8] => [[1,4,5,8],[2,6],[3,7]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,5,8,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => [3,2,1,5,8,6,7,4] => [[1,4,5,7],[2,6],[3,8]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,7,5,4] => [3,2,1,5,7,6,8,4] => [[1,4,5,7],[2,6],[3,8]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [3,2,1,8,6,7,5,4] => [[1,4,6],[2,5],[3,7],[8]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => [3,2,1,5,8,7,6,4] => [[1,4,5],[2,6],[3,7],[8]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [3,2,1,5,6,8,7,4] => [[1,4,5,6],[2,7],[3,8]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [3,2,1,5,6,7,8,4] => [[1,4,5,6,7],[2,8],[3]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [4,2,3,1,5,7,6,8] => [[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [4,2,3,1,5,7,8,6] => [[1,3,5,6,7],[2,8],[4]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [4,2,3,1,7,6,8,5] => [[1,3,5,7],[2,6],[4,8]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [4,2,3,1,8,7,6,5] => [[1,3,5],[2,6],[4,7],[8]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [4,2,3,1,6,8,7,5] => [[1,3,5,6],[2,7],[4,8]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,2,3,1,6,7,8,5] => [[1,3,5,6,7],[2,8],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [5,2,3,4,1,6,8,7] => [[1,3,4,6,7],[2,8],[5]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [5,2,3,4,1,7,8,6] => [[1,3,4,6,7],[2,8],[5]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => [[1,3,4,5,7],[2,8],[6]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [7,2,3,4,5,6,8,1] => [[1,3,4,5,6,7],[2],[8]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [6,2,3,4,5,7,1,8] => [[1,3,4,5,6,8],[2],[7]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [8,2,3,4,5,7,6,1] => [[1,3,4,5,6],[2],[7],[8]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [6,2,3,4,5,8,7,1] => [[1,3,4,5,6],[2,7],[8]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [6,2,3,4,5,7,8,1] => [[1,3,4,5,6,7],[2],[8]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [5,2,3,4,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,4,6,5,1,8,7] => [5,2,3,4,6,1,8,7] => [[1,3,4,5,7],[2,8],[6]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [7,2,3,4,6,5,1,8] => [[1,3,4,5,8],[2],[6],[7]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => [5,2,3,4,7,6,1,8] => [[1,3,4,5,8],[2,6],[7]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [5,2,3,4,8,6,7,1] => [[1,3,4,5,7],[2,6],[8]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [5,2,3,4,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => [5,2,3,4,8,7,6,1] => [[1,3,4,5],[2,6],[7],[8]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [5,2,3,4,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [4,2,3,5,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [4,2,3,5,1,6,8,7] => [[1,3,4,6,7],[2,8],[5]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,3,5,4,1,7,8,6] => [4,2,3,5,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [4,2,3,5,1,7,8,6] => [[1,3,4,6,7],[2,8],[5]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [6,2,3,5,4,1,7,8] => [[1,3,4,7,8],[2],[5],[6]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [7,2,3,5,4,6,1,8] => [[1,3,4,6,8],[2],[5],[7]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [8,2,3,5,4,6,7,1] => [[1,3,4,6,7],[2],[5],[8]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,3,5,4,7,6,1,8] => [6,2,3,5,4,7,1,8] => [[1,3,4,6,8],[2],[5],[7]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [6,2,3,5,4,7,8,1] => [[1,3,4,6,7],[2],[5],[8]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,4,7,1,8] => [7,2,3,6,5,4,1,8] => [[1,3,4,8],[2],[5],[6],[7]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => [8,2,3,6,5,4,7,1] => [[1,3,4,7],[2],[5],[6],[8]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,4,1,8] => [4,2,3,7,5,6,1,8] => [[1,3,4,6,8],[2,5],[7]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [8,2,3,7,5,6,4,1] => [[1,3,4,6],[2],[5],[7],[8]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [4,2,3,8,5,6,7,1] => [[1,3,4,6,7],[2,5],[8]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [4,2,3,7,5,6,8,1] => [[1,3,4,6,7],[2,5],[8]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,6,8,4,1] => [4,2,3,8,5,7,6,1] => [[1,3,4,6],[2,5],[7],[8]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [4,2,3,6,5,8,7,1] => [[1,3,4,6],[2,5,7],[8]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [4,2,3,5,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [4,2,3,5,6,1,8,7] => [[1,3,4,5,7],[2,8],[6]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => [4,2,3,7,6,5,8,1] => [[1,3,4,7],[2,5],[6],[8]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,6,7,5,4,8,1] => [8,2,3,5,7,6,4,1] => [[1,3,4,5],[2],[6],[7],[8]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,6,7,5,8,4,1] => [4,2,3,8,7,6,5,1] => [[1,3,4],[2,5],[6],[7],[8]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [4,2,3,5,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [8,2,3,5,6,7,4,1] => [[1,3,4,5,6],[2],[7],[8]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,7,6,8,5,4,1] => [4,2,3,5,8,7,6,1] => [[1,3,4,5],[2,6],[7],[8]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,7,8,6,5,4,1] => [4,2,3,5,6,8,7,1] => [[1,3,4,5,6],[2,7],[8]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [4,2,3,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,4,3,1,5,6,8,7] => [3,2,4,1,5,6,8,7] => [[1,3,5,6,7],[2,8],[4]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,4,3,1,5,7,6,8] => [3,2,4,1,5,7,6,8] => [[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,4,3,1,5,7,8,6] => [3,2,4,1,5,8,7,6] => [[1,3,5,6],[2,7],[4,8]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [3,2,4,1,5,7,8,6] => [[1,3,5,6,7],[2,8],[4]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [3,2,4,1,6,5,7,8] => [[1,3,5,7,8],[2,6],[4]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [3,2,4,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [3,2,4,1,7,6,8,5] => [[1,3,5,7],[2,6],[4,8]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [3,2,4,1,8,7,6,5] => [[1,3,5],[2,6],[4,7],[8]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [3,2,4,1,6,8,7,5] => [[1,3,5,6],[2,7],[4,8]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [3,2,4,1,6,7,8,5] => [[1,3,5,6,7],[2,8],[4]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [5,2,4,3,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [5,2,4,3,1,6,8,7] => [[1,3,6,7],[2,8],[4],[5]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [5,2,4,3,1,7,6,8] => [[1,3,6,8],[2,7],[4],[5]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [5,2,4,3,1,8,7,6] => [[1,3,6],[2,7],[4,8],[5]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [6,2,4,3,5,1,8,7] => [[1,3,5,7],[2,8],[4],[6]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [5,2,4,3,6,1,7,8] => [[1,3,5,7,8],[2],[4],[6]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [5,2,4,3,6,1,8,7] => [[1,3,5,7],[2,8],[4],[6]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [7,2,4,3,6,5,1,8] => [[1,3,5,8],[2,6],[4],[7]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [8,2,4,3,6,5,7,1] => [[1,3,5,7],[2,6],[4],[8]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [7,2,4,3,6,5,8,1] => [[1,3,5,7],[2,6],[4],[8]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [5,2,4,3,7,6,8,1] => [[1,3,5,7],[2,6],[4],[8]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,4,3,7,6,5,1,8] => [5,2,4,3,6,7,1,8] => [[1,3,5,6,8],[2],[4],[7]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [8,2,4,3,6,7,5,1] => [[1,3,5,6],[2,7],[4],[8]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,7,6,8,5,1] => [5,2,4,3,8,7,6,1] => [[1,3,5],[2,6],[4,7],[8]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => [3,2,5,4,1,6,7,8] => [[1,3,6,7,8],[2,4],[5]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,4,5,3,1,6,8,7] => [3,2,5,4,1,6,8,7] => [[1,3,6,7],[2,4,8],[5]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,3,1,7,6,8] => [3,2,5,4,1,7,6,8] => [[1,3,6,8],[2,4,7],[5]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => [3,2,5,4,1,8,7,6] => [[1,3,6],[2,4,7],[5,8]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [3,2,5,4,1,7,8,6] => [[1,3,6,7],[2,4,8],[5]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,3,6,1,8,7] => [6,2,5,4,3,1,8,7] => [[1,3,7],[2,8],[4],[5],[6]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,4,5,3,6,7,1,8] => [7,2,5,4,3,6,1,8] => [[1,3,6,8],[2],[4],[5],[7]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [8,2,5,4,3,6,7,1] => [[1,3,6,7],[2],[4],[5],[8]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,4,5,3,7,6,8,1] => [8,2,5,4,3,7,6,1] => [[1,3,6],[2,7],[4],[5],[8]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,4,5,3,8,7,6,1] => [6,2,5,4,3,7,8,1] => [[1,3,6,7],[2],[4],[5],[8]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,4,5,6,3,1,8,7] => [3,2,6,4,5,1,8,7] => [[1,3,5,7],[2,4,8],[6]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,3,7,1,8] => [7,2,6,4,5,3,1,8] => [[1,3,5,8],[2],[4],[6],[7]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => [8,2,6,4,5,3,7,1] => [[1,3,5,7],[2],[4],[6],[8]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => [7,2,6,4,5,3,8,1] => [[1,3,5,7],[2],[4],[6],[8]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => [3,2,7,4,5,6,1,8] => [[1,3,5,6,8],[2,4],[7]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => [8,2,7,4,5,6,3,1] => [[1,3,5,6],[2],[4],[7],[8]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => [3,2,8,4,5,6,7,1] => [[1,3,5,6,7],[2,4],[8]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,4,5,7,6,3,8,1] => [8,2,6,4,5,7,3,1] => [[1,3,5,6],[2],[4],[7],[8]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [3,2,5,4,6,1,8,7] => [[1,3,5,7],[2,4,8],[6]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [7,2,5,4,6,3,8,1] => [[1,3,5,7],[2],[4],[6],[8]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [8,2,7,4,6,5,3,1] => [[1,3,5],[2],[4],[6],[7],[8]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => [3,2,8,4,6,5,7,1] => [[1,3,5,7],[2,4],[6],[8]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [3,2,7,4,6,5,8,1] => [[1,3,5,7],[2,4],[6],[8]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [3,2,5,4,7,6,1,8] => [[1,3,5,8],[2,4,6],[7]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => [8,2,5,4,7,6,3,1] => [[1,3,5],[2,6],[4],[7],[8]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [3,2,5,4,8,6,7,1] => [[1,3,5,7],[2,4,6],[8]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [3,2,5,4,7,6,8,1] => [[1,3,5,7],[2,4,6],[8]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => [3,2,5,4,6,8,7,1] => [[1,3,5,6],[2,4,7],[8]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [3,2,5,4,6,7,8,1] => [[1,3,5,6,7],[2,4],[8]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [3,2,4,5,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [3,2,4,5,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,5,4,3,6,1,7,8] => [6,2,4,5,3,1,7,8] => [[1,3,4,7,8],[2],[5],[6]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [7,2,4,5,3,6,1,8] => [[1,3,4,6,8],[2],[5],[7]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [7,2,4,5,3,6,8,1] => [[1,3,4,6,7],[2],[5],[8]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [8,2,4,5,3,7,6,1] => [[1,3,4,6],[2,7],[5],[8]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,5,4,6,3,1,8,7] => [3,2,6,5,4,1,8,7] => [[1,3,7],[2,4,8],[5],[6]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,4,6,3,7,8,1] => [8,2,6,5,4,3,7,1] => [[1,3,7],[2],[4],[5],[6],[8]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [3,2,7,5,4,6,1,8] => [[1,3,6,8],[2,4],[5],[7]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [8,2,7,5,4,6,3,1] => [[1,3,6],[2],[4],[5],[7],[8]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,4,6,7,8,3,1] => [3,2,8,5,4,6,7,1] => [[1,3,6,7],[2,4],[5],[8]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,4,7,6,3,1,8] => [3,2,6,5,4,7,1,8] => [[1,3,6,8],[2,4],[5],[7]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,4,7,6,3,8,1] => [8,2,6,5,4,7,3,1] => [[1,3,6],[2],[4],[5],[7],[8]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,4,7,6,8,3,1] => [3,2,8,5,4,7,6,1] => [[1,3,6],[2,4,7],[5],[8]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => [3,2,6,5,4,8,7,1] => [[1,3,6],[2,4,7],[5],[8]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,4,7,3,1,8] => [3,2,7,6,5,4,1,8] => [[1,3,8],[2,4],[5],[6],[7]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,5,6,4,7,3,8,1] => [8,2,7,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7],[8]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => [3,2,7,6,5,4,8,1] => [[1,3,7],[2,4],[5],[6],[8]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => [8,2,4,7,5,6,3,1] => [[1,3,4,6],[2],[5],[7],[8]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => [3,2,8,7,5,6,4,1] => [[1,3,6],[2,4],[5],[7],[8]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [3,2,4,8,5,6,7,1] => [[1,3,4,6,7],[2,5],[8]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,5,6,8,7,4,3,1] => [3,2,4,7,5,6,8,1] => [[1,3,4,6,7],[2,5],[8]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,5,7,6,4,8,3,1] => [3,2,8,6,5,7,4,1] => [[1,3,6],[2,4],[5],[7],[8]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,5,7,8,6,4,3,1] => [3,2,4,6,5,8,7,1] => [[1,3,4,6],[2,5,7],[8]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,5,4,7,8,3,1] => [3,2,8,5,6,4,7,1] => [[1,3,5,7],[2,4],[6],[8]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [3,2,7,5,6,4,8,1] => [[1,3,5,7],[2,4],[6],[8]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => [8,2,4,7,6,5,3,1] => [[1,3,4],[2],[5],[6],[7],[8]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,6,5,7,4,8,3,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,6,5,8,7,4,3,1] => [3,2,4,7,6,5,8,1] => [[1,3,4,7],[2,5],[6],[8]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,6,7,5,4,8,3,1] => [3,2,8,5,7,6,4,1] => [[1,3,5],[2,4],[6],[7],[8]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [3,2,4,8,7,6,5,1] => [[1,3,4],[2,5],[6],[7],[8]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,5,4,3,1] => [3,2,4,5,8,6,7,1] => [[1,3,4,5,7],[2,6],[8]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [3,2,4,5,7,6,8,1] => [[1,3,4,5,7],[2,6],[8]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [3,2,4,5,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [8,2,4,5,6,7,3,1] => [[1,3,4,5,6],[2],[7],[8]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,7,6,5,8,4,3,1] => [3,2,4,8,6,7,5,1] => [[1,3,4,6],[2,5],[7],[8]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [3,2,4,5,6,8,7,1] => [[1,3,4,5,6],[2,7],[8]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [2,3,1,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [2,3,1,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [2,3,1,4,5,7,8,6] => [[1,2,4,5,6,7],[3,8]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,2,1,4,6,5,8,7] => [2,3,1,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [2,3,1,4,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [2,3,1,4,6,7,5,8] => [[1,2,4,5,6,8],[3,7]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [2,3,1,4,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [2,3,1,4,6,7,8,5] => [[1,2,4,5,6,7],[3,8]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [2,3,1,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [2,3,1,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [2,3,1,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,5,6,4,8,7] => [2,3,1,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,5,6,7,4,8] => [2,3,1,7,5,6,4,8] => [[1,2,4,6,8],[3,5],[7]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [2,3,1,8,5,6,7,4] => [[1,2,4,6,7],[3,5],[8]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [2,3,1,6,5,7,4,8] => [[1,2,4,6,8],[3,5],[7]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [2,3,1,6,5,8,7,4] => [[1,2,4,6],[3,5,7],[8]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [2,3,1,5,6,4,7,8] => [[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [2,3,1,7,6,5,8,4] => [[1,2,4,7],[3,5],[6],[8]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [2,3,1,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [2,3,1,5,7,6,8,4] => [[1,2,4,5,7],[3,6],[8]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [2,3,1,5,6,7,4,8] => [[1,2,4,5,6,8],[3,7]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [2,3,1,8,6,7,5,4] => [[1,2,4,6],[3,5],[7],[8]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [2,3,1,5,6,7,8,4] => [[1,2,4,5,6,7],[3,8]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [[1,5,6,7,8],[2],[3],[4]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [4,3,2,1,5,6,8,7] => [[1,5,6,7],[2,8],[3],[4]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [4,3,2,1,5,7,6,8] => [[1,5,6,8],[2,7],[3],[4]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [4,3,2,1,5,8,7,6] => [[1,5,6],[2,7],[3,8],[4]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [4,3,2,1,5,7,8,6] => [[1,5,6,7],[2,8],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [4,3,2,1,6,5,7,8] => [[1,5,7,8],[2,6],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [[1,5,7],[2,6,8],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [4,3,2,1,7,6,5,8] => [[1,5,8],[2,6],[3,7],[4]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [4,3,2,1,8,6,7,5] => [[1,5,7],[2,6],[3,8],[4]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [4,3,2,1,7,6,8,5] => [[1,5,7],[2,6],[3,8],[4]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [4,3,2,1,6,7,5,8] => [[1,5,6,8],[2,7],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [4,3,2,1,6,8,7,5] => [[1,5,6],[2,7],[3,8],[4]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [4,3,2,1,6,7,8,5] => [[1,5,6,7],[2,8],[3],[4]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [5,3,2,4,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [3,2,4,5,1,6,8,7] => [5,3,2,4,1,6,8,7] => [[1,4,6,7],[2,8],[3],[5]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,2,4,5,1,7,6,8] => [5,3,2,4,1,7,6,8] => [[1,4,6,8],[2,7],[3],[5]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,2,4,5,1,7,8,6] => [5,3,2,4,1,8,7,6] => [[1,4,6],[2,7],[3,8],[5]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [8,3,2,4,5,6,7,1] => [[1,4,5,6,7],[2],[3],[8]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [7,3,2,4,5,6,8,1] => [[1,4,5,6,7],[2],[3],[8]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,2,4,5,7,6,1,8] => [6,3,2,4,5,7,1,8] => [[1,4,5,6,8],[2],[3],[7]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,2,4,6,5,1,8,7] => [5,3,2,4,6,1,8,7] => [[1,4,5,7],[2,8],[3],[6]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,6,7,5,1,8] => [5,3,2,4,7,6,1,8] => [[1,4,5,8],[2,6],[3],[7]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [8,3,2,4,6,7,5,1] => [[1,4,5,6],[2,7],[3],[8]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [5,3,2,4,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [4,3,2,5,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [4,3,2,5,1,8,7,6] => [[1,4,6],[2,7],[3,8],[5]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [4,3,2,5,1,7,8,6] => [[1,4,6,7],[2,8],[3],[5]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,5,4,6,1,7,8] => [6,3,2,5,4,1,7,8] => [[1,4,7,8],[2,5],[3],[6]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [6,3,2,5,4,1,8,7] => [[1,4,7],[2,5,8],[3],[6]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,5,4,6,7,1,8] => [7,3,2,5,4,6,1,8] => [[1,4,6,8],[2,5],[3],[7]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [6,3,2,5,4,7,1,8] => [[1,4,6,8],[2,5],[3],[7]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [8,3,2,5,4,7,6,1] => [[1,4,6],[2,5,7],[3],[8]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,7,8,6,1] => [6,3,2,5,4,8,7,1] => [[1,4,6],[2,5,7],[3],[8]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,5,6,4,1,8,7] => [4,3,2,6,5,1,8,7] => [[1,4,7],[2,5,8],[3],[6]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [8,3,2,7,5,6,4,1] => [[1,4,6],[2,5],[3],[7],[8]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [4,3,2,8,5,6,7,1] => [[1,4,6,7],[2,5],[3],[8]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,2,5,6,8,7,4,1] => [4,3,2,7,5,6,8,1] => [[1,4,6,7],[2,5],[3],[8]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,5,7,6,4,1,8] => [4,3,2,6,5,7,1,8] => [[1,4,6,8],[2,5],[3],[7]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => [8,3,2,6,5,7,4,1] => [[1,4,6],[2,5],[3],[7],[8]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,5,7,6,8,4,1] => [4,3,2,8,5,7,6,1] => [[1,4,6],[2,5],[3,7],[8]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,5,7,8,6,4,1] => [4,3,2,6,5,8,7,1] => [[1,4,6],[2,5,7],[3],[8]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,2,5,8,7,6,4,1] => [4,3,2,6,5,7,8,1] => [[1,4,6,7],[2,5],[3],[8]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [4,3,2,5,6,1,8,7] => [[1,4,5,7],[2,8],[3],[6]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [7,3,2,5,6,4,8,1] => [[1,4,5,7],[2,6],[3],[8]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [8,3,2,7,6,5,4,1] => [[1,4],[2,5],[3],[6],[7],[8]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,6,5,8,7,4,1] => [4,3,2,7,6,5,8,1] => [[1,4,7],[2,5],[3,6],[8]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [4,3,2,5,7,6,1,8] => [[1,4,5,8],[2,6],[3],[7]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [8,3,2,5,7,6,4,1] => [[1,4,5],[2,6],[3],[7],[8]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,6,7,5,8,4,1] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => [4,3,2,5,7,6,8,1] => [[1,4,5,7],[2,6],[3],[8]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [4,3,2,5,6,7,1,8] => [[1,4,5,6,8],[2],[3],[7]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [8,3,2,5,6,7,4,1] => [[1,4,5,6],[2,7],[3],[8]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,2,7,6,5,8,4,1] => [4,3,2,8,6,7,5,1] => [[1,4,6],[2,5],[3,7],[8]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,7,6,8,5,4,1] => [4,3,2,5,8,7,6,1] => [[1,4,5],[2,6],[3,7],[8]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => [4,3,2,5,6,8,7,1] => [[1,4,5,6],[2,7],[3],[8]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [4,3,2,5,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [2,4,3,1,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,4,2,1,5,7,8,6] => [2,4,3,1,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,4,2,1,6,5,7,8] => [2,4,3,1,6,5,7,8] => [[1,2,5,7,8],[3,6],[4]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [2,4,3,1,6,5,8,7] => [[1,2,5,7],[3,6,8],[4]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [2,4,3,1,7,6,8,5] => [[1,2,5,7],[3,6],[4,8]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [2,4,3,1,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [2,4,3,1,6,8,7,5] => [[1,2,5,6],[3,7],[4,8]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [2,4,3,1,6,7,8,5] => [[1,2,5,6,7],[3,8],[4]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [5,4,3,2,1,6,7,8] => [[1,6,7,8],[2],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [3,4,2,5,1,6,8,7] => [5,4,3,2,1,6,8,7] => [[1,6,7],[2,8],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,2,5,1,7,6,8] => [5,4,3,2,1,7,6,8] => [[1,6,8],[2,7],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [5,4,3,2,1,7,8,6] => [[1,6,7],[2,8],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => [6,4,3,2,5,1,7,8] => [[1,5,7,8],[2],[3],[4],[6]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => [6,4,3,2,5,1,8,7] => [[1,5,7],[2,8],[3],[4],[6]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [8,4,3,2,5,6,7,1] => [[1,5,6,7],[2],[3],[4],[8]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => [7,4,3,2,5,6,8,1] => [[1,5,6,7],[2],[3],[4],[8]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [6,4,3,2,5,8,7,1] => [[1,5,6],[2,7],[3],[4],[8]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,4,2,6,5,1,7,8] => [5,4,3,2,6,1,7,8] => [[1,5,7,8],[2],[3],[4],[6]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,2,6,5,1,8,7] => [5,4,3,2,6,1,8,7] => [[1,5,7],[2,8],[3],[4],[6]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,4,2,6,5,8,7,1] => [7,4,3,2,6,5,8,1] => [[1,5,7],[2,6],[3],[4],[8]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,2,6,7,5,1,8] => [5,4,3,2,7,6,1,8] => [[1,5,8],[2,6],[3],[4],[7]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [8,4,3,2,7,6,5,1] => [[1,5],[2,6],[3,7],[4],[8]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,4,2,6,7,8,5,1] => [5,4,3,2,8,6,7,1] => [[1,5,7],[2,6],[3],[4],[8]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,4,2,6,8,7,5,1] => [5,4,3,2,7,6,8,1] => [[1,5,7],[2,6],[3],[4],[8]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,4,2,7,6,5,1,8] => [5,4,3,2,6,7,1,8] => [[1,5,6,8],[2],[3],[4],[7]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,2,7,6,5,8,1] => [8,4,3,2,6,7,5,1] => [[1,5,6],[2,7],[3],[4],[8]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,4,2,7,6,8,5,1] => [5,4,3,2,8,7,6,1] => [[1,5],[2,6],[3,7],[4],[8]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,4,2,7,8,6,5,1] => [5,4,3,2,6,8,7,1] => [[1,5,6],[2,7],[3],[4],[8]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [5,4,3,2,6,7,8,1] => [[1,5,6,7],[2],[3],[4],[8]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [2,5,3,4,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,2,1,7,8,6] => [2,5,3,4,1,8,7,6] => [[1,2,4,6],[3,7],[5,8]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [6,5,3,4,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => [6,5,3,4,2,1,8,7] => [[1,4,7],[2,8],[3],[5],[6]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [7,5,3,4,2,6,1,8] => [[1,4,6,8],[2],[3],[5],[7]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [8,5,3,4,2,6,7,1] => [[1,4,6,7],[2],[3],[5],[8]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [8,5,3,4,2,7,6,1] => [[1,4,6],[2,7],[3],[5],[8]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,5,2,8,7,6,1] => [6,5,3,4,2,7,8,1] => [[1,4,6,7],[2],[3],[5],[8]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [2,6,3,4,5,1,7,8] => [[1,2,4,5,7,8],[3],[6]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [7,6,3,4,5,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [8,6,3,4,5,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [7,6,3,4,5,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [2,7,3,4,5,6,1,8] => [[1,2,4,5,6,8],[3],[7]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [8,7,3,4,5,6,2,1] => [[1,4,5,6],[2],[3],[7],[8]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [2,8,3,4,5,6,7,1] => [[1,2,4,5,6,7],[3],[8]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [2,8,3,4,5,7,6,1] => [[1,2,4,5,6],[3],[7],[8]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [2,6,3,4,5,8,7,1] => [[1,2,4,5,6],[3,7],[8]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [2,6,3,4,5,7,8,1] => [[1,2,4,5,6,7],[3],[8]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [8,7,3,4,6,5,2,1] => [[1,4,5],[2],[3],[6],[7],[8]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => [8,5,3,4,7,6,2,1] => [[1,4,5],[2,6],[3],[7],[8]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [2,5,3,4,8,6,7,1] => [[1,2,4,5,7],[3,6],[8]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,6,8,7,5,2,1] => [2,5,3,4,7,6,8,1] => [[1,2,4,5,7],[3,6],[8]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [2,5,3,4,6,7,1,8] => [[1,2,4,5,6,8],[3],[7]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,6,5,2,8,1] => [8,5,3,4,6,7,2,1] => [[1,4,5,6],[2],[3],[7],[8]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,4,7,6,8,5,2,1] => [2,5,3,4,8,7,6,1] => [[1,2,4,5],[3,6],[7],[8]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,7,8,6,5,2,1] => [2,5,3,4,6,8,7,1] => [[1,2,4,5,6],[3,7],[8]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => [2,5,3,4,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => [2,4,3,5,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,4,2,1,6,8,7] => [2,4,3,5,1,6,8,7] => [[1,2,4,6,7],[3,8],[5]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,4,2,1,7,6,8] => [2,4,3,5,1,7,6,8] => [[1,2,4,6,8],[3,7],[5]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,4,2,1,7,8,6] => [2,4,3,5,1,8,7,6] => [[1,2,4,6],[3,7],[5,8]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [2,4,3,5,1,7,8,6] => [[1,2,4,6,7],[3,8],[5]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,4,2,6,1,8,7] => [6,4,3,5,2,1,8,7] => [[1,4,7],[2,8],[3],[5],[6]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,4,2,6,7,1,8] => [7,4,3,5,2,6,1,8] => [[1,4,6,8],[2],[3],[5],[7]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,5,4,2,6,8,7,1] => [7,4,3,5,2,6,8,1] => [[1,4,6,7],[2],[3],[5],[8]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,4,2,7,6,8,1] => [8,4,3,5,2,7,6,1] => [[1,4,6],[2,7],[3],[5],[8]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,4,6,2,1,8,7] => [2,6,3,5,4,1,8,7] => [[1,2,4,7],[3,8],[5],[6]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [7,6,3,5,4,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,5,4,6,2,8,7,1] => [7,6,3,5,4,2,8,1] => [[1,4,7],[2],[3],[5],[6],[8]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,4,6,7,2,8,1] => [8,7,3,5,4,6,2,1] => [[1,4,6],[2],[3],[5],[7],[8]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,5,4,6,8,7,2,1] => [2,7,3,5,4,6,8,1] => [[1,2,4,6,7],[3],[5],[8]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => [8,6,3,5,4,7,2,1] => [[1,4,6],[2],[3],[5],[7],[8]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [2,8,3,5,4,7,6,1] => [[1,2,4,6],[3,7],[5],[8]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,4,7,8,6,2,1] => [2,6,3,5,4,8,7,1] => [[1,2,4,6],[3,7],[5],[8]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,5,4,8,7,6,2,1] => [2,6,3,5,4,7,8,1] => [[1,2,4,6,7],[3],[5],[8]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,5,6,4,2,1,7,8] => [2,4,3,6,5,1,7,8] => [[1,2,4,7,8],[3,5],[6]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => [2,4,3,6,5,1,8,7] => [[1,2,4,7],[3,5,8],[6]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,4,2,7,1,8] => [7,4,3,6,5,2,1,8] => [[1,4,8],[2,5],[3],[6],[7]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,4,2,8,7,1] => [7,4,3,6,5,2,8,1] => [[1,4,7],[2,5],[3],[6],[8]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,4,7,2,1,8] => [2,7,3,6,5,4,1,8] => [[1,2,4,8],[3],[5],[6],[7]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [8,7,3,6,5,4,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => [8,4,3,7,5,6,2,1] => [[1,4,6],[2,5],[3],[7],[8]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,4,8,2,1] => [2,8,3,7,5,6,4,1] => [[1,2,4,6],[3],[5],[7],[8]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [2,4,3,8,5,6,7,1] => [[1,2,4,6,7],[3,5],[8]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [2,4,3,7,5,6,8,1] => [[1,2,4,6,7],[3,5],[8]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [2,4,3,6,5,7,1,8] => [[1,2,4,6,8],[3,5],[7]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,5,7,6,8,4,2,1] => [2,4,3,8,5,7,6,1] => [[1,2,4,6],[3,5],[7],[8]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [2,4,3,6,5,8,7,1] => [[1,2,4,6],[3,5,7],[8]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [2,4,3,6,5,7,8,1] => [[1,2,4,6,7],[3,5],[8]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [2,4,3,5,6,1,8,7] => [[1,2,4,5,7],[3,8],[6]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,5,4,2,7,8,1] => [8,4,3,5,6,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [8,7,3,5,6,4,2,1] => [[1,4,5],[2],[3],[6],[7],[8]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,5,4,8,7,2,1] => [2,7,3,5,6,4,8,1] => [[1,2,4,5,7],[3],[6],[8]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,6,5,7,4,2,8,1] => [8,4,3,7,6,5,2,1] => [[1,4],[2,5],[3],[6],[7],[8]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,6,5,7,4,8,2,1] => [2,8,3,7,6,5,4,1] => [[1,2,4],[3],[5],[6],[7],[8]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,5,7,8,4,2,1] => [2,4,3,8,6,5,7,1] => [[1,2,4,7],[3,5],[6],[8]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,6,5,8,7,4,2,1] => [2,4,3,7,6,5,8,1] => [[1,2,4,7],[3,5],[6],[8]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,6,7,5,4,2,8,1] => [8,4,3,5,7,6,2,1] => [[1,4,5],[2,6],[3],[7],[8]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,6,7,5,4,8,2,1] => [2,8,3,5,7,6,4,1] => [[1,2,4,5],[3],[6],[7],[8]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,6,7,5,8,4,2,1] => [2,4,3,8,7,6,5,1] => [[1,2,4],[3,5],[6],[7],[8]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,6,7,8,5,4,2,1] => [2,4,3,5,8,6,7,1] => [[1,2,4,5,7],[3,6],[8]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [2,4,3,5,7,6,8,1] => [[1,2,4,5,7],[3,6],[8]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,7,6,5,4,2,8,1] => [8,4,3,5,6,7,2,1] => [[1,4,5,6],[2],[3],[7],[8]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [2,8,3,5,6,7,4,1] => [[1,2,4,5,6],[3],[7],[8]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [2,4,3,5,6,8,7,1] => [[1,2,4,5,6],[3,7],[8]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [2,4,3,5,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [[1,2,3,5,6,7,8],[4]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [2,3,4,1,5,6,8,7] => [[1,2,3,5,6,7],[4,8]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [2,3,4,1,5,7,6,8] => [[1,2,3,5,6,8],[4,7]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [2,3,4,1,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [2,3,4,1,5,7,8,6] => [[1,2,3,5,6,7],[4,8]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [2,3,4,1,6,5,7,8] => [[1,2,3,5,7,8],[4,6]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => [[1,2,3,5,7],[4,6,8]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [2,3,4,1,7,6,5,8] => [[1,2,3,5,8],[4,6],[7]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [2,3,4,1,8,6,7,5] => [[1,2,3,5,7],[4,6],[8]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [2,3,4,1,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [2,3,4,1,6,7,5,8] => [[1,2,3,5,6,8],[4,7]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [2,3,4,1,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [2,3,4,1,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5] => [[1,2,3,5,6,7],[4,8]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [5,3,4,2,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,3,2,5,1,6,8,7] => [5,3,4,2,1,6,8,7] => [[1,3,6,7],[2,8],[4],[5]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [5,3,4,2,1,8,7,6] => [[1,3,6],[2,7],[4,8],[5]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [5,3,4,2,1,7,8,6] => [[1,3,6,7],[2,8],[4],[5]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [6,3,4,2,5,1,8,7] => [[1,3,5,7],[2,8],[4],[6]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [8,3,4,2,5,6,7,1] => [[1,3,5,6,7],[2],[4],[8]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [5,3,4,2,6,1,8,7] => [[1,3,5,7],[2,8],[4],[6]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [7,3,4,2,6,5,1,8] => [[1,3,5,8],[2,6],[4],[7]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [8,3,4,2,6,5,7,1] => [[1,3,5,7],[2,6],[4],[8]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [7,3,4,2,6,5,8,1] => [[1,3,5,7],[2,6],[4],[8]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,3,2,6,7,5,1,8] => [5,3,4,2,7,6,1,8] => [[1,3,5,8],[2,6],[4],[7]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,6,7,8,5,1] => [5,3,4,2,8,6,7,1] => [[1,3,5,7],[2,6],[4],[8]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => [5,3,4,2,7,6,8,1] => [[1,3,5,7],[2,6],[4],[8]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [5,3,4,2,6,7,8,1] => [[1,3,5,6,7],[2],[4],[8]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => [2,5,4,3,1,6,7,8] => [[1,2,6,7,8],[3],[4],[5]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,3,5,2,1,6,8,7] => [2,5,4,3,1,6,8,7] => [[1,2,6,7],[3,8],[4],[5]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,3,5,2,1,7,6,8] => [2,5,4,3,1,7,6,8] => [[1,2,6,8],[3,7],[4],[5]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,3,5,2,1,7,8,6] => [2,5,4,3,1,8,7,6] => [[1,2,6],[3,7],[4,8],[5]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,3,5,2,1,8,7,6] => [2,5,4,3,1,7,8,6] => [[1,2,6,7],[3,8],[4],[5]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [6,5,4,3,2,1,7,8] => [[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [6,5,4,3,2,1,8,7] => [[1,7],[2,8],[3],[4],[5],[6]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,3,5,2,6,7,1,8] => [7,5,4,3,2,6,1,8] => [[1,6,8],[2],[3],[4],[5],[7]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [8,5,4,3,2,6,7,1] => [[1,6,7],[2],[3],[4],[5],[8]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,3,5,2,6,8,7,1] => [7,5,4,3,2,6,8,1] => [[1,6,7],[2],[3],[4],[5],[8]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => [6,5,4,3,2,7,1,8] => [[1,6,8],[2],[3],[4],[5],[7]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [8,5,4,3,2,7,6,1] => [[1,6],[2,7],[3],[4],[5],[8]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,3,5,2,8,7,6,1] => [6,5,4,3,2,7,8,1] => [[1,6,7],[2],[3],[4],[5],[8]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [2,6,4,3,5,1,8,7] => [[1,2,5,7],[3,8],[4],[6]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,3,5,6,2,7,1,8] => [7,6,4,3,5,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [8,6,4,3,5,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,3,5,6,7,2,8,1] => [8,7,4,3,5,6,2,1] => [[1,5,6],[2],[3],[4],[7],[8]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [2,8,4,3,5,6,7,1] => [[1,2,5,6,7],[3],[4],[8]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,3,5,6,8,7,2,1] => [2,7,4,3,5,6,8,1] => [[1,2,5,6,7],[3],[4],[8]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,3,5,7,6,2,8,1] => [8,6,4,3,5,7,2,1] => [[1,5,6],[2],[3],[4],[7],[8]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => [2,8,4,3,5,7,6,1] => [[1,2,5,6],[3,7],[4],[8]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,7,8,6,2,1] => [2,6,4,3,5,8,7,1] => [[1,2,5,6],[3,7],[4],[8]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,3,5,8,7,6,2,1] => [2,6,4,3,5,7,8,1] => [[1,2,5,6,7],[3],[4],[8]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [2,5,4,3,6,1,8,7] => [[1,2,5,7],[3,8],[4],[6]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,3,6,5,2,7,1,8] => [7,5,4,3,6,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,3,6,5,2,7,8,1] => [8,5,4,3,6,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [7,5,4,3,6,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [8,7,4,3,6,5,2,1] => [[1,5],[2,6],[3],[4],[7],[8]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [2,8,4,3,6,5,7,1] => [[1,2,5,7],[3,6],[4],[8]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [2,7,4,3,6,5,8,1] => [[1,2,5,7],[3,6],[4],[8]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,3,6,7,5,2,8,1] => [8,5,4,3,7,6,2,1] => [[1,5],[2,6],[3],[4],[7],[8]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,3,6,7,5,8,2,1] => [2,8,4,3,7,6,5,1] => [[1,2,5],[3,6],[4],[7],[8]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [2,5,4,3,8,6,7,1] => [[1,2,5,7],[3,6],[4],[8]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,3,6,8,7,5,2,1] => [2,5,4,3,7,6,8,1] => [[1,2,5,7],[3,6],[4],[8]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => [2,5,4,3,6,7,1,8] => [[1,2,5,6,8],[3],[4],[7]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,7,6,5,2,8,1] => [8,5,4,3,6,7,2,1] => [[1,5,6],[2],[3],[4],[7],[8]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,7,6,5,8,2,1] => [2,8,4,3,6,7,5,1] => [[1,2,5,6],[3,7],[4],[8]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,3,7,6,8,5,2,1] => [2,5,4,3,8,7,6,1] => [[1,2,5],[3,6],[4,7],[8]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,7,8,6,5,2,1] => [2,5,4,3,6,8,7,1] => [[1,2,5,6],[3,7],[4],[8]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => [2,5,4,3,6,7,8,1] => [[1,2,5,6,7],[3],[4],[8]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [2,3,5,4,1,6,7,8] => [[1,2,3,6,7,8],[4],[5]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,3,2,1,6,8,7] => [2,3,5,4,1,6,8,7] => [[1,2,3,6,7],[4,8],[5]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,3,2,1,7,6,8] => [2,3,5,4,1,7,6,8] => [[1,2,3,6,8],[4,7],[5]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,5,3,2,1,7,8,6] => [2,3,5,4,1,8,7,6] => [[1,2,3,6],[4,7],[5,8]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,3,2,6,1,8,7] => [6,3,5,4,2,1,8,7] => [[1,3,7],[2,8],[4],[5],[6]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,5,3,2,6,7,1,8] => [7,3,5,4,2,6,1,8] => [[1,3,6,8],[2],[4],[5],[7]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,3,2,6,7,8,1] => [8,3,5,4,2,6,7,1] => [[1,3,6,7],[2],[4],[5],[8]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,3,2,7,6,1,8] => [6,3,5,4,2,7,1,8] => [[1,3,6,8],[2],[4],[5],[7]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,5,3,2,7,6,8,1] => [8,3,5,4,2,7,6,1] => [[1,3,6],[2,7],[4],[5],[8]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,5,3,2,7,8,6,1] => [6,3,5,4,2,8,7,1] => [[1,3,6],[2,7],[4],[5],[8]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,3,2,8,7,6,1] => [6,3,5,4,2,7,8,1] => [[1,3,6,7],[2],[4],[5],[8]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [2,6,5,4,3,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [7,6,5,4,3,2,1,8] => [[1,8],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,5,3,6,2,7,8,1] => [8,6,5,4,3,2,7,1] => [[1,7],[2],[3],[4],[5],[6],[8]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => [7,6,5,4,3,2,8,1] => [[1,7],[2],[3],[4],[5],[6],[8]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,3,6,7,2,8,1] => [8,7,5,4,3,6,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,3,6,7,8,2,1] => [2,8,5,4,3,6,7,1] => [[1,2,6,7],[3],[4],[5],[8]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => [2,7,5,4,3,6,8,1] => [[1,2,6,7],[3],[4],[5],[8]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,5,3,7,6,2,8,1] => [8,6,5,4,3,7,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,3,7,6,8,2,1] => [2,8,5,4,3,7,6,1] => [[1,2,6],[3,7],[4],[5],[8]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,3,7,8,6,2,1] => [2,6,5,4,3,8,7,1] => [[1,2,6],[3,7],[4],[5],[8]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,3,8,7,6,2,1] => [2,6,5,4,3,7,8,1] => [[1,2,6,7],[3],[4],[5],[8]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => [2,3,6,4,5,1,7,8] => [[1,2,3,5,7,8],[4],[6]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [2,3,6,4,5,1,8,7] => [[1,2,3,5,7],[4,8],[6]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [8,3,6,4,5,2,7,1] => [[1,3,5,7],[2],[4],[6],[8]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,3,2,8,7,1] => [7,3,6,4,5,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [8,7,6,4,5,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => [2,7,6,4,5,3,8,1] => [[1,2,5,7],[3],[4],[6],[8]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [8,3,7,4,5,6,2,1] => [[1,3,5,6],[2],[4],[7],[8]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [2,8,7,4,5,6,3,1] => [[1,2,5,6],[3],[4],[7],[8]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [2,3,8,4,5,6,7,1] => [[1,2,3,5,6,7],[4],[8]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [2,3,7,4,5,6,8,1] => [[1,2,3,5,6,7],[4],[8]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,6,3,2,1] => [2,3,6,4,5,8,7,1] => [[1,2,3,5,6],[4,7],[8]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [2,3,6,4,5,7,8,1] => [[1,2,3,5,6,7],[4],[8]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => [7,3,5,4,6,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [8,7,5,4,6,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,6,5,3,8,7,2,1] => [2,7,5,4,6,3,8,1] => [[1,2,5,7],[3],[4],[6],[8]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [8,3,7,4,6,5,2,1] => [[1,3,5],[2],[4],[6],[7],[8]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,6,5,7,3,8,2,1] => [2,8,7,4,6,5,3,1] => [[1,2,5],[3],[4],[6],[7],[8]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,5,8,7,3,2,1] => [2,3,7,4,6,5,8,1] => [[1,2,3,5,7],[4],[6],[8]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [8,3,5,4,7,6,2,1] => [[1,3,5],[2,6],[4],[7],[8]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,6,7,5,3,8,2,1] => [2,8,5,4,7,6,3,1] => [[1,2,5],[3,6],[4],[7],[8]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,5,3,2,1] => [2,3,5,4,8,6,7,1] => [[1,2,3,5,7],[4,6],[8]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [2,3,5,4,7,6,8,1] => [[1,2,3,5,7],[4,6],[8]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [2,3,5,4,6,7,1,8] => [[1,2,3,5,6,8],[4],[7]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [8,3,5,4,6,7,2,1] => [[1,3,5,6],[2],[4],[7],[8]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,6,5,3,8,2,1] => [2,8,5,4,6,7,3,1] => [[1,2,5,6],[3],[4],[7],[8]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [2,3,8,4,6,7,5,1] => [[1,2,3,5,6],[4],[7],[8]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => [2,3,5,4,8,7,6,1] => [[1,2,3,5],[4,6],[7],[8]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [2,3,5,4,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [2,3,4,5,1,6,7,8] => [[1,2,3,4,6,7,8],[5]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [2,3,4,5,1,6,8,7] => [[1,2,3,4,6,7],[5,8]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [2,3,4,5,1,7,6,8] => [[1,2,3,4,6,8],[5,7]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [2,3,4,5,1,8,7,6] => [[1,2,3,4,6],[5,7],[8]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [2,3,4,5,1,7,8,6] => [[1,2,3,4,6,7],[5,8]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [6,3,4,5,2,1,8,7] => [[1,3,4,7],[2,8],[5],[6]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [8,3,4,5,2,6,7,1] => [[1,3,4,6,7],[2],[5],[8]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [6,3,4,5,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [8,3,4,5,2,7,6,1] => [[1,3,4,6],[2,7],[5],[8]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [6,3,4,5,2,8,7,1] => [[1,3,4,6],[2,7],[5],[8]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [6,3,4,5,2,7,8,1] => [[1,3,4,6,7],[2],[5],[8]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,4,3,6,2,1,7,8] => [2,6,4,5,3,1,7,8] => [[1,2,4,7,8],[3],[5],[6]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [7,6,4,5,3,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,4,3,6,2,7,8,1] => [8,6,4,5,3,2,7,1] => [[1,4,7],[2],[3],[5],[6],[8]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => [7,6,4,5,3,2,8,1] => [[1,4,7],[2],[3],[5],[6],[8]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,4,3,6,7,2,8,1] => [8,7,4,5,3,6,2,1] => [[1,4,6],[2],[3],[5],[7],[8]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => [2,8,4,5,3,6,7,1] => [[1,2,4,6,7],[3],[5],[8]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => [2,6,4,5,3,7,8,1] => [[1,2,4,6,7],[3],[5],[8]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => [2,3,6,5,4,1,7,8] => [[1,2,3,7,8],[4],[5],[6]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [2,3,6,5,4,1,8,7] => [[1,2,3,7],[4,8],[5],[6]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,4,6,3,2,7,1,8] => [7,3,6,5,4,2,1,8] => [[1,3,8],[2],[4],[5],[6],[7]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => [8,3,6,5,4,2,7,1] => [[1,3,7],[2],[4],[5],[6],[8]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => [7,3,6,5,4,2,8,1] => [[1,3,7],[2],[4],[5],[6],[8]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [2,7,6,5,4,3,1,8] => [[1,2,8],[3],[4],[5],[6],[7]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,4,6,3,8,7,2,1] => [2,7,6,5,4,3,8,1] => [[1,2,7],[3],[4],[5],[6],[8]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => [2,3,7,5,4,6,1,8] => [[1,2,3,6,8],[4],[5],[7]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,4,6,7,3,2,8,1] => [8,3,7,5,4,6,2,1] => [[1,3,6],[2],[4],[5],[7],[8]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [2,8,7,5,4,6,3,1] => [[1,2,6],[3],[4],[5],[7],[8]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [2,3,8,5,4,6,7,1] => [[1,2,3,6,7],[4],[5],[8]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [5,4,6,8,7,3,2,1] => [2,3,7,5,4,6,8,1] => [[1,2,3,6,7],[4],[5],[8]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,4,7,6,3,2,8,1] => [8,3,6,5,4,7,2,1] => [[1,3,6],[2],[4],[5],[7],[8]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,4,8,7,6,3,2,1] => [2,3,6,5,4,7,8,1] => [[1,2,3,6,7],[4],[5],[8]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => [2,3,4,6,5,1,7,8] => [[1,2,3,4,7,8],[5],[6]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,6,4,3,2,7,1,8] => [7,3,4,6,5,2,1,8] => [[1,3,4,8],[2],[5],[6],[7]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [2,7,4,6,5,3,1,8] => [[1,2,4,8],[3],[5],[6],[7]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,6,4,3,7,2,8,1] => [8,7,4,6,5,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,6,4,3,7,8,2,1] => [2,8,4,6,5,3,7,1] => [[1,2,4,7],[3],[5],[6],[8]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,4,3,8,7,2,1] => [2,7,4,6,5,3,8,1] => [[1,2,4,7],[3],[5],[6],[8]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,4,7,3,2,1,8] => [2,3,7,6,5,4,1,8] => [[1,2,3,8],[4],[5],[6],[7]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,6,4,7,3,2,8,1] => [8,3,7,6,5,4,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,6,4,7,3,8,2,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [2,3,8,6,5,4,7,1] => [[1,2,3,7],[4],[5],[6],[8]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => [2,3,7,6,5,4,8,1] => [[1,2,3,7],[4],[5],[6],[8]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [2,3,4,7,5,6,1,8] => [[1,2,3,4,6,8],[5],[7]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [2,3,4,8,5,6,7,1] => [[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [2,3,4,7,5,6,8,1] => [[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [2,3,4,6,5,7,1,8] => [[1,2,3,4,6,8],[5],[7]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [2,3,4,8,5,7,6,1] => [[1,2,3,4,6],[5],[7],[8]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [2,3,4,6,5,8,7,1] => [[1,2,3,4,6],[5,7],[8]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [2,3,4,6,5,7,8,1] => [[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [2,3,4,5,6,1,7,8] => [[1,2,3,4,5,7,8],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7] => [[1,2,3,4,5,7],[6,8]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [7,3,4,5,6,2,1,8] => [[1,3,4,5,8],[2],[6],[7]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [8,3,4,5,6,2,7,1] => [[1,3,4,5,7],[2],[6],[8]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [7,3,4,5,6,2,8,1] => [[1,3,4,5,7],[2],[6],[8]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [2,7,4,5,6,3,1,8] => [[1,2,4,5,8],[3],[6],[7]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [8,7,4,5,6,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [2,8,4,5,6,3,7,1] => [[1,2,4,5,7],[3],[6],[8]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [2,7,4,5,6,3,8,1] => [[1,2,4,5,7],[3],[6],[8]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [2,3,7,5,6,4,1,8] => [[1,2,3,5,8],[4],[6],[7]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => [8,3,7,5,6,4,2,1] => [[1,3,5],[2],[4],[6],[7],[8]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [2,8,7,5,6,4,3,1] => [[1,2,5],[3],[4],[6],[7],[8]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [2,3,8,5,6,4,7,1] => [[1,2,3,5,7],[4],[6],[8]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,5,4,8,7,3,2,1] => [2,3,7,5,6,4,8,1] => [[1,2,3,5,7],[4],[6],[8]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [2,3,4,7,6,5,1,8] => [[1,2,3,4,8],[5],[6],[7]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [8,3,4,7,6,5,2,1] => [[1,3,4],[2],[5],[6],[7],[8]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [2,8,4,7,6,5,3,1] => [[1,2,4],[3],[5],[6],[7],[8]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [2,3,8,7,6,5,4,1] => [[1,2,3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [2,3,4,8,6,5,7,1] => [[1,2,3,4,7],[5],[6],[8]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [2,3,4,7,6,5,8,1] => [[1,2,3,4,7],[5],[6],[8]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [2,3,4,5,7,6,1,8] => [[1,2,3,4,5,8],[6],[7]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [8,3,4,5,7,6,2,1] => [[1,3,4,5],[2],[6],[7],[8]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [2,3,8,5,7,6,4,1] => [[1,2,3,5],[4],[6],[7],[8]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [2,3,4,8,7,6,5,1] => [[1,2,3,4],[5],[6],[7],[8]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [2,3,4,5,8,6,7,1] => [[1,2,3,4,5,7],[6],[8]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [2,3,4,5,7,6,8,1] => [[1,2,3,4,5,7],[6],[8]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,1,8] => [[1,2,3,4,5,6,8],[7]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [8,3,4,5,6,7,2,1] => [[1,3,4,5,6],[2],[7],[8]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [2,8,4,5,6,7,3,1] => [[1,2,4,5,6],[3],[7],[8]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [2,3,8,5,6,7,4,1] => [[1,2,3,5,6],[4],[7],[8]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [2,3,4,8,6,7,5,1] => [[1,2,3,4,6],[5],[7],[8]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [2,3,4,5,8,7,6,1] => [[1,2,3,4,5],[6],[7],[8]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [2,3,4,5,6,8,7,1] => [[1,2,3,4,5,6],[7],[8]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => [[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] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,1,9] => [[1,2,3,4,5,6,7,9],[8]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,2] => [[1,2,3,4,5,6,7,8],[9]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,1,10] => [[1,2,3,4,5,6,7,8,10],[9]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,6,5,4,3,2,1,9] => [2,3,4,5,6,8,7,1,9] => [[1,2,3,4,5,6,9],[7],[8]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => [1,3,4,5,6,7,9,8,2] => [[1,2,3,4,5,6,7],[8],[9]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,2] => [[1,2,3,4,5,6,7,8,9],[10]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [2,3,4,5,6,7,8,9,10,1,11] => [[1,2,3,4,5,6,7,8,9,11],[10]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,9,8,1,10] => [[1,2,3,4,5,6,7,10],[8],[9]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,7,5,4,3,2,1,9] => [2,3,4,5,7,6,8,1,9] => [[1,2,3,4,5,7,9],[6],[8]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,8,6,5,4,3,2] => [1,3,4,5,6,8,7,9,2] => [[1,2,3,4,5,6,8],[7],[9]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,10,9,2] => [[1,2,3,4,5,6,7,8],[9],[10]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,11,2] => [[1,2,3,4,5,6,7,8,9,10],[11]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,8,4,3,2,1,9] => [2,3,4,8,5,6,7,1,9] => [[1,2,3,4,6,7,9],[5],[8]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [3,2,4,5,6,7,8,1,9] => [[1,3,4,5,6,7,9],[2],[8]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [2,3,4,5,6,7,1,9,8] => [[1,2,3,4,5,6,8],[7,9]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,3] => [[1,3,4,5,6,7,8],[2,9]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [1,4,3,5,6,7,8,9,2] => [[1,2,4,5,6,7,8],[3],[9]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [2,3,4,5,6,7,1,8,9] => [[1,2,3,4,5,6,8,9],[7]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [1,3,4,5,6,7,8,2,9] => [[1,2,3,4,5,6,7,9],[8]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,3] => [[1,2,3,4,5,6,7,8],[9]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [2,3,4,5,6,7,8,1,10,9] => [[1,2,3,4,5,6,7,9],[8,10]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9] => [2,3,4,5,7,6,1,8,9] => [[1,2,3,4,5,8,9],[6],[7]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,3] => [[1,3,4,5,6,7,8,9],[2,10]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [2,3,4,5,6,7,8,1,9,10] => [[1,2,3,4,5,6,7,9,10],[8]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [1,3,4,5,6,7,8,9,2,10] => [[1,2,3,4,5,6,7,8,10],[9]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,10,3] => [[1,2,3,4,5,6,7,8,9],[10]]
[] => [] => [] => []
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => [[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] => [2,3,4,5,6,7,9,8,1] => [8,2,3,4,5,6,7,9,1] => [[1,3,4,5,6,7,8],[2],[9]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,7,1] => [7,2,3,4,5,6,9,8,1] => [[1,3,4,5,6,7],[2,8],[9]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,7,8,9,6,1] => [6,2,3,4,5,9,7,8,1] => [[1,3,4,5,6,8],[2,7],[9]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,9,5,1] => [5,2,3,4,9,6,7,8,1] => [[1,3,4,5,7,8],[2,6],[9]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,4,1] => [4,2,3,9,5,6,7,8,1] => [[1,3,4,6,7,8],[2,5],[9]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [4,2,3,5,6,7,8,9,1] => [[1,3,4,5,6,7,8],[2],[9]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,3,1] => [3,2,9,4,5,6,7,8,1] => [[1,3,5,6,7,8],[2,4],[9]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8],[2],[9]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [9,3,2,4,5,6,7,8,1] => [[1,4,5,6,7,8],[2],[3],[9]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => [4,3,2,5,6,7,8,9,1] => [[1,4,5,6,7,8],[2],[3],[9]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => [9,4,3,2,5,6,7,8,1] => [[1,5,6,7,8],[2],[3],[4],[9]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => [2,9,3,4,5,6,7,8,1] => [[1,2,4,5,6,7,8],[3],[9]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,9,8,7,6,5,4,2,1] => [2,4,3,5,6,7,8,9,1] => [[1,2,4,5,6,7,8],[3],[9]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [9,3,4,2,5,6,7,8,1] => [[1,3,5,6,7,8],[2],[4],[9]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,9,2,1] => [2,9,4,3,5,6,7,8,1] => [[1,2,5,6,7,8],[3],[4],[9]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [2,3,9,4,5,6,7,8,1] => [[1,2,3,5,6,7,8],[4],[9]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => [9,3,4,5,2,6,7,8,1] => [[1,3,4,6,7,8],[2],[5],[9]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => [2,3,9,5,4,6,7,8,1] => [[1,2,3,6,7,8],[4],[5],[9]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,6,4,7,3,8,2,9,1] => [9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [2,3,4,9,5,6,7,8,1] => [[1,2,3,4,6,7,8],[5],[9]]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [5,6,9,8,7,4,3,2,1] => [2,3,4,7,5,6,8,9,1] => [[1,2,3,4,6,7,8],[5],[9]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,8,7,6,4,3,2,1] => [2,3,4,6,5,7,8,9,1] => [[1,2,3,4,6,7,8],[5],[9]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => [2,3,4,9,6,5,7,8,1] => [[1,2,3,4,7,8],[5],[6],[9]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [2,3,4,5,9,6,7,8,1] => [[1,2,3,4,5,7,8],[6],[9]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,7,9,8,5,4,3,2,1] => [2,3,4,5,8,6,7,9,1] => [[1,2,3,4,5,7,8],[6],[9]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,8,7,9,5,4,3,2,1] => [2,3,4,5,9,6,8,7,1] => [[1,2,3,4,5,7],[6],[8],[9]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,9,8,7,5,4,3,2,1] => [2,3,4,5,7,6,8,9,1] => [[1,2,3,4,5,7,8],[6],[9]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,6,8,9,5,4,3,2,1] => [2,3,4,5,9,7,6,8,1] => [[1,2,3,4,5,8],[6],[7],[9]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,6,9,8,5,4,3,2,1] => [2,3,4,5,8,7,6,9,1] => [[1,2,3,4,5,8],[6],[7],[9]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,8,6,5,4,3,2,9,1] => [9,3,4,5,6,8,7,2,1] => [[1,3,4,5,6],[2],[7],[8],[9]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,6,5,4,3,2,1] => [2,3,4,5,6,9,7,8,1] => [[1,2,3,4,5,6,8],[7],[9]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,8,6,5,4,3,2,1] => [2,3,4,5,6,8,7,9,1] => [[1,2,3,4,5,6,8],[7],[9]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [9,3,4,5,6,7,8,2,1] => [[1,3,4,5,6,7],[2],[8],[9]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1] => [2,9,4,5,6,7,8,3,1] => [[1,2,4,5,6,7],[3],[8],[9]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,7,6,5,4,9,3,2,1] => [2,3,9,5,6,7,8,4,1] => [[1,2,3,5,6,7],[4],[8],[9]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,7,6,5,9,4,3,2,1] => [2,3,4,9,6,7,8,5,1] => [[1,2,3,4,6,7],[5],[8],[9]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,7,6,9,5,4,3,2,1] => [2,3,4,5,9,7,8,6,1] => [[1,2,3,4,5,7],[6],[8],[9]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,7,9,6,5,4,3,2,1] => [2,3,4,5,6,9,8,7,1] => [[1,2,3,4,5,6],[7],[8],[9]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => [2,3,4,5,6,7,9,8,1] => [[1,2,3,4,5,6,7],[8],[9]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,1] => [[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] => [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]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => [[1,2,3,4,5,6,7],[8],[9]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,7,8,6] => [[1,2,3,4,5,6,8],[7],[9]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,6,7,8,5] => [[1,2,3,4,5,7,8],[6],[9]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,5,6,7,8,4] => [[1,2,3,4,6,7,8],[5],[9]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,4,5,6,7,8,3] => [[1,2,3,5,6,7,8],[4],[9]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,3,4,5,6,7,8,2] => [[1,2,4,5,6,7,8],[3],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,8,9,7] => [[1,2,3,4,5,6,7,8],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,9,8] => [[1,2,3,4,5,6,7,8],[9],[10]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [1,2,3,4,5,9,8,7,6] => [[1,2,3,4,5,6],[7],[8],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,8,9,7] => [[1,2,3,4,5,6,7,9],[8],[10]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => [1,2,3,4,9,7,6,8,5] => [[1,2,3,4,5,8],[6],[7],[9]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,7,8,9,6] => [[1,2,3,4,5,6,8,9],[7],[10]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => [1,2,3,9,6,5,7,8,4] => [[1,2,3,4,7,8],[5],[6],[9]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,6,7,8,9,5] => [[1,2,3,4,5,7,8,9],[6],[10]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => [1,2,9,5,4,6,7,8,3] => [[1,2,3,6,7,8],[4],[5],[9]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,5,6,7,8,9,4] => [[1,2,3,4,6,7,8,9],[5],[10]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [1,9,4,3,5,6,7,8,2] => [[1,2,5,6,7,8],[3],[4],[9]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,4,5,6,7,8,9,3] => [[1,2,3,5,6,7,8,9],[4],[10]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,3,4,5,6,7,8,9,2] => [[1,2,4,5,6,7,8,9],[3],[10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [[1,2,3,4,5,6,7,8,9,10],[11]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,9,10,8] => [[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,10,9] => [[1,2,3,4,5,6,7,8,9],[10],[11]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,8,9,7,6] => [1,2,3,4,5,7,9,8,6] => [[1,2,3,4,5,6,7],[8],[9]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [1,2,3,4,5,7,8,9,6] => [[1,2,3,4,5,6,7,8],[9]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [10,3,2,4,5,6,7,8,9,1] => [[1,4,5,6,7,8,9],[2],[3],[10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9,10],[2],[11]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [1,2,3,4,5,6,7,8,10,11,9] => [[1,2,3,4,5,6,7,8,9,10],[11]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [1,2,3,4,5,6,8,9,10,7] => [[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [1,2,3,4,6,7,8,9,5] => [[1,2,3,4,5,6,7,8],[9]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [1,2,3,4,5,7,8,9,10,6] => [[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,8,3,9,2] => [1,9,8,4,5,6,7,3,2] => [[1,2,5,6,7],[3],[4],[8],[9]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,3,2] => [1,3,9,4,5,6,7,8,2] => [[1,2,3,5,6,7,8],[4],[9]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,4] => [[1,2,3,4,5,6,7,8],[9]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [1,2,3,4,6,7,8,9,10,5] => [[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [[1,2,3,4,5,6,7,9],[8]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [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]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [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]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [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]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => [1,2,3,4,6,5,8,7,9] => [[1,2,3,4,5,7,9],[6,8]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [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]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => [[1,2,3,5,7,9],[4,6,8]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,8,7] => [1,3,2,4,5,6,8,9,7] => [[1,2,4,5,6,7,8],[3,9]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [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]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => [[1,2,4,6,8],[3,5,7,9]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9] => [[1,2,3,5,6,7,8,9],[4]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,7,6,5,4,3,2,8,9] => [1,3,4,5,6,7,2,8,9] => [[1,2,3,4,5,6,8,9],[7]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => [1,3,4,5,6,7,2,9,8] => [[1,2,3,4,5,6,8],[7,9]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => [[1,3,4,5,6,7,8],[2,9]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [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]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,9,8,7] => [2,1,3,4,5,6,8,9,7] => [[1,3,4,5,6,7,8],[2,9]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [[1,3,5,7,9],[2,4,6,8]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,9,8,7,6,5] => [2,1,4,3,6,7,8,9,5] => [[1,3,5,6,7,8],[2,4,9]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => [2,1,4,5,6,7,8,3,9] => [[1,3,4,5,6,7,9],[2,8]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,7,9,8] => [2,3,1,4,5,6,7,9,8] => [[1,2,4,5,6,7,8],[3,9]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9] => [2,3,1,5,4,6,7,8,9] => [[1,2,4,6,7,8,9],[3,5]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6,9,8] => [2,3,1,5,4,7,6,9,8] => [[1,2,4,6,8],[3,5,7,9]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [2,3,1,5,6,7,8,9,4] => [[1,2,4,5,6,7,8],[3,9]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [[1,2,3,5,6,7,8,9],[4]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,3,2,1,6,5,7,8,9] => [2,3,4,1,6,5,7,8,9] => [[1,2,3,5,7,8,9],[4,6]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,8,7,9] => [2,3,4,1,6,5,8,7,9] => [[1,2,3,5,7,9],[4,6,8]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [2,3,4,1,6,7,8,9,5] => [[1,2,3,5,6,7,8],[4,9]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [[1,2,3,4,6,7,8,9],[5]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,4,3,2,1,7,6,8,9] => [2,3,4,5,1,7,6,8,9] => [[1,2,3,4,6,8,9],[5,7]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [2,3,4,5,1,7,8,9,6] => [[1,2,3,4,6,7,8],[5,9]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [2,3,4,5,6,1,7,8,9] => [[1,2,3,4,5,7,8,9],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,5,4,3,2,1,8,7,9] => [2,3,4,5,6,1,8,7,9] => [[1,2,3,4,5,7,9],[6,8]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [2,3,4,5,6,1,8,9,7] => [[1,2,3,4,5,7,8],[6,9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [[1,2,3,4,5,6,7,8,10],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [[1,2,3,4,5,6,7,9,10],[8]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => [[1,2,3,4,5,6,7,9],[8,10]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,10,4] => [[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => [[1,2,3,5,7,9],[4,6,8,10]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => [1,3,2,5,4,7,6,9,10,8] => [[1,2,4,6,8,9],[3,5,7,10]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => [[1,3,4,5,6,7,8,9],[2,10]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => [2,1,4,3,5,6,7,8,9,10] => [[1,3,5,6,7,8,9,10],[2,4]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => [2,1,4,5,6,3,8,9,10,7] => [[1,3,4,5,7,8,9],[2,6,10]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => [2,1,4,5,6,7,8,3,10,9] => [[1,3,4,5,6,7,9],[2,8,10]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,9,8,10] => [2,3,1,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [2,3,1,5,6,7,8,9,10,4] => [[1,2,4,5,6,7,8,9],[3,10]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => [2,3,4,1,6,5,8,7,10,9] => [[1,2,3,5,7,9],[4,6,8,10]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => [2,3,4,1,6,5,8,9,10,7] => [[1,2,3,5,7,8,9],[4,6,10]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [2,3,4,1,6,7,8,5,10,9] => [[1,2,3,5,6,7,9],[4,8,10]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,5] => [[1,2,3,5,6,7,8,9],[4,10]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,9,8,10] => [2,3,4,5,1,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [2,3,4,5,1,7,8,9,10,6] => [[1,2,3,4,6,7,8,9],[5,10]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [2,3,4,5,6,1,8,9,10,7] => [[1,2,3,4,5,7,8,9],[6,10]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,6,5,4,3,2,1,9,8,10] => [2,3,4,5,6,7,1,9,8,10] => [[1,2,3,4,5,6,8,10],[7,9]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [2,3,4,5,6,7,1,9,10,8] => [[1,2,3,4,5,6,8,9],[7,10]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => [[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] => [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]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => [[1,3,5,6,7,8,9],[2],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => [[1,3,4,6,7,8,9],[2],[5]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => [[1,3,4,5,7,8,9],[2],[6]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9] => [[1,3,4,5,6,8,9],[2],[7]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9] => [[1,3,4,5,6,7,9],[2],[8]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [[1,4,5,6,7,8,9,10],[2],[3]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => [[1,3,5,6,7,8,9],[2],[4]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10] => [[1,3,4,5,6,7,8,10],[2],[9]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,8,10,9,4,3,2,1] => [2,3,4,9,5,6,7,8,10,1] => [[1,2,3,4,6,7,8,9],[5],[10]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [9,2,3,4,5,6,7,8,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,8,10,7,6,5,4,3,2,1] => [2,3,4,5,6,7,10,9,8,1] => [[1,2,3,4,5,6,7],[8],[9],[10]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [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]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,2,1,9] => [2,8,3,4,5,6,7,1,9] => [[1,2,4,5,6,7,9],[3],[8]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3],[4]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [10,3,4,5,6,7,8,9,2,1] => [[1,3,4,5,6,7,8],[2],[9],[10]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [11,3,4,5,6,7,8,9,10,2,1] => [[1,3,4,5,6,7,8,9],[2],[10],[11]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,9,7,6,5,4,3,2,10,1] => [10,3,4,5,6,7,9,8,2,1] => [[1,3,4,5,6,7],[2],[8],[9],[10]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [[1,5,6,7,8,9],[2],[3],[4]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,10,9,1] => [[1,2,3,4,5,6,7,8],[9],[10]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,10,9,8,7,5,4,3,2,1] => [2,3,4,5,7,6,8,9,10,1] => [[1,2,3,4,5,7,8,9],[6],[10]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,10,9,8,7,6,4,3,2,1] => [2,3,4,6,5,7,8,9,10,1] => [[1,2,3,4,6,7,8,9],[5],[10]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,9,4,3] => [2,1,4,9,5,6,7,8,3] => [[1,3,4,6,7,8],[2,5],[9]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,10,3,1] => [3,2,10,4,5,6,7,8,9,1] => [[1,3,5,6,7,8,9],[2,4],[10]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,11,10,1] => [[1,2,3,4,5,6,7,8,9],[10],[11]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => [3,2,1,5,6,7,8,9,4] => [[1,4,5,6,7,8],[2,9],[3]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [1,8,3,4,5,6,7,9,2] => [[1,2,4,5,6,7,8],[3],[9]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [7,2,3,4,5,6,1,9,8] => [[1,3,4,5,6,8],[2,9],[7]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,4,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4],[9]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => [6,2,3,4,5,1,8,9,7] => [[1,3,4,5,7,8],[2,9],[6]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [2,3,10,4,5,6,7,8,9,1] => [[1,2,3,5,6,7,8,9],[4],[10]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => [2,3,4,5,6,1,9,8,7] => [[1,2,3,4,5,7],[6,8],[9]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1] => [2,10,4,5,6,7,8,9,3,1] => [[1,2,4,5,6,7,8],[3],[9],[10]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,8,7,6,5,4,10,3,2,1] => [2,3,10,5,6,7,8,9,4,1] => [[1,2,3,5,6,7,8],[4],[9],[10]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,8,7,6,5,10,4,3,2,1] => [2,3,4,10,6,7,8,9,5,1] => [[1,2,3,4,6,7,8],[5],[9],[10]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,8,7,6,10,5,4,3,2,1] => [2,3,4,5,10,7,8,9,6,1] => [[1,2,3,4,5,7,8],[6],[9],[10]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,8,7,10,6,5,4,3,2,1] => [2,3,4,5,6,10,8,9,7,1] => [[1,2,3,4,5,6,8],[7],[9],[10]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,5,7,8,9,10,6,1] => [6,2,3,4,5,10,7,8,9,1] => [[1,3,4,5,6,8,9],[2,7],[10]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8,9] => [3,2,1,5,4,6,7,8,9] => [[1,4,6,7,8,9],[2,5],[3]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,8,7,9] => [3,2,4,1,6,5,8,7,9] => [[1,3,5,7,9],[2,6,8],[4]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9] => [3,2,4,1,6,5,8,7,10,9] => [[1,3,5,7,9],[2,6,8,10],[4]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,1,5,4,7,6,9,8,10] => [[1,4,6,8,10],[2,5,7,9],[3]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,9,10,8,1] => [8,2,3,4,5,6,7,10,9,1] => [[1,3,4,5,6,7,8],[2,9],[10]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,8,9,10,7,1] => [7,2,3,4,5,6,10,8,9,1] => [[1,3,4,5,6,7,9],[2,8],[10]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,9,10,5,1] => [5,2,3,4,10,6,7,8,9,1] => [[1,3,4,5,7,8,9],[2,6],[10]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,10,4,1] => [4,2,3,10,5,6,7,8,9,1] => [[1,3,4,6,7,8,9],[2,5],[10]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [2,10,3,4,5,6,7,8,9,1] => [[1,2,4,5,6,7,8,9],[3],[10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => [10,2,3,4,5,6,7,8,9,11,1] => [[1,3,4,5,6,7,8,9,10],[2],[11]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,5,7,9,10,8,6,4,2] => [1,4,3,6,5,8,7,10,9,2] => [[1,2,4,6,8],[3,5,7,9],[10]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,3,6,7,5,9,10,8,4,2] => [1,4,3,8,7,6,5,10,9,2] => [[1,2,4,8],[3,5,9],[6],[7],[10]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,5,3,7,9,10,8,6,2] => [1,6,5,4,3,8,7,10,9,2] => [[1,2,6,8],[3,7,9],[4],[5],[10]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,4,6,7,5,3,9,10,8,2] => [1,8,5,4,7,6,3,10,9,2] => [[1,2,5,8],[3,6,9],[4],[7],[10]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,6,4,7,3,9,10,8,2] => [1,8,7,6,5,4,3,10,9,2] => [[1,2,8],[3,9],[4],[5],[6],[7],[10]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,4,6,8,9,7,5,3,10,2] => [1,10,5,4,7,6,9,8,3,2] => [[1,2,5,7],[3,6,8],[4],[9],[10]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,4,7,8,6,9,5,3,10,2] => [1,10,5,4,9,8,7,6,3,2] => [[1,2,5],[3,6],[4],[7],[8],[9],[10]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,8,9,7,3,10,2] => [1,10,7,6,5,4,9,8,3,2] => [[1,2,7],[3,8],[4],[5],[6],[9],[10]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,5,7,8,6,4,9,3,10,2] => [1,10,9,6,5,8,7,4,3,2] => [[1,2,6],[3,7],[4],[5],[8],[9],[10]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,7,5,8,4,9,3,10,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,1,5,7,9,10,8,6,4] => [3,2,1,6,5,8,7,10,9,4] => [[1,4,6,8],[2,5,7,9],[3,10]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,3,1,6,7,5,9,10,8,4] => [3,2,1,8,7,6,5,10,9,4] => [[1,4,8],[2,5,9],[3,6],[7],[10]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,3,1,6,8,9,7,5,10,4] => [3,2,1,10,7,6,9,8,5,4] => [[1,4,7],[2,5,8],[3,6],[9],[10]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,7,8,6,9,5,10,4] => [3,2,1,10,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1,7,9,10,8,6] => [3,2,5,4,1,8,7,10,9,6] => [[1,3,6,8],[2,4,7,9],[5,10]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [2,4,5,3,1,8,9,7,10,6] => [3,2,5,4,1,10,9,8,7,6] => [[1,3,6],[2,4,7],[5,8],[9],[10]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,2,5,1,7,9,10,8,6] => [5,4,3,2,1,8,7,10,9,6] => [[1,6,8],[2,7,9],[3,10],[4],[5]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1,8,9,7,10,6] => [5,4,3,2,1,10,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5,10]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [2,4,6,7,5,3,1,9,10,8] => [3,2,5,4,7,6,1,10,9,8] => [[1,3,5,8],[2,4,6,9],[7,10]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [2,5,6,4,7,3,1,9,10,8] => [3,2,7,6,5,4,1,10,9,8] => [[1,3,8],[2,4,9],[5,10],[6],[7]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,6,7,5,1,9,10,8] => [5,4,3,2,7,6,1,10,9,8] => [[1,5,8],[2,6,9],[3,10],[4],[7]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [3,5,6,4,2,7,1,9,10,8] => [7,4,3,6,5,2,1,10,9,8] => [[1,4,8],[2,5,9],[3,10],[6],[7]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,5,3,6,2,7,1,9,10,8] => [7,6,5,4,3,2,1,10,9,8] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,6,4,7,3,8,2,9,1,10] => [9,8,7,6,5,4,3,2,1,10] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,3,5,7,9,11,12,10,8,6,4,2] => [1,4,3,6,5,8,7,10,9,12,11,2] => [[1,2,4,6,8,10],[3,5,7,9,11],[12]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [1,3,5,8,9,7,11,12,10,6,4,2] => [1,4,3,6,5,10,9,8,7,12,11,2] => [[1,2,4,6,10],[3,5,7,11],[8],[9],[12]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,6,7,5,9,11,12,10,8,4,2] => [1,4,3,8,7,6,5,10,9,12,11,2] => [[1,2,4,8,10],[3,5,9,11],[6],[7],[12]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [1,3,6,8,9,7,5,11,12,10,4,2] => [1,4,3,10,7,6,9,8,5,12,11,2] => [[1,2,4,7,10],[3,5,8,11],[6],[9],[12]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [1,3,7,8,6,9,5,11,12,10,4,2] => [1,4,3,10,9,8,7,6,5,12,11,2] => [[1,2,4,10],[3,5,11],[6],[7],[8],[9],[12]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,4,5,3,7,9,11,12,10,8,6,2] => [1,6,5,4,3,8,7,10,9,12,11,2] => [[1,2,6,8,10],[3,7,9,11],[4],[5],[12]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,4,5,3,8,9,7,11,12,10,6,2] => [1,6,5,4,3,10,9,8,7,12,11,2] => [[1,2,6,10],[3,7,11],[4,8],[5,9],[12]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,9,11,12,10,8,2] => [1,8,5,4,7,6,3,10,9,12,11,2] => [[1,2,5,8,10],[3,6,9,11],[4],[7],[12]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,5,6,4,7,3,9,11,12,10,8,2] => [1,8,7,6,5,4,3,10,9,12,11,2] => [[1,2,8,10],[3,9,11],[4],[5],[6],[7],[12]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => [1,4,6,8,9,7,5,3,11,12,10,2] => [1,10,5,4,7,6,9,8,3,12,11,2] => [[1,2,5,7,10],[3,6,8,11],[4],[9],[12]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [1,4,7,8,6,9,5,3,11,12,10,2] => [1,10,5,4,9,8,7,6,3,12,11,2] => [[1,2,5,10],[3,6,11],[4],[7],[8],[9],[12]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,4,8,9,7,3,11,12,10,2] => [1,10,7,6,5,4,9,8,3,12,11,2] => [[1,2,7,10],[3,8,11],[4],[5],[6],[9],[12]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,7,8,6,4,9,3,11,12,10,2] => [1,10,9,6,5,8,7,4,3,12,11,2] => [[1,2,6,10],[3,7,11],[4],[5],[8],[9],[12]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,6,7,5,8,4,9,3,11,12,10,2] => [1,10,9,8,7,6,5,4,3,12,11,2] => [[1,2,10],[3,11],[4],[5],[6],[7],[8],[9],[12]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [1,4,6,8,10,11,9,7,5,3,12,2] => [1,12,5,4,7,6,9,8,11,10,3,2] => [[1,2,5,7,9],[3,6,8,10],[4],[11],[12]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [1,4,6,9,10,8,11,7,5,3,12,2] => [1,12,5,4,7,6,11,10,9,8,3,2] => [[1,2,5,7],[3,6,8],[4],[9],[10],[11],[12]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [1,4,7,8,6,10,11,9,5,3,12,2] => [1,12,5,4,9,8,7,6,11,10,3,2] => [[1,2,5,9],[3,6,10],[4],[7],[8],[11],[12]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [1,4,7,9,10,8,6,11,5,3,12,2] => [1,12,5,4,11,8,7,10,9,6,3,2] => [[1,2,5,8],[3,6,9],[4],[7],[10],[11],[12]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [1,4,8,9,7,10,6,11,5,3,12,2] => [1,12,5,4,11,10,9,8,7,6,3,2] => [[1,2,5],[3,6],[4],[7],[8],[9],[10],[11],[12]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,5,6,4,8,10,11,9,7,3,12,2] => [1,12,7,6,5,4,9,8,11,10,3,2] => [[1,2,7,9],[3,8,10],[4],[5],[6],[11],[12]]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,5,6,4,9,10,8,11,7,3,12,2] => [1,12,7,6,5,4,11,10,9,8,3,2] => [[1,2,7],[3,8],[4,9],[5,10],[6],[11],[12]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,7,8,6,4,10,11,9,3,12,2] => [1,12,9,6,5,8,7,4,11,10,3,2] => [[1,2,6,9],[3,7,10],[4],[5],[8],[11],[12]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,6,7,5,8,4,10,11,9,3,12,2] => [1,12,9,8,7,6,5,4,11,10,3,2] => [[1,2,9],[3,10],[4],[5],[6],[7],[8],[11],[12]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [1,5,7,9,10,8,6,4,11,3,12,2] => [1,12,11,6,5,8,7,10,9,4,3,2] => [[1,2,6,8],[3,7,9],[4],[5],[10],[11],[12]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [1,5,8,9,7,10,6,4,11,3,12,2] => [1,12,11,6,5,10,9,8,7,4,3,2] => [[1,2,6],[3,7],[4],[5],[8],[9],[10],[11],[12]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,6,7,5,9,10,8,4,11,3,12,2] => [1,12,11,8,7,6,5,10,9,4,3,2] => [[1,2,8],[3,9],[4],[5],[6],[7],[10],[11],[12]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [1,6,8,9,7,5,10,4,11,3,12,2] => [1,12,11,10,7,6,9,8,5,4,3,2] => [[1,2,7],[3,8],[4],[5],[6],[9],[10],[11],[12]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,7,8,6,9,5,10,4,11,3,12,2] => [1,12,11,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,1,5,7,9,11,12,10,8,6,4] => [3,2,1,6,5,8,7,10,9,12,11,4] => [[1,4,6,8,10],[2,5,7,9,11],[3,12]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [2,3,1,5,8,9,7,11,12,10,6,4] => [3,2,1,6,5,10,9,8,7,12,11,4] => [[1,4,6,10],[2,5,7,11],[3,8],[9],[12]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,1,6,7,5,9,11,12,10,8,4] => [3,2,1,8,7,6,5,10,9,12,11,4] => [[1,4,8,10],[2,5,9,11],[3,6],[7],[12]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [2,3,1,6,8,9,7,5,11,12,10,4] => [3,2,1,10,7,6,9,8,5,12,11,4] => [[1,4,7,10],[2,5,8,11],[3,6],[9],[12]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [2,3,1,7,8,6,9,5,11,12,10,4] => [3,2,1,10,9,8,7,6,5,12,11,4] => [[1,4,10],[2,5,11],[3,6],[7],[8],[9],[12]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [2,3,1,6,8,10,11,9,7,5,12,4] => [3,2,1,12,7,6,9,8,11,10,5,4] => [[1,4,7,9],[2,5,8,10],[3,6],[11],[12]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [2,3,1,6,9,10,8,11,7,5,12,4] => [3,2,1,12,7,6,11,10,9,8,5,4] => [[1,4,7],[2,5,8],[3,6],[9],[10],[11],[12]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [2,3,1,7,8,6,10,11,9,5,12,4] => [3,2,1,12,9,8,7,6,11,10,5,4] => [[1,4,9],[2,5,10],[3,6],[7],[8],[11],[12]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [2,3,1,7,9,10,8,6,11,5,12,4] => [3,2,1,12,11,8,7,10,9,6,5,4] => [[1,4,8],[2,5,9],[3,6],[7],[10],[11],[12]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [2,3,1,8,9,7,10,6,11,5,12,4] => [3,2,1,12,11,10,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9],[10],[11],[12]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,5,3,1,7,9,11,12,10,8,6] => [3,2,5,4,1,8,7,10,9,12,11,6] => [[1,3,6,8,10],[2,4,7,9,11],[5,12]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,1,8,9,7,11,12,10,6] => [3,2,5,4,1,10,9,8,7,12,11,6] => [[1,3,6,10],[2,4,7,11],[5,8],[9],[12]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,5,3,1,8,10,11,9,7,12,6] => [3,2,5,4,1,12,9,8,11,10,7,6] => [[1,3,6,9],[2,4,7,10],[5,8],[11],[12]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,4,5,3,1,9,10,8,11,7,12,6] => [3,2,5,4,1,12,11,10,9,8,7,6] => [[1,3,6],[2,4,7],[5,8],[9],[10],[11],[12]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,2,5,1,7,9,11,12,10,8,6] => [5,4,3,2,1,8,7,10,9,12,11,6] => [[1,6,8,10],[2,7,9,11],[3,12],[4],[5]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,5,1,8,9,7,11,12,10,6] => [5,4,3,2,1,10,9,8,7,12,11,6] => [[1,6,10],[2,7,11],[3,8],[4,9],[5,12]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,2,5,1,8,10,11,9,7,12,6] => [5,4,3,2,1,12,9,8,11,10,7,6] => [[1,6,9],[2,7,10],[3,8],[4,11],[5,12]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,4,2,5,1,9,10,8,11,7,12,6] => [5,4,3,2,1,12,11,10,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5,10],[11],[12]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,7,5,3,1,9,11,12,10,8] => [3,2,5,4,7,6,1,10,9,12,11,8] => [[1,3,5,8,10],[2,4,6,9,11],[7,12]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [2,4,6,7,5,3,1,10,11,9,12,8] => [3,2,5,4,7,6,1,12,11,10,9,8] => [[1,3,5,8],[2,4,6,9],[7,10],[11],[12]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5,6,4,7,3,1,9,11,12,10,8] => [3,2,7,6,5,4,1,10,9,12,11,8] => [[1,3,8,10],[2,4,9,11],[5,12],[6],[7]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5,6,4,7,3,1,10,11,9,12,8] => [3,2,7,6,5,4,1,12,11,10,9,8] => [[1,3,8],[2,4,9],[5,10],[6,11],[7,12]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1,9,11,12,10,8] => [5,4,3,2,7,6,1,10,9,12,11,8] => [[1,5,8,10],[2,6,9,11],[3,12],[4],[7]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,1,10,11,9,12,8] => [5,4,3,2,7,6,1,12,11,10,9,8] => [[1,5,8],[2,6,9],[3,10],[4,11],[7,12]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5,6,4,2,7,1,9,11,12,10,8] => [7,4,3,6,5,2,1,10,9,12,11,8] => [[1,4,8,10],[2,5,9,11],[3,12],[6],[7]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5,6,4,2,7,1,10,11,9,12,8] => [7,4,3,6,5,2,1,12,11,10,9,8] => [[1,4,8],[2,5,9],[3,10],[6,11],[7,12]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,5,3,6,2,7,1,9,11,12,10,8] => [7,6,5,4,3,2,1,10,9,12,11,8] => [[1,8,10],[2,9,11],[3,12],[4],[5],[6],[7]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1,10,11,9,12,8] => [7,6,5,4,3,2,1,12,11,10,9,8] => [[1,8],[2,9],[3,10],[4,11],[5,12],[6],[7]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [2,4,6,8,9,7,5,3,1,11,12,10] => [3,2,5,4,7,6,9,8,1,12,11,10] => [[1,3,5,7,10],[2,4,6,8,11],[9,12]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [2,4,7,8,6,9,5,3,1,11,12,10] => [3,2,5,4,9,8,7,6,1,12,11,10] => [[1,3,5,10],[2,4,6,11],[7,12],[8],[9]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [2,5,6,4,8,9,7,3,1,11,12,10] => [3,2,7,6,5,4,9,8,1,12,11,10] => [[1,3,7,10],[2,4,8,11],[5,12],[6],[9]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [2,5,7,8,6,4,9,3,1,11,12,10] => [3,2,9,6,5,8,7,4,1,12,11,10] => [[1,3,6,10],[2,4,7,11],[5,12],[8],[9]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [2,6,7,5,8,4,9,3,1,11,12,10] => [3,2,9,8,7,6,5,4,1,12,11,10] => [[1,3,10],[2,4,11],[5,12],[6],[7],[8],[9]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [3,4,2,6,8,9,7,5,1,11,12,10] => [5,4,3,2,7,6,9,8,1,12,11,10] => [[1,5,7,10],[2,6,8,11],[3,12],[4],[9]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,7,8,6,9,5,1,11,12,10] => [5,4,3,2,9,8,7,6,1,12,11,10] => [[1,5,10],[2,6,11],[3,7,12],[4,8],[9]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,5,6,4,2,8,9,7,1,11,12,10] => [7,4,3,6,5,2,9,8,1,12,11,10] => [[1,4,7,10],[2,5,8,11],[3,12],[6],[9]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,5,3,6,2,8,9,7,1,11,12,10] => [7,6,5,4,3,2,9,8,1,12,11,10] => [[1,7,10],[2,8,11],[3,12],[4],[5],[6],[9]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [3,5,7,8,6,4,2,9,1,11,12,10] => [9,4,3,6,5,8,7,2,1,12,11,10] => [[1,4,6,10],[2,5,7,11],[3,12],[8],[9]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [3,6,7,5,8,4,2,9,1,11,12,10] => [9,4,3,8,7,6,5,2,1,12,11,10] => [[1,4,10],[2,5,11],[3,12],[6],[7],[8],[9]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,5,3,7,8,6,2,9,1,11,12,10] => [9,6,5,4,3,8,7,2,1,12,11,10] => [[1,6,10],[2,7,11],[3,12],[4],[5],[8],[9]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,6,7,5,3,8,2,9,1,11,12,10] => [9,8,5,4,7,6,3,2,1,12,11,10] => [[1,5,10],[2,6,11],[3,12],[4],[7],[8],[9]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [5,6,4,7,3,8,2,9,1,11,12,10] => [9,8,7,6,5,4,3,2,1,12,11,10] => [[1,10],[2,11],[3,12],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,1] => [[1,2,3,4,5,6,7,8,9,10],[11]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,9,10,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,10,9,1] => [[1,3,4,5,6,7,8],[2,9],[10]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,11,10,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,10,11,1] => [[1,3,4,5,6,7,8,9,10],[2],[11]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [1,2,5,4,6,7,8,9,3] => [[1,2,3,5,6,7,8],[4],[9]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [1,2,3,6,5,7,8,9,4] => [[1,2,3,4,6,7,8],[5],[9]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [1,2,3,4,7,6,8,9,5] => [[1,2,3,4,5,7,8],[6],[9]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [1,2,3,4,5,8,7,9,6] => [[1,2,3,4,5,6,8],[7],[9]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,8,7,6,5,4,3,2,1,11,10] => [2,3,4,5,6,7,8,9,1,11,10] => [[1,2,3,4,5,6,7,8,10],[9,11]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [2,3,4,10,5,6,7,8,9,1] => [[1,2,3,4,6,7,8,9],[5],[10]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9] => [2,3,4,6,5,1,7,8,9] => [[1,2,3,4,7,8,9],[5],[6]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8,9] => [2,3,5,4,1,6,7,8,9] => [[1,2,3,6,7,8,9],[4],[5]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3],[4]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [2,3,4,5,6,7,10,8,9,1] => [[1,2,3,4,5,6,7,9],[8],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => [[1,2,3,4,5,6,7,8,9,11],[10]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [[1,6,7,8,9],[2],[3],[4],[5]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [2,3,4,5,10,6,7,8,9,1] => [[1,2,3,4,5,7,8,9],[6],[10]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [2,3,4,5,6,10,7,8,9,1] => [[1,2,3,4,5,6,8,9],[7],[10]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,2,10,9,8,7,6,5,4,1] => [4,3,2,5,6,7,8,9,10,1] => [[1,4,5,6,7,8,9],[2],[3],[10]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9,10] => [2,4,3,1,5,6,7,8,9,10] => [[1,2,5,6,7,8,9,10],[3],[4]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => [1,3,2,5,4,7,6,9,8,11,10] => [[1,2,4,6,8,10],[3,5,7,9,11]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7,10,9] => [2,4,3,1,6,5,8,7,10,9] => [[1,2,5,7,9],[3,6,8,10],[4]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,8,7,9] => [4,3,2,1,6,5,8,7,9] => [[1,5,7,9],[2,6,8],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => [[1,5,7,9],[2,6,8,10],[3],[4]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,8,10,7] => [2,1,4,3,6,5,10,9,8,7] => [[1,3,5,7],[2,4,6,8],[9],[10]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [1,3,2,5,4,7,6,10,9,8] => [[1,2,4,6,8],[3,5,7,9],[10]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9,10] => [3,2,4,1,5,6,7,8,9,10] => [[1,3,5,6,7,8,9,10],[2],[4]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [[1,5,6,7,8,9,10],[2],[3],[4]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,5,7,9,8,6,4,2] => [1,4,3,6,5,8,7,9,2] => [[1,2,4,6,8],[3,5,7],[9]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7,10,9] => [6,5,4,3,2,1,8,7,10,9] => [[1,7,9],[2,8,10],[3],[4],[5],[6]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,4,6,3,7,2,8,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,7,6,8,5,10,9] => [4,3,2,1,8,7,6,5,10,9] => [[1,5,9],[2,6,10],[3,7],[4,8]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,8,7,9,6,10,5] => [2,1,4,3,10,9,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8],[9],[10]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,2,4,1,8,7,9,6,10,5] => [4,3,2,1,10,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9],[10]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,10,1] => [10,9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,7,6,8,5,9,4,10,3] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,3,5,2,6,1,9,8,10,7] => [6,5,4,3,2,1,10,9,8,7] => [[1,7],[2,8],[3,9],[4,10],[5],[6]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3,9,8,10,7] => [2,1,6,5,4,3,10,9,8,7] => [[1,3,7],[2,4,8],[5,9],[6,10]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[1,3,5,7,9,11],[2,4,6,8,10,12]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1,10,9,11,8,12,7] => [6,5,4,3,2,1,12,11,10,9,8,7] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,6,8,5,9,4,10,3,11,2,12,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11] => [[1,2,3,4,5,6,7,8,9,11],[10,12]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9] => [2,1,5,4,6,3,8,7,10,9] => [[1,3,5,7,9],[2,4,8,10],[6]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9] => [2,1,4,3,7,6,8,5,10,9] => [[1,3,5,7,9],[2,4,6,10],[8]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [2,1,4,3,6,5,9,8,10,7] => [[1,3,5,7,9],[2,4,6,8],[10]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,4,6,3,7,2,8,1,9] => [8,7,6,5,4,3,2,1,9] => [[1,9],[2],[3],[4],[5],[6],[7],[8]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,5,7,4,8,3,9,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,1,7,8,9,10,6,5,4,3] => [2,1,4,5,6,10,7,8,9,3] => [[1,3,4,5,6,8,9],[2,7],[10]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,6,5,9,10,8,7] => [2,4,3,1,6,5,8,10,9,7] => [[1,2,5,7,8],[3,6,9],[4,10]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [5,6,4,7,3,8,2,10,9,1] => [9,8,7,6,5,4,3,2,10,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,5,3,6,2,7,1,8,9] => [7,6,5,4,3,2,1,8,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [5,7,6,4,8,3,9,2,10,1] => [10,9,8,6,5,7,4,3,2,1] => [[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation σ is a pair i<j such that i<σ(j)<σ(i). The element σ(j) is then an invisible inversion bottom.
A descent view in a permutation π is an element π(j) such that π(i+1)<π(j)<π(i), and additionally the smallest element in the decreasing run containing π(i) is smaller than the smallest element in the decreasing run containing π(j).
This map is a bijection χ:Sn→Sn, such that
  • the multiset of descent views in π is the multiset of invisible inversion bottoms in χ(π),
  • the set of left-to-right maxima of π is the set of maximal elements in the cycles of χ(π),
  • the set of global ascent of π is the set of global ascent of χ(π),
  • the set of maximal elements in the decreasing runs of π is the set of weak deficiency positions of χ(π), and
  • the set of minimal elements in the decreasing runs of π is the set of weak deficiency values of χ(π).
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length n and pairs of standard Young tableaux of the same shape and of size n, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.