- FindStat

Identifier

Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux

Images

[1,0] => [2,1] => [[1],[2]] => [[1],[2]]

[1,0,1,0] => [3,1,2] => [[1,2],[3]] => [[1,3],[2]]

[1,1,0,0] => [2,3,1] => [[1,3],[2]] => [[1,2],[3]]

[1,0,1,0,1,0] => [4,1,2,3] => [[1,2,3],[4]] => [[1,3,4],[2]]

[1,0,1,1,0,0] => [3,1,4,2] => [[1,2],[3,4]] => [[1,2],[3,4]]

[1,1,0,0,1,0] => [2,4,1,3] => [[1,3],[2,4]] => [[1,3],[2,4]]

[1,1,0,1,0,0] => [4,3,1,2] => [[1,2],[3],[4]] => [[1,4],[2],[3]]

[1,1,1,0,0,0] => [2,3,4,1] => [[1,3,4],[2]] => [[1,2,3],[4]]

[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [[1,2,3,4],[5]] => [[1,3,4,5],[2]]

[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [[1,2,3],[4,5]] => [[1,2,5],[3,4]]

[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [[1,2,4],[3,5]] => [[1,3,5],[2,4]]

[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [[1,2,3],[4],[5]] => [[1,4,5],[2],[3]]

[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [[1,2,5],[3,4]] => [[1,2,3],[4,5]]

[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [[1,3,4],[2,5]] => [[1,3,4],[2,5]]

[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [[1,3,5],[2,4]] => [[1,2,4],[3,5]]

[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [[1,2,4],[3],[5]] => [[1,3,5],[2],[4]]

[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [[1,2,3],[4],[5]] => [[1,4,5],[2],[3]]

[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [[1,2],[3,5],[4]] => [[1,2],[3,5],[4]]

[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [[1,3,4],[2,5]] => [[1,3,4],[2,5]]

[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [[1,3],[2,4],[5]] => [[1,4],[2,5],[3]]

[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [[1,2],[3,4],[5]] => [[1,3],[2,5],[4]]

[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[1,3,4,5],[2]] => [[1,2,3,4],[5]]

[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [[1,2,3,4,5],[6]] => [[1,3,4,5,6],[2]]

[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [[1,2,3,4],[5,6]] => [[1,2,5,6],[3,4]]

[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [[1,2,3,5],[4,6]] => [[1,3,5,6],[2,4]]

[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [[1,2,3,4],[5],[6]] => [[1,4,5,6],[2],[3]]

[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [[1,2,3,6],[4,5]] => [[1,2,3,6],[4,5]]

[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [[1,2,4,5],[3,6]] => [[1,3,4,6],[2,5]]

[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [[1,2,4],[3,5,6]] => [[1,2,4],[3,5,6]]

[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [[1,2,3,5],[4],[6]] => [[1,3,5,6],[2],[4]]

[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [[1,2,3,4],[5],[6]] => [[1,4,5,6],[2],[3]]

[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [[1,2,3],[4,6],[5]] => [[1,2,6],[3,5],[4]]

[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [[1,2,5],[3,4,6]] => [[1,3,4],[2,5,6]]

[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [[1,2,4],[3,5],[6]] => [[1,4,6],[2,5],[3]]

[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [[1,2,3],[4,5],[6]] => [[1,3,6],[2,5],[4]]

[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [[1,2,5,6],[3,4]] => [[1,2,3,4],[5,6]]

[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [[1,3,4,5],[2,6]] => [[1,3,4,5],[2,6]]

[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [[1,3,4],[2,5,6]] => [[1,2,5],[3,4,6]]

[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [[1,3,5],[2,4,6]] => [[1,3,5],[2,4,6]]

[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [[1,3,4],[2,5],[6]] => [[1,4,5],[2,6],[3]]

[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [[1,3,5,6],[2,4]] => [[1,2,3,5],[4,6]]

[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [[1,2,4,5],[3],[6]] => [[1,3,4,6],[2],[5]]

[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [[1,2,4],[3,6],[5]] => [[1,2,6],[3,4],[5]]

[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [[1,2,3,5],[4],[6]] => [[1,3,5,6],[2],[4]]

[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [[1,2,3,4],[5,6]] => [[1,2,5,6],[3,4]]

[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [[1,2,3],[4,6],[5]] => [[1,2,6],[3,5],[4]]

[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [[1,2,5],[3,6],[4]] => [[1,3,6],[2,4],[5]]

[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [[1,2,4],[3,5],[6]] => [[1,4,6],[2,5],[3]]

[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [[1,2,3],[4,5],[6]] => [[1,3,6],[2,5],[4]]

[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [[1,2,6],[3,5],[4]] => [[1,2,3],[4,6],[5]]

[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [[1,3,4,5],[2,6]] => [[1,3,4,5],[2,6]]

[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [[1,3,4,6],[2,5]] => [[1,2,4,5],[3,6]]

[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [[1,3,5],[2,4],[6]] => [[1,3,5],[2,6],[4]]

[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [[1,3,4],[2,5],[6]] => [[1,4,5],[2,6],[3]]

[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [[1,3,6],[2,4],[5]] => [[1,2,5],[3,6],[4]]

[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [[1,2,5],[3,4],[6]] => [[1,3,4],[2,6],[5]]

[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [[1,2,4],[3,5],[6]] => [[1,4,6],[2,5],[3]]

[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [[1,2,3],[4],[5],[6]] => [[1,5,6],[2],[3],[4]]

[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [[1,2,6],[3,4],[5]] => [[1,2,4],[3,6],[5]]

[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [[1,3,4,5],[2,6]] => [[1,3,4,5],[2,6]]

[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [[1,3,4],[2,5],[6]] => [[1,4,5],[2,6],[3]]

[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [[1,3,5],[2,4],[6]] => [[1,3,5],[2,6],[4]]

[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [[1,2,5],[3,4],[6]] => [[1,3,4],[2,6],[5]]

[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[1,3,4,5,6],[2]] => [[1,2,3,4,5],[6]]

[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7]] => [[1,3,4,5,6,7],[2]]

[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [[1,2,3,4,5],[6,7]] => [[1,2,5,6,7],[3,4]]

[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [[1,2,3,4,6],[5,7]] => [[1,3,5,6,7],[2,4]]

[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [[1,2,3,4,5],[6],[7]] => [[1,4,5,6,7],[2],[3]]

[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [[1,2,3,4,7],[5,6]] => [[1,2,3,6,7],[4,5]]

[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [[1,2,3,5,6],[4,7]] => [[1,3,4,6,7],[2,5]]

[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [[1,2,3,5],[4,6,7]] => [[1,2,4,7],[3,5,6]]

[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [[1,2,3,4,6],[5],[7]] => [[1,3,5,6,7],[2],[4]]

[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [[1,2,3,4,5],[6],[7]] => [[1,4,5,6,7],[2],[3]]

[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => [[1,2,3,4],[5,7],[6]] => [[1,2,6,7],[3,5],[4]]

[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [[1,2,3,6],[4,5,7]] => [[1,3,4,7],[2,5,6]]

[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => [[1,2,3,5],[4,6],[7]] => [[1,4,6,7],[2,5],[3]]

[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [[1,2,3,4],[5,6],[7]] => [[1,3,6,7],[2,5],[4]]

[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [[1,2,3,6,7],[4,5]] => [[1,2,3,4,7],[5,6]]

[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [[1,2,4,5,6],[3,7]] => [[1,3,4,5,7],[2,6]]

[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [[1,2,4,5],[3,6,7]] => [[1,2,5,7],[3,4,6]]

[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [[1,2,4,6],[3,5,7]] => [[1,3,5,7],[2,4,6]]

[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [[1,2,4,5],[3,6],[7]] => [[1,4,5,7],[2,6],[3]]

[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [[1,2,4,7],[3,5,6]] => [[1,2,3,5],[4,6,7]]

[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [[1,2,3,5,6],[4],[7]] => [[1,3,4,6,7],[2],[5]]

[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [[1,2,3,5],[4,7],[6]] => [[1,2,6,7],[3,4],[5]]

[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [[1,2,3,4,6],[5],[7]] => [[1,3,5,6,7],[2],[4]]

[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [[1,2,3,4,5],[6,7]] => [[1,2,5,6,7],[3,4]]

[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [[1,2,3,4],[5,7],[6]] => [[1,2,6,7],[3,5],[4]]

[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [[1,2,3,6],[4,7],[5]] => [[1,3,6,7],[2,4],[5]]

[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [[1,2,3,5],[4,6],[7]] => [[1,4,6,7],[2,5],[3]]

[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [[1,2,3,4],[5,6],[7]] => [[1,3,6,7],[2,5],[4]]

[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => [[1,2,3,7],[4,6],[5]] => [[1,2,3,7],[4,6],[5]]

[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [[1,2,5,6],[3,4,7]] => [[1,3,4,5],[2,6,7]]

[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [[1,2,5,7],[3,4,6]] => [[1,2,4,5],[3,6,7]]

[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [[1,2,4,6],[3,5],[7]] => [[1,3,5,7],[2,6],[4]]

[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [[1,2,4,5],[3,6],[7]] => [[1,4,5,7],[2,6],[3]]

[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [[1,2,4],[3,5,7],[6]] => [[1,2,5],[3,6,7],[4]]

[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [[1,2,3,6],[4,5],[7]] => [[1,3,4,7],[2,6],[5]]

[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [[1,2,3,5],[4,6],[7]] => [[1,4,6,7],[2,5],[3]]

[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [[1,2,3,4],[5],[6],[7]] => [[1,5,6,7],[2],[3],[4]]

[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => [[1,2,3,7],[4,5],[6]] => [[1,2,4,7],[3,6],[5]]

>>> Load all 808 entries. <<<

[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [[1,2,5,6],[3,4,7]] => [[1,3,4,5],[2,6,7]]

[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [[1,2,5],[3,4,6],[7]] => [[1,4,5],[2,6,7],[3]]

[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [[1,2,4],[3,5,6],[7]] => [[1,3,5],[2,6,7],[4]]

[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [[1,2,3,6],[4,5],[7]] => [[1,3,4,7],[2,6],[5]]

[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [[1,2,5,6,7],[3,4]] => [[1,2,3,4,5],[6,7]]

[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [[1,3,4,5,6],[2,7]] => [[1,3,4,5,6],[2,7]]

[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [[1,3,4,5],[2,6,7]] => [[1,2,5,6],[3,4,7]]

[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [[1,3,4,6],[2,5,7]] => [[1,3,5,6],[2,4,7]]

[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [[1,3,4,5],[2,6],[7]] => [[1,4,5,6],[2,7],[3]]

[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [[1,3,4,7],[2,5,6]] => [[1,2,3,6],[4,5,7]]

[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [[1,3,5,6],[2,4,7]] => [[1,3,4,6],[2,5,7]]

[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [[1,3,5,7],[2,4,6]] => [[1,2,4,6],[3,5,7]]

[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [[1,3,4,6],[2,5],[7]] => [[1,3,5,6],[2,7],[4]]

[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [[1,3,4,5],[2,6],[7]] => [[1,4,5,6],[2,7],[3]]

[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => [[1,3,4],[2,5,7],[6]] => [[1,2,6],[3,5,7],[4]]

[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [[1,3,5,6],[2,4,7]] => [[1,3,4,6],[2,5,7]]

[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [[1,3,5],[2,4,6],[7]] => [[1,4,6],[2,5,7],[3]]

[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [[1,3,4],[2,5,6],[7]] => [[1,3,6],[2,5,7],[4]]

[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [[1,3,5,6,7],[2,4]] => [[1,2,3,4,6],[5,7]]

[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [[1,2,4,5,6],[3],[7]] => [[1,3,4,5,7],[2],[6]]

[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [[1,2,4,5],[3,7],[6]] => [[1,2,5,7],[3,4],[6]]

[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [[1,2,4,6],[3,7],[5]] => [[1,3,5,7],[2,4],[6]]

[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [[1,2,4,5],[3,6],[7]] => [[1,4,5,7],[2,6],[3]]

[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => [[1,2,4,7],[3,6],[5]] => [[1,2,3,7],[4,5],[6]]

[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [[1,2,3,5,6],[4],[7]] => [[1,3,4,6,7],[2],[5]]

[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [[1,2,3,5],[4,7],[6]] => [[1,2,6,7],[3,4],[5]]

[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [[1,2,3,4,6],[5,7]] => [[1,3,5,6,7],[2,4]]

[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [[1,2,3,4,5],[6],[7]] => [[1,4,5,6,7],[2],[3]]

[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [[1,2,3,4],[5,6,7]] => [[1,2,3,7],[4,5,6]]

[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [[1,2,3,6],[4,7],[5]] => [[1,3,6,7],[2,4],[5]]

[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [[1,2,3,5],[4,6],[7]] => [[1,4,6,7],[2,5],[3]]

[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [[1,2,3,4],[5,6],[7]] => [[1,3,6,7],[2,5],[4]]

[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => [[1,2,3,7],[4,6],[5]] => [[1,2,3,7],[4,6],[5]]

[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [[1,2,5,6],[3,7],[4]] => [[1,3,4,7],[2,5],[6]]

[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [[1,2,5],[3,6,7],[4]] => [[1,2,4],[3,5,7],[6]]

[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [[1,2,4,6],[3,5],[7]] => [[1,3,5,7],[2,6],[4]]

[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [[1,2,4,5],[3,6],[7]] => [[1,4,5,7],[2,6],[3]]

[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [[1,2,4],[3,5,7],[6]] => [[1,2,5],[3,6,7],[4]]

[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [[1,2,3,6],[4,5],[7]] => [[1,3,4,7],[2,6],[5]]

[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [[1,2,3,5],[4,6],[7]] => [[1,4,6,7],[2,5],[3]]

[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [[1,2,3,4],[5,7],[6]] => [[1,2,6,7],[3,5],[4]]

[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [[1,2,3],[4,5,7],[6]] => [[1,2,4],[3,6,7],[5]]

[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [[1,2,6],[3,5,7],[4]] => [[1,3,4],[2,5,7],[6]]

[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [[1,2,5],[3,6],[4,7]] => [[1,4,7],[2,5],[3,6]]

[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [[1,2,4],[3,5,6],[7]] => [[1,3,5],[2,6,7],[4]]

[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [[1,2,3],[4,5,6],[7]] => [[1,3,4],[2,6,7],[5]]

[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [[1,2,6,7],[3,5],[4]] => [[1,2,3,4],[5,7],[6]]

[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [[1,3,4,5,6],[2,7]] => [[1,3,4,5,6],[2,7]]

[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [[1,3,4,5],[2,6,7]] => [[1,2,5,6],[3,4,7]]

[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [[1,3,4,6],[2,5,7]] => [[1,3,5,6],[2,4,7]]

[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [[1,3,4,5],[2,6],[7]] => [[1,4,5,6],[2,7],[3]]

[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [[1,3,4,6,7],[2,5]] => [[1,2,3,5,6],[4,7]]

[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [[1,3,5,6],[2,4],[7]] => [[1,3,4,6],[2,7],[5]]

[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => [[1,3,5],[2,4,7],[6]] => [[1,2,6],[3,4,7],[5]]

[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [[1,3,4,6],[2,5],[7]] => [[1,3,5,6],[2,7],[4]]

[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [[1,3,4,5],[2,6,7]] => [[1,2,5,6],[3,4,7]]

[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [[1,3,4],[2,5,7],[6]] => [[1,2,6],[3,5,7],[4]]

[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => [[1,3,6],[2,4,7],[5]] => [[1,3,6],[2,4,7],[5]]

[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [[1,3,5],[2,4,6],[7]] => [[1,4,6],[2,5,7],[3]]

[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [[1,3,4],[2,5,6],[7]] => [[1,3,6],[2,5,7],[4]]

[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => [[1,3,6,7],[2,4],[5]] => [[1,2,3,6],[4,7],[5]]

[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [[1,2,5,6],[3,4],[7]] => [[1,3,4,5],[2,7],[6]]

[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [[1,2,5],[3,4,7],[6]] => [[1,2,5],[3,4,7],[6]]

[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [[1,2,4,6],[3,5],[7]] => [[1,3,5,7],[2,6],[4]]

[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [[1,2,4,5],[3,7],[6]] => [[1,2,5,7],[3,4],[6]]

[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [[1,2,4],[3,5,7],[6]] => [[1,2,5],[3,6,7],[4]]

[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [[1,2,3,6],[4],[5],[7]] => [[1,3,6,7],[2],[4],[5]]

[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [[1,2,3,5],[4,7],[6]] => [[1,2,6,7],[3,4],[5]]

[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [[1,2,3,4],[5,7],[6]] => [[1,2,6,7],[3,5],[4]]

[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [[1,2,3],[4,7],[5],[6]] => [[1,2,7],[3,6],[4],[5]]

[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [[1,2,6],[3,4,7],[5]] => [[1,3,5],[2,4,7],[6]]

[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [[1,2,5],[3,4,6],[7]] => [[1,4,5],[2,6,7],[3]]

[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [[1,2,4],[3,5,6],[7]] => [[1,3,5],[2,6,7],[4]]

[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [[1,2,3],[4,6],[5],[7]] => [[1,3,7],[2,6],[4],[5]]

[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => [[1,2,6,7],[3,4],[5]] => [[1,2,3,5],[4,7],[6]]

[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [[1,3,4,5,6],[2,7]] => [[1,3,4,5,6],[2,7]]

[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [[1,3,4,5,7],[2,6]] => [[1,2,4,5,6],[3,7]]

[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => [[1,3,4,6],[2,5],[7]] => [[1,3,5,6],[2,7],[4]]

[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [[1,3,4,5],[2,6],[7]] => [[1,4,5,6],[2,7],[3]]

[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => [[1,3,4,7],[2,5],[6]] => [[1,2,5,6],[3,7],[4]]

[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [[1,3,5,6],[2,4],[7]] => [[1,3,4,6],[2,7],[5]]

[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [[1,3,5],[2,4,6],[7]] => [[1,4,6],[2,5,7],[3]]

[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [[1,3,4],[2,5],[6],[7]] => [[1,5,6],[2,7],[3],[4]]

[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => [[1,3,5,7],[2,4],[6]] => [[1,2,4,6],[3,7],[5]]

[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [[1,2,5,6],[3,4],[7]] => [[1,3,4,5],[2,7],[6]]

[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [[1,2,5],[3,4,6],[7]] => [[1,4,5],[2,6,7],[3]]

[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [[1,2,4],[3,5],[6],[7]] => [[1,5,7],[2,6],[3],[4]]

[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [[1,2,3],[4,5],[6],[7]] => [[1,4,7],[2,6],[3],[5]]

[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [[1,2,5,7],[3,4],[6]] => [[1,2,4,5],[3,7],[6]]

[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [[1,3,4,5,6],[2,7]] => [[1,3,4,5,6],[2,7]]

[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => [[1,3,4,5],[2,6],[7]] => [[1,4,5,6],[2,7],[3]]

[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => [[1,3,4,6],[2,5],[7]] => [[1,3,5,6],[2,7],[4]]

[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [[1,3,5,6],[2,4],[7]] => [[1,3,4,6],[2,7],[5]]

[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [[1,2,5,6],[3,4],[7]] => [[1,3,4,5],[2,7],[6]]

[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2]] => [[1,2,3,4,5,6],[7]]

[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8]] => [[1,3,4,5,6,7,8],[2]]

[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [[1,2,3,4,5,6],[7,8]] => [[1,2,5,6,7,8],[3,4]]

[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => [[1,2,3,4,5,7],[6,8]] => [[1,3,5,6,7,8],[2,4]]

[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6] => [[1,2,3,4,5,6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]]

[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [[1,2,3,4,5,8],[6,7]] => [[1,2,3,6,7,8],[4,5]]

[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => [[1,2,3,4,6,7],[5,8]] => [[1,3,4,6,7,8],[2,5]]

[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [[1,2,3,4,6],[5,7,8]] => [[1,2,4,7,8],[3,5,6]]

[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,1,2,3,6,4,5,7] => [[1,2,3,4,5,7],[6],[8]] => [[1,3,5,6,7,8],[2],[4]]

[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,1,2,3,7,4,5,6] => [[1,2,3,4,5,6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]]

[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,1,2,3,6,4,8,5] => [[1,2,3,4,5],[6,8],[7]] => [[1,2,6,7,8],[3,5],[4]]

[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [[1,2,3,4,7],[5,6,8]] => [[1,3,4,7,8],[2,5,6]]

[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,1,2,3,8,7,4,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,4,6,7,8],[2,5],[3]]

[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7],[8]] => [[1,3,6,7,8],[2,5],[4]]

[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [[1,2,3,4,7,8],[5,6]] => [[1,2,3,4,7,8],[5,6]]

[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [[1,2,3,5,6,7],[4,8]] => [[1,3,4,5,7,8],[2,6]]

[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => [[1,2,3,5,6],[4,7,8]] => [[1,2,5,7,8],[3,4,6]]

[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [[1,2,3,5,7],[4,6,8]] => [[1,3,5,7,8],[2,4,6]]

[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [4,1,2,8,3,7,5,6] => [[1,2,3,5,6],[4,7],[8]] => [[1,4,5,7,8],[2,6],[3]]

[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [[1,2,3,5,8],[4,6,7]] => [[1,2,3,5,8],[4,6,7]]

[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,1,2,5,3,4,6,7] => [[1,2,3,4,6,7],[5],[8]] => [[1,3,4,6,7,8],[2],[5]]

[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,1,2,5,3,4,8,6] => [[1,2,3,4,6],[5,8],[7]] => [[1,2,6,7,8],[3,4],[5]]

[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,1,2,6,3,4,5,7] => [[1,2,3,4,5,7],[6],[8]] => [[1,3,5,6,7,8],[2],[4]]

[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,1,2,8,3,4,5,6] => [[1,2,3,4,5,6],[7,8]] => [[1,2,5,6,7,8],[3,4]]

[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [7,1,2,6,3,4,8,5] => [[1,2,3,4,5],[6,8],[7]] => [[1,2,6,7,8],[3,5],[4]]

[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,1,2,5,3,8,4,7] => [[1,2,3,4,7],[5,8],[6]] => [[1,3,6,7,8],[2,4],[5]]

[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [8,1,2,5,3,7,4,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,4,6,7,8],[2,5],[3]]

[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [8,1,2,6,3,7,4,5] => [[1,2,3,4,5],[6,7],[8]] => [[1,3,6,7,8],[2,5],[4]]

[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [6,1,2,5,3,7,8,4] => [[1,2,3,4,8],[5,7],[6]] => [[1,2,3,7,8],[4,6],[5]]

[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => [[1,2,3,6,7],[4,5,8]] => [[1,3,4,5,8],[2,6,7]]

[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [[1,2,3,6,8],[4,5,7]] => [[1,2,4,5,8],[3,6,7]]

[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [4,1,2,8,6,3,5,7] => [[1,2,3,5,7],[4,6],[8]] => [[1,3,5,7,8],[2,6],[4]]

[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [4,1,2,8,7,3,5,6] => [[1,2,3,5,6],[4,7],[8]] => [[1,4,5,7,8],[2,6],[3]]

[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,1,2,7,6,3,8,5] => [[1,2,3,5],[4,6,8],[7]] => [[1,2,5,8],[3,6,7],[4]]

[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,1,2,5,6,3,4,7] => [[1,2,3,4,7],[5,6],[8]] => [[1,3,4,7,8],[2,6],[5]]

[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [8,1,2,5,7,3,4,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,4,6,7,8],[2,5],[3]]

[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [8,1,2,7,6,3,4,5] => [[1,2,3,4,5],[6],[7],[8]] => [[1,5,6,7,8],[2],[3],[4]]

[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [7,1,2,5,6,3,8,4] => [[1,2,3,4,8],[5,6],[7]] => [[1,2,4,7,8],[3,6],[5]]

[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [[1,2,3,6,7],[4,5,8]] => [[1,3,4,5,8],[2,6,7]]

[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,8,7,3,6] => [[1,2,3,6],[4,5,7],[8]] => [[1,4,5,8],[2,6,7],[3]]

[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,1,2,8,6,7,3,5] => [[1,2,3,5],[4,6,7],[8]] => [[1,3,5,8],[2,6,7],[4]]

[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [[1,2,3,4,7],[5,6],[8]] => [[1,3,4,7,8],[2,6],[5]]

[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [[1,2,3,6,7,8],[4,5]] => [[1,2,3,4,5,8],[6,7]]

[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [[1,2,4,5,6,7],[3,8]] => [[1,3,4,5,6,8],[2,7]]

[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => [[1,2,4,5,6],[3,7,8]] => [[1,2,5,6,8],[3,4,7]]

[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,6,2,4,8,5,7] => [[1,2,4,5,7],[3,6,8]] => [[1,3,5,6,8],[2,4,7]]

[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [3,1,8,2,4,7,5,6] => [[1,2,4,5,6],[3,7],[8]] => [[1,4,5,6,8],[2,7],[3]]

[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [[1,2,4,5,8],[3,6,7]] => [[1,2,3,6,8],[4,5,7]]

[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [[1,2,4,6,7],[3,5,8]] => [[1,3,4,6,8],[2,5,7]]

[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [[1,2,4,6],[3,5,7,8]] => [[1,2,4,6],[3,5,7,8]]

[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,8,2,6,4,5,7] => [[1,2,4,5,7],[3,6],[8]] => [[1,3,5,6,8],[2,7],[4]]

[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [3,1,8,2,7,4,5,6] => [[1,2,4,5,6],[3,7],[8]] => [[1,4,5,6,8],[2,7],[3]]

[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,1,7,2,6,4,8,5] => [[1,2,4,5],[3,6,8],[7]] => [[1,2,6,8],[3,5,7],[4]]

[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [[1,2,4,7],[3,5,6,8]] => [[1,3,4,6],[2,5,7,8]]

[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,5,2,8,7,4,6] => [[1,2,4,6],[3,5,7],[8]] => [[1,4,6,8],[2,5,7],[3]]

[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,1,8,2,6,7,4,5] => [[1,2,4,5],[3,6,7],[8]] => [[1,3,6,8],[2,5,7],[4]]

[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [[1,2,4,7,8],[3,5,6]] => [[1,2,3,4,6],[5,7,8]]

[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,1,4,2,3,5,6,7] => [[1,2,3,5,6,7],[4],[8]] => [[1,3,4,5,7,8],[2],[6]]

[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,1,4,2,3,5,8,6] => [[1,2,3,5,6],[4,8],[7]] => [[1,2,5,7,8],[3,4],[6]]

[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,1,4,2,3,8,5,7] => [[1,2,3,5,7],[4,8],[6]] => [[1,3,5,7,8],[2,4],[6]]

[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [8,1,4,2,3,7,5,6] => [[1,2,3,5,6],[4,7],[8]] => [[1,4,5,7,8],[2,6],[3]]

[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,1,4,2,3,7,8,5] => [[1,2,3,5,8],[4,7],[6]] => [[1,2,3,7,8],[4,5],[6]]

[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,1,5,2,3,4,6,7] => [[1,2,3,4,6,7],[5],[8]] => [[1,3,4,6,7,8],[2],[5]]

[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,1,5,2,3,4,8,6] => [[1,2,3,4,6],[5,8],[7]] => [[1,2,6,7,8],[3,4],[5]]

[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => [[1,2,3,4,5,7],[6,8]] => [[1,3,5,6,7,8],[2,4]]

[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,1,7,2,3,4,5,6] => [[1,2,3,4,5,6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]]

[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,1,7,2,3,4,8,5] => [[1,2,3,4,5],[6,7,8]] => [[1,2,3,7,8],[4,5,6]]

[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,1,5,2,3,8,4,7] => [[1,2,3,4,7],[5,8],[6]] => [[1,3,6,7,8],[2,4],[5]]

[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [8,1,5,2,3,7,4,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,4,6,7,8],[2,5],[3]]

[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,1,8,2,3,7,4,5] => [[1,2,3,4,5],[6,7],[8]] => [[1,3,6,7,8],[2,5],[4]]

[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,1,5,2,3,7,8,4] => [[1,2,3,4,8],[5,7],[6]] => [[1,2,3,7,8],[4,6],[5]]

[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [5,1,4,2,8,3,6,7] => [[1,2,3,6,7],[4,8],[5]] => [[1,3,4,7,8],[2,5],[6]]

[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,1,4,2,7,3,8,6] => [[1,2,3,6],[4,7,8],[5]] => [[1,2,4,8],[3,5,7],[6]]

[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,1,4,2,6,3,5,7] => [[1,2,3,5,7],[4,6],[8]] => [[1,3,5,7,8],[2,6],[4]]

[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [8,1,4,2,7,3,5,6] => [[1,2,3,5,6],[4,7],[8]] => [[1,4,5,7,8],[2,6],[3]]

[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [7,1,4,2,6,3,8,5] => [[1,2,3,5],[4,6,8],[7]] => [[1,2,5,8],[3,6,7],[4]]

[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,1,5,2,6,3,4,7] => [[1,2,3,4,7],[5,6],[8]] => [[1,3,4,7,8],[2,6],[5]]

[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [8,1,5,2,7,3,4,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,4,6,7,8],[2,5],[3]]

[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [7,1,8,2,6,3,4,5] => [[1,2,3,4,5],[6,8],[7]] => [[1,2,6,7,8],[3,5],[4]]

[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [7,1,5,2,6,3,8,4] => [[1,2,3,4],[5,6,8],[7]] => [[1,2,4,8],[3,6,7],[5]]

[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,4,2,6,8,3,7] => [[1,2,3,7],[4,6,8],[5]] => [[1,3,4,8],[2,5,7],[6]]

[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,1,4,2,8,7,3,6] => [[1,2,3,6],[4,7],[5,8]] => [[1,4,7,8],[2,5],[3,6]]

[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [8,1,4,2,6,7,3,5] => [[1,2,3,5],[4,6,7],[8]] => [[1,3,5,8],[2,6,7],[4]]

[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [8,1,5,2,6,7,3,4] => [[1,2,3,4],[5,6,7],[8]] => [[1,3,4,8],[2,6,7],[5]]

[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [5,1,4,2,6,7,8,3] => [[1,2,3,7,8],[4,6],[5]] => [[1,2,3,4,8],[5,7],[6]]

[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7] => [[1,2,5,6,7],[3,4,8]] => [[1,3,4,5,6],[2,7,8]]

[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => [[1,2,5,6],[3,4,7,8]] => [[1,2,5,6],[3,4,7,8]]

[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [[1,2,5,7],[3,4,6,8]] => [[1,3,5,6],[2,4,7,8]]

[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,4,8,2,7,5,6] => [[1,2,5,6],[3,4,7],[8]] => [[1,4,5,6],[2,7,8],[3]]

[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [[1,2,5,7,8],[3,4,6]] => [[1,2,3,5,6],[4,7,8]]

[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,8,5,2,4,6,7] => [[1,2,4,6,7],[3,5],[8]] => [[1,3,4,6,8],[2,7],[5]]

[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,7,5,2,4,8,6] => [[1,2,4,6],[3,5,8],[7]] => [[1,2,6,8],[3,4,7],[5]]

[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,8,6,2,4,5,7] => [[1,2,4,5,7],[3,6],[8]] => [[1,3,5,6,8],[2,7],[4]]

[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,7,8,2,4,5,6] => [[1,2,4,5,6],[3,7,8]] => [[1,2,5,6,8],[3,4,7]]

[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,7,6,2,4,8,5] => [[1,2,4,5],[3,6,8],[7]] => [[1,2,6,8],[3,5,7],[4]]

[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,6,5,2,8,4,7] => [[1,2,4,7],[3,5,8],[6]] => [[1,3,6,8],[2,4,7],[5]]

[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,8,5,2,7,4,6] => [[1,2,4,6],[3,5,7],[8]] => [[1,4,6,8],[2,5,7],[3]]

[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,8,6,2,7,4,5] => [[1,2,4,5],[3,6,7],[8]] => [[1,3,6,8],[2,5,7],[4]]

[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,5,2,7,8,4] => [[1,2,4,8],[3,5,7],[6]] => [[1,2,3,6],[4,7,8],[5]]

[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,1,4,5,2,3,6,7] => [[1,2,3,6,7],[4,5],[8]] => [[1,3,4,5,8],[2,7],[6]]

[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,1,4,5,2,3,8,6] => [[1,2,3,6],[4,5,8],[7]] => [[1,2,5,8],[3,4,7],[6]]

[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,1,4,6,2,3,5,7] => [[1,2,3,5,7],[4,6],[8]] => [[1,3,5,7,8],[2,6],[4]]

[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,1,4,8,2,3,5,6] => [[1,2,3,5,6],[4,8],[7]] => [[1,2,5,7,8],[3,4],[6]]

[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [7,1,4,6,2,3,8,5] => [[1,2,3,5],[4,6,8],[7]] => [[1,2,5,8],[3,6,7],[4]]

[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,1,6,5,2,3,4,7] => [[1,2,3,4,7],[5],[6],[8]] => [[1,3,6,7,8],[2],[4],[5]]

[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,1,8,5,2,3,4,6] => [[1,2,3,4,6],[5,8],[7]] => [[1,2,6,7,8],[3,4],[5]]

[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,1,8,6,2,3,4,5] => [[1,2,3,4,5],[6,8],[7]] => [[1,2,6,7,8],[3,5],[4]]

[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [7,1,6,5,2,3,8,4] => [[1,2,3,4],[5,8],[6],[7]] => [[1,2,7,8],[3,6],[4],[5]]

[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,1,4,5,2,8,3,7] => [[1,2,3,7],[4,5,8],[6]] => [[1,3,5,8],[2,4,7],[6]]

[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [8,1,4,5,2,7,3,6] => [[1,2,3,6],[4,5,7],[8]] => [[1,4,5,8],[2,6,7],[3]]

[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [8,1,4,6,2,7,3,5] => [[1,2,3,5],[4,6,7],[8]] => [[1,3,5,8],[2,6,7],[4]]

[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [8,1,6,5,2,7,3,4] => [[1,2,3,4],[5,7],[6],[8]] => [[1,3,7,8],[2,6],[4],[5]]

[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [6,1,4,5,2,7,8,3] => [[1,2,3,7,8],[4,5],[6]] => [[1,2,3,5,8],[4,7],[6]]

[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => [[1,2,5,6,7],[3,4,8]] => [[1,3,4,5,6],[2,7,8]]

[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,1,4,5,7,2,8,6] => [[1,2,5,6,8],[3,4,7]] => [[1,2,4,5,6],[3,7,8]]

[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,8,6,2,5,7] => [[1,2,5,7],[3,4,6],[8]] => [[1,3,5,6],[2,7,8],[4]]

[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,1,4,8,7,2,5,6] => [[1,2,5,6],[3,4,7],[8]] => [[1,4,5,6],[2,7,8],[3]]

[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,1,4,7,6,2,8,5] => [[1,2,5,8],[3,4,6],[7]] => [[1,2,5,6],[3,7,8],[4]]

[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,8,5,6,2,4,7] => [[1,2,4,7],[3,5,6],[8]] => [[1,3,4,6],[2,7,8],[5]]

[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,8,5,7,2,4,6] => [[1,2,4,6],[3,5,7],[8]] => [[1,4,6,8],[2,5,7],[3]]

[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,1,8,7,6,2,4,5] => [[1,2,4,5],[3,6],[7],[8]] => [[1,5,6,8],[2,7],[3],[4]]

[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,1,7,5,6,2,8,4] => [[1,2,4,8],[3,5,6],[7]] => [[1,2,4,6],[3,7,8],[5]]

[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,1,4,5,6,2,3,7] => [[1,2,3,6,7],[4,5],[8]] => [[1,3,4,5,8],[2,7],[6]]

[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [8,1,4,5,7,2,3,6] => [[1,2,3,6],[4,5,7],[8]] => [[1,4,5,8],[2,6,7],[3]]

[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [8,1,4,7,6,2,3,5] => [[1,2,3,5],[4,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]]

[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [8,1,7,5,6,2,3,4] => [[1,2,3,4],[5,6],[7],[8]] => [[1,4,7,8],[2,6],[3],[5]]

[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [7,1,4,5,6,2,8,3] => [[1,2,3,6,8],[4,5],[7]] => [[1,2,4,5,8],[3,7],[6]]

[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [[1,2,5,6,7],[3,4,8]] => [[1,3,4,5,6],[2,7,8]]

[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,1,4,5,8,7,2,6] => [[1,2,5,6],[3,4,7],[8]] => [[1,4,5,6],[2,7,8],[3]]

[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,1,4,8,6,7,2,5] => [[1,2,5,7],[3,4,6],[8]] => [[1,3,5,6],[2,7,8],[4]]

[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,8,5,6,7,2,4] => [[1,2,4,7],[3,5,6],[8]] => [[1,3,4,6],[2,7,8],[5]]

[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [8,1,4,5,6,7,2,3] => [[1,2,3,6,7],[4,5],[8]] => [[1,3,4,5,8],[2,7],[6]]

[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [[1,2,5,6,7,8],[3,4]] => [[1,2,3,4,5,6],[7,8]]

[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [[1,3,4,5,6,7],[2,8]]

[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [[1,3,4,5,6],[2,7,8]] => [[1,2,5,6,7],[3,4,8]]

[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,6,1,3,4,8,5,7] => [[1,3,4,5,7],[2,6,8]] => [[1,3,5,6,7],[2,4,8]]

[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,8,1,3,4,7,5,6] => [[1,3,4,5,6],[2,7],[8]] => [[1,4,5,6,7],[2,8],[3]]

[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,6,1,3,4,7,8,5] => [[1,3,4,5,8],[2,6,7]] => [[1,2,3,6,7],[4,5,8]]

[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => [[1,3,4,6,7],[2,5,8]] => [[1,3,4,6,7],[2,5,8]]

[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [[1,3,4,6],[2,5,7,8]] => [[1,2,4,7],[3,5,6,8]]

[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,8,1,3,6,4,5,7] => [[1,3,4,5,7],[2,6],[8]] => [[1,3,5,6,7],[2,8],[4]]

[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,8,1,3,7,4,5,6] => [[1,3,4,5,6],[2,7],[8]] => [[1,4,5,6,7],[2,8],[3]]

[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,7,1,3,6,4,8,5] => [[1,3,4,5],[2,6,8],[7]] => [[1,2,6,7],[3,5,8],[4]]

[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,5,1,3,6,8,4,7] => [[1,3,4,7],[2,5,6,8]] => [[1,3,4,7],[2,5,6,8]]

[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,5,1,3,8,7,4,6] => [[1,3,4,6],[2,5,7],[8]] => [[1,4,6,7],[2,5,8],[3]]

[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,8,1,3,6,7,4,5] => [[1,3,4,5],[2,6,7],[8]] => [[1,3,6,7],[2,5,8],[4]]

[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,1,3,6,7,8,4] => [[1,3,4,7,8],[2,5,6]] => [[1,2,3,4,7],[5,6,8]]

[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => [[1,3,5,6,7],[2,4,8]] => [[1,3,4,5,7],[2,6,8]]

[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,7,3,5,8,6] => [[1,3,5,6],[2,4,7,8]] => [[1,2,5,7],[3,4,6,8]]

[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [[1,3,5,7],[2,4,6,8]] => [[1,3,5,7],[2,4,6,8]]

[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,8,3,7,5,6] => [[1,3,5,6],[2,4,7],[8]] => [[1,4,5,7],[2,6,8],[3]]

[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [[1,3,5,7,8],[2,4,6]] => [[1,2,3,5,7],[4,6,8]]

[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,8,1,5,3,4,6,7] => [[1,3,4,6,7],[2,5],[8]] => [[1,3,4,6,7],[2,8],[5]]

[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,7,1,5,3,4,8,6] => [[1,3,4,6],[2,5,8],[7]] => [[1,2,6,7],[3,4,8],[5]]

[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,8,1,6,3,4,5,7] => [[1,3,4,5,7],[2,6],[8]] => [[1,3,5,6,7],[2,8],[4]]

[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => [[1,3,4,5,6],[2,7,8]] => [[1,2,5,6,7],[3,4,8]]

[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,7,1,6,3,4,8,5] => [[1,3,4,5],[2,6,8],[7]] => [[1,2,6,7],[3,5,8],[4]]

[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,6,1,5,3,8,4,7] => [[1,3,4,7],[2,5,8],[6]] => [[1,3,6,7],[2,4,8],[5]]

[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,8,1,5,3,7,4,6] => [[1,3,4,6],[2,5,7],[8]] => [[1,4,6,7],[2,5,8],[3]]

[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,6,1,5,3,7,8,4] => [[1,3,4,8],[2,5,7],[6]] => [[1,2,3,7],[4,6,8],[5]]

[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [[1,3,5,6,7],[2,4,8]] => [[1,3,4,5,7],[2,6,8]]

[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,5,7,3,8,6] => [[1,3,5,6,8],[2,4,7]] => [[1,2,4,5,7],[3,6,8]]

[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1,8,6,3,5,7] => [[1,3,5,7],[2,4,6],[8]] => [[1,3,5,7],[2,6,8],[4]]

[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,8,7,3,5,6] => [[1,3,5,6],[2,4,7],[8]] => [[1,4,5,7],[2,6,8],[3]]

[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,4,1,7,6,3,8,5] => [[1,3,5,8],[2,4,6],[7]] => [[1,2,5,7],[3,6,8],[4]]

[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,8,1,5,6,3,4,7] => [[1,3,4,7],[2,5,6],[8]] => [[1,3,4,7],[2,6,8],[5]]

[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,8,1,5,7,3,4,6] => [[1,3,4,6],[2,5,7],[8]] => [[1,4,6,7],[2,5,8],[3]]

[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,8,1,7,6,3,4,5] => [[1,3,4,5],[2,6],[7],[8]] => [[1,5,6,7],[2,8],[3],[4]]

[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,7,1,5,6,3,8,4] => [[1,3,4,8],[2,5,6],[7]] => [[1,2,4,7],[3,6,8],[5]]

[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1,5,6,8,3,7] => [[1,3,5,6,7],[2,4,8]] => [[1,3,4,5,7],[2,6,8]]

[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,8,7,3,6] => [[1,3,5,6],[2,4,7],[8]] => [[1,4,5,7],[2,6,8],[3]]

[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1,8,6,7,3,5] => [[1,3,5,7],[2,4,6],[8]] => [[1,3,5,7],[2,6,8],[4]]

[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,8,1,5,6,7,3,4] => [[1,3,4,7],[2,5,6],[8]] => [[1,3,4,7],[2,6,8],[5]]

[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4]] => [[1,2,3,4,5,7],[6,8]]

[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => [[1,2,4,5,6,7],[3],[8]] => [[1,3,4,5,6,8],[2],[7]]

[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,3,1,2,4,5,8,6] => [[1,2,4,5,6],[3,8],[7]] => [[1,2,5,6,8],[3,4],[7]]

[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,3,1,2,4,8,5,7] => [[1,2,4,5,7],[3,8],[6]] => [[1,3,5,6,8],[2,4],[7]]

[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [8,3,1,2,4,7,5,6] => [[1,2,4,5,6],[3,7],[8]] => [[1,4,5,6,8],[2,7],[3]]

[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,3,1,2,4,7,8,5] => [[1,2,4,5,8],[3,7],[6]] => [[1,2,3,6,8],[4,5],[7]]

[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,3,1,2,8,4,6,7] => [[1,2,4,6,7],[3,8],[5]] => [[1,3,4,6,8],[2,5],[7]]

[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,3,1,2,7,4,8,6] => [[1,2,4,6],[3,7,8],[5]] => [[1,2,4,8],[3,5,6],[7]]

[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,3,1,2,6,4,5,7] => [[1,2,4,5,7],[3,6],[8]] => [[1,3,5,6,8],[2,7],[4]]

[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [8,3,1,2,7,4,5,6] => [[1,2,4,5,6],[3,7],[8]] => [[1,4,5,6,8],[2,7],[3]]

[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [7,3,1,2,6,4,8,5] => [[1,2,4,5],[3,6,8],[7]] => [[1,2,6,8],[3,5,7],[4]]

[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,1,2,6,8,4,7] => [[1,2,4,7],[3,6,8],[5]] => [[1,3,4,8],[2,5,6],[7]]

[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,1,2,8,7,4,6] => [[1,2,4,6],[3,7],[5,8]] => [[1,4,6,8],[2,5],[3,7]]

[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [8,3,1,2,6,7,4,5] => [[1,2,4,5],[3,6,7],[8]] => [[1,3,6,8],[2,5,7],[4]]

[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,3,1,2,6,7,8,4] => [[1,2,4,7,8],[3,6],[5]] => [[1,2,3,4,8],[5,6],[7]]

[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => [[1,2,3,5,6,7],[4],[8]] => [[1,3,4,5,7,8],[2],[6]]

[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,4,1,2,3,5,8,6] => [[1,2,3,5,6],[4,8],[7]] => [[1,2,5,7,8],[3,4],[6]]

[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,1,2,3,8,5,7] => [[1,2,3,5,7],[4,8],[6]] => [[1,3,5,7,8],[2,4],[6]]

[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [8,4,1,2,3,7,5,6] => [[1,2,3,5,6],[4,7],[8]] => [[1,4,5,7,8],[2,6],[3]]

[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,4,1,2,3,7,8,5] => [[1,2,3,5,8],[4,7],[6]] => [[1,2,3,7,8],[4,5],[6]]

[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,8,1,2,3,4,6,7] => [[1,2,3,4,6,7],[5,8]] => [[1,3,4,6,7,8],[2,5]]

[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [[1,2,3,4,6],[5,7,8]] => [[1,2,4,7,8],[3,5,6]]

[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [[1,2,3,4,5,7],[6],[8]] => [[1,3,5,6,7,8],[2],[4]]

[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]]

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,6,1,2,3,4,8,5] => [[1,2,3,4,5],[6,8],[7]] => [[1,2,6,7,8],[3,5],[4]]

[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [5,6,1,2,3,8,4,7] => [[1,2,3,4,7],[5,6,8]] => [[1,3,4,7,8],[2,5,6]]

[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,8,1,2,3,7,4,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,4,6,7,8],[2,5],[3]]

[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,6,1,2,3,7,4,5] => [[1,2,3,4,5],[6,7],[8]] => [[1,3,6,7,8],[2,5],[4]]

[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,1,2,3,7,8,4] => [[1,2,3,4,8],[5,6,7]] => [[1,2,3,4,8],[5,6,7]]

[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,2,8,3,6,7] => [[1,2,3,6,7],[4,8],[5]] => [[1,3,4,7,8],[2,5],[6]]

[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,4,1,2,7,3,8,6] => [[1,2,3,6],[4,7,8],[5]] => [[1,2,4,8],[3,5,7],[6]]

[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,4,1,2,6,3,5,7] => [[1,2,3,5,7],[4,6],[8]] => [[1,3,5,7,8],[2,6],[4]]

[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,4,1,2,7,3,5,6] => [[1,2,3,5,6],[4,7],[8]] => [[1,4,5,7,8],[2,6],[3]]

[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7,4,1,2,6,3,8,5] => [[1,2,3,5],[4,6,8],[7]] => [[1,2,5,8],[3,6,7],[4]]

[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [5,8,1,2,6,3,4,7] => [[1,2,3,4,7],[5,6],[8]] => [[1,3,4,7,8],[2,6],[5]]

[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,8,1,2,7,3,4,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,4,6,7,8],[2,5],[3]]

[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,1,2,6,3,4,5] => [[1,2,3,4,5],[6],[7],[8]] => [[1,5,6,7,8],[2],[3],[4]]

[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,7,1,2,6,3,8,4] => [[1,2,3,4],[5,6,8],[7]] => [[1,2,4,8],[3,6,7],[5]]

[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [5,4,1,2,6,8,3,7] => [[1,2,3,7],[4,6,8],[5]] => [[1,3,4,8],[2,5,7],[6]]

[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,4,1,2,8,7,3,6] => [[1,2,3,6],[4,7],[5,8]] => [[1,4,7,8],[2,5],[3,6]]

[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8,4,1,2,6,7,3,5] => [[1,2,3,5],[4,6,7],[8]] => [[1,3,5,8],[2,6,7],[4]]

[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,8,1,2,6,7,3,4] => [[1,2,3,4],[5,6,7],[8]] => [[1,3,4,8],[2,6,7],[5]]

[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,4,1,2,6,7,8,3] => [[1,2,3,7,8],[4,6],[5]] => [[1,2,3,4,8],[5,7],[6]]

[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,3,1,8,2,5,6,7] => [[1,2,5,6,7],[3,8],[4]] => [[1,3,4,5,8],[2,6],[7]]

[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,3,1,7,2,5,8,6] => [[1,2,5,6],[3,7,8],[4]] => [[1,2,5,8],[3,4,6],[7]]

[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,3,1,6,2,8,5,7] => [[1,2,5,7],[3,6,8],[4]] => [[1,3,5,8],[2,4,6],[7]]

[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3,1,8,2,7,5,6] => [[1,2,5,6],[3,7],[4,8]] => [[1,4,5,8],[2,6],[3,7]]

[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3,1,6,2,7,8,5] => [[1,2,5,8],[3,6,7],[4]] => [[1,2,3,5],[4,6,8],[7]]

[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,3,1,5,2,4,6,7] => [[1,2,4,6,7],[3,5],[8]] => [[1,3,4,6,8],[2,7],[5]]

[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,3,1,5,2,4,8,6] => [[1,2,4,6],[3,5,8],[7]] => [[1,2,6,8],[3,4,7],[5]]

[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,3,1,6,2,4,5,7] => [[1,2,4,5,7],[3,6],[8]] => [[1,3,5,6,8],[2,7],[4]]

[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,3,1,8,2,4,5,6] => [[1,2,4,5,6],[3,8],[7]] => [[1,2,5,6,8],[3,4],[7]]

[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7,3,1,6,2,4,8,5] => [[1,2,4,5],[3,6,8],[7]] => [[1,2,6,8],[3,5,7],[4]]

[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,1,5,2,8,4,7] => [[1,2,4,7],[3,5,8],[6]] => [[1,3,6,8],[2,4,7],[5]]

[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8,3,1,5,2,7,4,6] => [[1,2,4,6],[3,5,7],[8]] => [[1,4,6,8],[2,5,7],[3]]

[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8,3,1,6,2,7,4,5] => [[1,2,4,5],[3,6,7],[8]] => [[1,3,6,8],[2,5,7],[4]]

[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [6,3,1,5,2,7,8,4] => [[1,2,4,8],[3,5,7],[6]] => [[1,2,3,6],[4,7,8],[5]]

[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,4,1,5,2,3,6,7] => [[1,2,3,6,7],[4,5],[8]] => [[1,3,4,5,8],[2,7],[6]]

[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,4,1,5,2,3,8,6] => [[1,2,3,6],[4,5,8],[7]] => [[1,2,5,8],[3,4,7],[6]]

[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,4,1,6,2,3,5,7] => [[1,2,3,5,7],[4,6],[8]] => [[1,3,5,7,8],[2,6],[4]]

[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,4,1,8,2,3,5,6] => [[1,2,3,5,6],[4,8],[7]] => [[1,2,5,7,8],[3,4],[6]]

[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7,4,1,6,2,3,8,5] => [[1,2,3,5],[4,6,8],[7]] => [[1,2,5,8],[3,6,7],[4]]

[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,8,1,5,2,3,4,7] => [[1,2,3,4,7],[5,8],[6]] => [[1,3,6,7,8],[2,4],[5]]

[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8,7,1,5,2,3,4,6] => [[1,2,3,4,6],[5],[7],[8]] => [[1,4,6,7,8],[2],[3],[5]]

[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,1,6,2,3,4,5] => [[1,2,3,4,5],[6],[7],[8]] => [[1,5,6,7,8],[2],[3],[4]]

[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [6,7,1,5,2,3,8,4] => [[1,2,3,4],[5,7,8],[6]] => [[1,2,3,8],[4,6,7],[5]]

[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,4,1,5,2,8,3,7] => [[1,2,3,7],[4,5,8],[6]] => [[1,3,5,8],[2,4,7],[6]]

[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8,4,1,5,2,7,3,6] => [[1,2,3,6],[4,5,7],[8]] => [[1,4,5,8],[2,6,7],[3]]

[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8,4,1,6,2,7,3,5] => [[1,2,3,5],[4,6,7],[8]] => [[1,3,5,8],[2,6,7],[4]]

[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [6,8,1,5,2,7,3,4] => [[1,2,3,4],[5,7],[6,8]] => [[1,3,7,8],[2,4],[5,6]]

[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [6,4,1,5,2,7,8,3] => [[1,2,3,8],[4,5,7],[6]] => [[1,2,3,5],[4,7,8],[6]]

[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,5,8,2,6,7] => [[1,2,6,7],[3,5,8],[4]] => [[1,3,4,5],[2,6,8],[7]]

[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [4,3,1,5,7,2,8,6] => [[1,2,6,8],[3,5,7],[4]] => [[1,2,4,5],[3,6,8],[7]]

[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [4,3,1,8,6,2,5,7] => [[1,2,5,7],[3,6],[4,8]] => [[1,3,5,8],[2,6],[4,7]]

[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [4,3,1,8,7,2,5,6] => [[1,2,5,6],[3,7],[4,8]] => [[1,4,5,8],[2,6],[3,7]]

[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,3,1,7,6,2,8,5] => [[1,2,5],[3,6,8],[4,7]] => [[1,2,5],[3,6,8],[4,7]]

[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,3,1,5,6,2,4,7] => [[1,2,4,7],[3,5,6],[8]] => [[1,3,4,6],[2,7,8],[5]]

[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8,3,1,5,7,2,4,6] => [[1,2,4,6],[3,5,7],[8]] => [[1,4,6,8],[2,5,7],[3]]

[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8,3,1,7,6,2,4,5] => [[1,2,4,5],[3,6],[7],[8]] => [[1,5,6,8],[2,7],[3],[4]]

[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7,3,1,5,6,2,8,4] => [[1,2,4,8],[3,5,6],[7]] => [[1,2,4,6],[3,7,8],[5]]

[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,1,5,6,2,3,7] => [[1,2,3,7],[4,5,6],[8]] => [[1,3,4,5],[2,7,8],[6]]

[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8,4,1,5,7,2,3,6] => [[1,2,3,6],[4,5,7],[8]] => [[1,4,5,8],[2,6,7],[3]]

[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8,4,1,7,6,2,3,5] => [[1,2,3,5],[4,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]]

[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [[1,2,3,4],[5,6],[7,8]] => [[1,2,7,8],[3,4],[5,6]]

[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7,4,1,5,6,2,8,3] => [[1,2,3,8],[4,5,6],[7]] => [[1,2,4,5],[3,7,8],[6]]

[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [4,3,1,5,6,8,2,7] => [[1,2,6,7],[3,5,8],[4]] => [[1,3,4,5],[2,6,8],[7]]

[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [4,3,1,5,8,7,2,6] => [[1,2,6],[3,5,7],[4,8]] => [[1,4,5],[2,6,8],[3,7]]

[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,3,1,8,6,7,2,5] => [[1,2,5],[3,6,7],[4,8]] => [[1,3,5],[2,6,8],[4,7]]

[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8,3,1,5,6,7,2,4] => [[1,2,4,7],[3,5,6],[8]] => [[1,3,4,6],[2,7,8],[5]]

[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8,4,1,5,6,7,2,3] => [[1,2,3,7],[4,5,6],[8]] => [[1,3,4,5],[2,7,8],[6]]

[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [[1,2,6,7,8],[3,5],[4]] => [[1,2,3,4,5],[6,8],[7]]

[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [[1,3,4,5,6,7],[2,8]]

[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6] => [[1,3,4,5,6],[2,7,8]] => [[1,2,5,6,7],[3,4,8]]

[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => [[1,3,4,5,7],[2,6,8]] => [[1,3,5,6,7],[2,4,8]]

[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,3,8,1,4,7,5,6] => [[1,3,4,5,6],[2,7],[8]] => [[1,4,5,6,7],[2,8],[3]]

[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [[1,3,4,5,8],[2,6,7]] => [[1,2,3,6,7],[4,5,8]]

[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => [[1,3,4,6,7],[2,5,8]] => [[1,3,4,6,7],[2,5,8]]

[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [[1,3,4,6,8],[2,5,7]] => [[1,2,4,6,7],[3,5,8]]

[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,3,8,1,6,4,5,7] => [[1,3,4,5,7],[2,6],[8]] => [[1,3,5,6,7],[2,8],[4]]

[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,3,8,1,7,4,5,6] => [[1,3,4,5,6],[2,7],[8]] => [[1,4,5,6,7],[2,8],[3]]

[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,3,7,1,6,4,8,5] => [[1,3,4,5],[2,6,8],[7]] => [[1,2,6,7],[3,5,8],[4]]

[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [[1,3,4,6,7],[2,5,8]] => [[1,3,4,6,7],[2,5,8]]

[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,3,5,1,8,7,4,6] => [[1,3,4,6],[2,5,7],[8]] => [[1,4,6,7],[2,5,8],[3]]

[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,3,8,1,6,7,4,5] => [[1,3,4,5],[2,6,7],[8]] => [[1,3,6,7],[2,5,8],[4]]

[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [[1,3,4,6,7,8],[2,5]] => [[1,2,3,4,6,7],[5,8]]

[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,8,4,1,3,5,6,7] => [[1,3,5,6,7],[2,4],[8]] => [[1,3,4,5,7],[2,8],[6]]

[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,7,4,1,3,5,8,6] => [[1,3,5,6],[2,4,8],[7]] => [[1,2,5,7],[3,4,8],[6]]

[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,6,4,1,3,8,5,7] => [[1,3,5,7],[2,4,8],[6]] => [[1,3,5,7],[2,4,8],[6]]

[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,8,4,1,3,7,5,6] => [[1,3,5,6],[2,4,7],[8]] => [[1,4,5,7],[2,6,8],[3]]

[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,6,4,1,3,7,8,5] => [[1,3,5,8],[2,4,7],[6]] => [[1,2,3,7],[4,5,8],[6]]

[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,8,5,1,3,4,6,7] => [[1,3,4,6,7],[2,5],[8]] => [[1,3,4,6,7],[2,8],[5]]

[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,7,5,1,3,4,8,6] => [[1,3,4,6],[2,5,8],[7]] => [[1,2,6,7],[3,4,8],[5]]

[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,8,1,3,4,5,7] => [[1,3,4,5,7],[2,6,8]] => [[1,3,5,6,7],[2,4,8]]

[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,8,7,1,3,4,5,6] => [[1,3,4,5,6],[2,7],[8]] => [[1,4,5,6,7],[2,8],[3]]

[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => [[1,3,4,5],[2,6,7,8]] => [[1,2,3,7],[4,5,6,8]]

[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,6,5,1,3,8,4,7] => [[1,3,4,7],[2,5,8],[6]] => [[1,3,6,7],[2,4,8],[5]]

[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,8,5,1,3,7,4,6] => [[1,3,4,6],[2,5,7],[8]] => [[1,4,6,7],[2,5,8],[3]]

[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,6,8,1,3,7,4,5] => [[1,3,4,5],[2,6,7],[8]] => [[1,3,6,7],[2,5,8],[4]]

[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,6,5,1,3,7,8,4] => [[1,3,4,8],[2,5,7],[6]] => [[1,2,3,7],[4,6,8],[5]]

[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,5,4,1,8,3,6,7] => [[1,3,6,7],[2,4,8],[5]] => [[1,3,4,7],[2,5,8],[6]]

[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,5,4,1,7,3,8,6] => [[1,3,6,8],[2,4,7],[5]] => [[1,2,4,7],[3,5,8],[6]]

[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,8,4,1,6,3,5,7] => [[1,3,5,7],[2,4,6],[8]] => [[1,3,5,7],[2,6,8],[4]]

[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6] => [[1,3,5,6],[2,4,7],[8]] => [[1,4,5,7],[2,6,8],[3]]

[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,7,4,1,6,3,8,5] => [[1,3,5,8],[2,4,6],[7]] => [[1,2,5,7],[3,6,8],[4]]

[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,8,5,1,6,3,4,7] => [[1,3,4,7],[2,5,6],[8]] => [[1,3,4,7],[2,6,8],[5]]

[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6] => [[1,3,4,6],[2,5,7],[8]] => [[1,4,6,7],[2,5,8],[3]]

[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,7,8,1,6,3,4,5] => [[1,3,4,5],[2,6,8],[7]] => [[1,2,6,7],[3,5,8],[4]]

[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,7,5,1,6,3,8,4] => [[1,3,4,8],[2,5,6],[7]] => [[1,2,4,7],[3,6,8],[5]]

[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,5,4,1,6,8,3,7] => [[1,3,6,7],[2,4,8],[5]] => [[1,3,4,7],[2,5,8],[6]]

[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,5,4,1,8,7,3,6] => [[1,3,6],[2,4,7],[5,8]] => [[1,4,7],[2,5,8],[3,6]]

[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,8,4,1,6,7,3,5] => [[1,3,5,7],[2,4,6],[8]] => [[1,3,5,7],[2,6,8],[4]]

[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,8,5,1,6,7,3,4] => [[1,3,4,7],[2,5,6],[8]] => [[1,3,4,7],[2,6,8],[5]]

[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,5,4,1,6,7,8,3] => [[1,3,6,7,8],[2,4],[5]] => [[1,2,3,4,7],[5,8],[6]]

[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,3,4,1,2,5,6,7] => [[1,2,5,6,7],[3,4],[8]] => [[1,3,4,5,6],[2,8],[7]]

[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,3,4,1,2,5,8,6] => [[1,2,5,6],[3,4,8],[7]] => [[1,2,5,6],[3,4,8],[7]]

[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,3,4,1,2,8,5,7] => [[1,2,5,7],[3,4,8],[6]] => [[1,3,5,6],[2,4,8],[7]]

[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [8,3,4,1,2,7,5,6] => [[1,2,5,6],[3,4,7],[8]] => [[1,4,5,6],[2,7,8],[3]]

[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,3,4,1,2,7,8,5] => [[1,2,5,8],[3,4,7],[6]] => [[1,2,3,6],[4,5,8],[7]]

[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,3,5,1,2,4,6,7] => [[1,2,4,6,7],[3,5],[8]] => [[1,3,4,6,8],[2,7],[5]]

[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,3,5,1,2,4,8,6] => [[1,2,4,6],[3,5,8],[7]] => [[1,2,6,8],[3,4,7],[5]]

[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,3,8,1,2,4,5,7] => [[1,2,4,5,7],[3,8],[6]] => [[1,3,5,6,8],[2,4],[7]]

[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,3,7,1,2,4,5,6] => [[1,2,4,5,6],[3,7],[8]] => [[1,4,5,6,8],[2,7],[3]]

[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,3,7,1,2,4,8,5] => [[1,2,4,5],[3,7,8],[6]] => [[1,2,3,8],[4,5,6],[7]]

[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,5,1,2,8,4,7] => [[1,2,4,7],[3,5,8],[6]] => [[1,3,6,8],[2,4,7],[5]]

[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8,3,5,1,2,7,4,6] => [[1,2,4,6],[3,5,7],[8]] => [[1,4,6,8],[2,5,7],[3]]

[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,3,8,1,2,7,4,5] => [[1,2,4,5],[3,7],[6,8]] => [[1,3,6,8],[2,5],[4,7]]

[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [6,3,5,1,2,7,8,4] => [[1,2,4,8],[3,5,7],[6]] => [[1,2,3,6],[4,7,8],[5]]

[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,5,4,1,2,3,6,7] => [[1,2,3,6,7],[4],[5],[8]] => [[1,3,4,7,8],[2],[5],[6]]

[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,5,4,1,2,3,8,6] => [[1,2,3,6],[4,8],[5],[7]] => [[1,2,7,8],[3,4],[5],[6]]

[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,8,4,1,2,3,5,7] => [[1,2,3,5,7],[4,8],[6]] => [[1,3,5,7,8],[2,4],[6]]

[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,4,1,2,3,5,6] => [[1,2,3,5,6],[4],[7],[8]] => [[1,4,5,7,8],[2],[3],[6]]

[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,1,2,3,8,5] => [[1,2,3,5],[4,7,8],[6]] => [[1,2,3,8],[4,5,7],[6]]

[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,8,5,1,2,3,4,7] => [[1,2,3,4,7],[5,8],[6]] => [[1,3,6,7,8],[2,4],[5]]

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8,7,5,1,2,3,4,6] => [[1,2,3,4,6],[5],[7],[8]] => [[1,4,6,7,8],[2],[3],[5]]

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5] => [[1,2,3,4,5],[6,7,8]] => [[1,2,3,7,8],[4,5,6]]

[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,1,2,3,8,4] => [[1,2,3,4],[5,7,8],[6]] => [[1,2,3,8],[4,6,7],[5]]

[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,5,4,1,2,8,3,7] => [[1,2,3,7],[4,8],[5],[6]] => [[1,3,7,8],[2,4],[5],[6]]

[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,4,1,2,7,3,6] => [[1,2,3,6],[4,7],[5],[8]] => [[1,4,7,8],[2,5],[3],[6]]

[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,8,4,1,2,7,3,5] => [[1,2,3,5],[4,7],[6,8]] => [[1,3,7,8],[2,5],[4,6]]

[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [6,8,5,1,2,7,3,4] => [[1,2,3,4],[5,7],[6,8]] => [[1,3,7,8],[2,4],[5,6]]

[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [6,5,4,1,2,7,8,3] => [[1,2,3,8],[4,7],[5],[6]] => [[1,2,3,8],[4,7],[5],[6]]

[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,3,4,1,8,2,6,7] => [[1,2,6,7],[3,4,8],[5]] => [[1,3,4,6],[2,5,8],[7]]

[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,3,4,1,7,2,8,6] => [[1,2,6,8],[3,4,7],[5]] => [[1,2,4,6],[3,5,8],[7]]

[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,3,4,1,6,2,5,7] => [[1,2,5,7],[3,4,6],[8]] => [[1,3,5,6],[2,7,8],[4]]

[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,3,4,1,7,2,5,6] => [[1,2,5,6],[3,4,7],[8]] => [[1,4,5,6],[2,7,8],[3]]

[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7,3,4,1,6,2,8,5] => [[1,2,5,8],[3,4,6],[7]] => [[1,2,5,6],[3,7,8],[4]]

[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,3,5,1,6,2,4,7] => [[1,2,4,7],[3,5,6],[8]] => [[1,3,4,6],[2,7,8],[5]]

[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8,3,5,1,7,2,4,6] => [[1,2,4,6],[3,5,7],[8]] => [[1,4,6,8],[2,5,7],[3]]

[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,3,8,1,6,2,4,5] => [[1,2,4,5],[3,6],[7,8]] => [[1,2,6,8],[3,5],[4,7]]

[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,3,5,1,6,2,8,4] => [[1,2,4,8],[3,5,6],[7]] => [[1,2,4,6],[3,7,8],[5]]

[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,5,4,1,6,2,3,7] => [[1,2,3,7],[4,6],[5],[8]] => [[1,3,4,8],[2,7],[5],[6]]

[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,1,7,2,3,6] => [[1,2,3,6],[4,7],[5],[8]] => [[1,4,7,8],[2,5],[3],[6]]

[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5] => [[1,2,3,5],[4,6],[7,8]] => [[1,2,7,8],[3,5],[4,6]]

[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,8,5,1,6,2,3,4] => [[1,2,3,4],[5,6],[7,8]] => [[1,2,7,8],[3,4],[5,6]]

[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,5,4,1,6,2,8,3] => [[1,2,3],[4,6,8],[5],[7]] => [[1,2,4],[3,7,8],[5],[6]]

[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [5,3,4,1,6,8,2,7] => [[1,2,6,7],[3,4,8],[5]] => [[1,3,4,6],[2,5,8],[7]]

[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,3,4,1,8,7,2,6] => [[1,2,6],[3,4,7],[5,8]] => [[1,4,6],[2,5,8],[3,7]]

[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => [[1,2,5,7],[3,4,6],[8]] => [[1,3,5,6],[2,7,8],[4]]

[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8,3,5,1,6,7,2,4] => [[1,2,4,7],[3,5,6],[8]] => [[1,3,4,6],[2,7,8],[5]]

[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8,5,4,1,6,7,2,3] => [[1,2,3],[4,6,7],[5],[8]] => [[1,3,4],[2,7,8],[5],[6]]

[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [5,3,4,1,6,7,8,2] => [[1,2,6,7,8],[3,4],[5]] => [[1,2,3,4,6],[5,8],[7]]

[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [[1,3,4,5,6,7],[2,8]]

[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6] => [[1,3,4,5,6],[2,7,8]] => [[1,2,5,6,7],[3,4,8]]

[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [[1,3,4,5,7],[2,6,8]] => [[1,3,5,6,7],[2,4,8]]

[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,4,8,1,7,5,6] => [[1,3,4,5,6],[2,7],[8]] => [[1,4,5,6,7],[2,8],[3]]

[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [[1,3,4,5,7,8],[2,6]] => [[1,2,3,5,6,7],[4,8]]

[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,8,5,1,4,6,7] => [[1,3,4,6,7],[2,5],[8]] => [[1,3,4,6,7],[2,8],[5]]

[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,7,5,1,4,8,6] => [[1,3,4,6],[2,5,8],[7]] => [[1,2,6,7],[3,4,8],[5]]

[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,8,6,1,4,5,7] => [[1,3,4,5,7],[2,6],[8]] => [[1,3,5,6,7],[2,8],[4]]

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,7,8,1,4,5,6] => [[1,3,4,5,6],[2,7,8]] => [[1,2,5,6,7],[3,4,8]]

[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,6,1,4,8,5] => [[1,3,4,5],[2,6,8],[7]] => [[1,2,6,7],[3,5,8],[4]]

[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,6,5,1,8,4,7] => [[1,3,4,7],[2,5,8],[6]] => [[1,3,6,7],[2,4,8],[5]]

[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,8,5,1,7,4,6] => [[1,3,4,6],[2,5,7],[8]] => [[1,4,6,7],[2,5,8],[3]]

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,8,6,1,7,4,5] => [[1,3,4,5],[2,6,7],[8]] => [[1,3,6,7],[2,5,8],[4]]

[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,6,5,1,7,8,4] => [[1,3,4,7,8],[2,5],[6]] => [[1,2,3,6,7],[4,8],[5]]

[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,8,4,5,1,3,6,7] => [[1,3,5,6,7],[2,4],[8]] => [[1,3,4,5,7],[2,8],[6]]

[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,4,5,1,3,8,6] => [[1,3,5,6],[2,4,8],[7]] => [[1,2,5,7],[3,4,8],[6]]

[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,8,4,6,1,3,5,7] => [[1,3,5,7],[2,4,6],[8]] => [[1,3,5,7],[2,6,8],[4]]

[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,7,4,8,1,3,5,6] => [[1,3,5,6],[2,4,8],[7]] => [[1,2,5,7],[3,4,8],[6]]

[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,7,4,6,1,3,8,5] => [[1,3,5,8],[2,4,6],[7]] => [[1,2,5,7],[3,6,8],[4]]

[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7] => [[1,3,4,7],[2,5],[6],[8]] => [[1,3,6,7],[2,8],[4],[5]]

[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,8,5,1,3,4,6] => [[1,3,4,6],[2,5,8],[7]] => [[1,2,6,7],[3,4,8],[5]]

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7,8,6,1,3,4,5] => [[1,3,4,5],[2,6,8],[7]] => [[1,2,6,7],[3,5,8],[4]]

[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4] => [[1,3,4],[2,5,8],[6],[7]] => [[1,2,7],[3,6,8],[4],[5]]

[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,6,4,5,1,8,3,7] => [[1,3,5,7],[2,4,8],[6]] => [[1,3,5,7],[2,4,8],[6]]

[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [[1,3,5,6],[2,4,7],[8]] => [[1,4,5,7],[2,6,8],[3]]

[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,6,1,7,3,5] => [[1,3,5,7],[2,4,6],[8]] => [[1,3,5,7],[2,6,8],[4]]

[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,6,5,1,7,3,4] => [[1,3,4],[2,5,7],[6],[8]] => [[1,3,7],[2,6,8],[4],[5]]

[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,6,4,5,1,7,8,3] => [[1,3,5,7,8],[2,4],[6]] => [[1,2,3,5,7],[4,8],[6]]

[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [8,3,4,5,1,2,6,7] => [[1,2,5,6,7],[3,4],[8]] => [[1,3,4,5,6],[2,8],[7]]

[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,3,4,5,1,2,8,6] => [[1,2,5,6],[3,4,8],[7]] => [[1,2,5,6],[3,4,8],[7]]

[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,3,4,6,1,2,5,7] => [[1,2,5,7],[3,4,6],[8]] => [[1,3,5,6],[2,7,8],[4]]

[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,3,4,8,1,2,5,6] => [[1,2,5,6],[3,4,8],[7]] => [[1,2,5,6],[3,4,8],[7]]

[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7,3,4,6,1,2,8,5] => [[1,2,5,8],[3,4,6],[7]] => [[1,2,5,6],[3,7,8],[4]]

[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,3,6,5,1,2,4,7] => [[1,2,4,7],[3,5],[6],[8]] => [[1,3,6,8],[2,7],[4],[5]]

[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,3,8,5,1,2,4,6] => [[1,2,4,6],[3,5],[7,8]] => [[1,2,6,8],[3,4],[5,7]]

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5] => [[1,2,4,5],[3,6],[7,8]] => [[1,2,6,8],[3,5],[4,7]]

[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,6,5,1,2,8,4] => [[1,2,4],[3,5,8],[6],[7]] => [[1,2,6],[3,7,8],[4],[5]]

[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,6,4,5,1,2,3,7] => [[1,2,3,7],[4,5],[6],[8]] => [[1,3,5,8],[2,7],[4],[6]]

[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,8,4,5,1,2,3,6] => [[1,2,3,6],[4,5],[7,8]] => [[1,2,5,8],[3,4],[6,7]]

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,8,4,6,1,2,3,5] => [[1,2,3,5],[4,6],[7,8]] => [[1,2,7,8],[3,5],[4,6]]

[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,6,5,1,2,3,4] => [[1,2,3,4],[5,8],[6],[7]] => [[1,2,7,8],[3,6],[4],[5]]

[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,6,4,5,1,2,8,3] => [[1,2,3],[4,5,8],[6],[7]] => [[1,2,5],[3,7,8],[4],[6]]

[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,4,5,1,8,2,7] => [[1,2,5,7],[3,4,8],[6]] => [[1,3,5,6],[2,4,8],[7]]

[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8,3,4,5,1,7,2,6] => [[1,2,5,6],[3,4,7],[8]] => [[1,4,5,6],[2,7,8],[3]]

[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,1,7,2,5] => [[1,2,5,7],[3,4,6],[8]] => [[1,3,5,6],[2,7,8],[4]]

[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8,3,6,5,1,7,2,4] => [[1,2,4],[3,5,7],[6],[8]] => [[1,3,6],[2,7,8],[4],[5]]

[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8,6,4,5,1,7,2,3] => [[1,2,3],[4,5,7],[6],[8]] => [[1,3,5],[2,7,8],[4],[6]]

[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [6,3,4,5,1,7,8,2] => [[1,2,5,7,8],[3,4],[6]] => [[1,2,3,5,6],[4,8],[7]]

[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => [[1,3,4,5,6,7],[2,8]] => [[1,3,4,5,6,7],[2,8]]

[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [[1,3,4,5,6,8],[2,7]] => [[1,2,4,5,6,7],[3,8]]

[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,3,4,8,6,1,5,7] => [[1,3,4,5,7],[2,6],[8]] => [[1,3,5,6,7],[2,8],[4]]

[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,4,8,7,1,5,6] => [[1,3,4,5,6],[2,7],[8]] => [[1,4,5,6,7],[2,8],[3]]

[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,4,7,6,1,8,5] => [[1,3,4,5,8],[2,6],[7]] => [[1,2,5,6,7],[3,8],[4]]

[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,3,8,5,6,1,4,7] => [[1,3,4,6,7],[2,5],[8]] => [[1,3,4,6,7],[2,8],[5]]

[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,8,5,7,1,4,6] => [[1,3,4,6],[2,5,7],[8]] => [[1,4,6,7],[2,5,8],[3]]

[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,8,7,6,1,4,5] => [[1,3,4,5],[2,6],[7],[8]] => [[1,5,6,7],[2,8],[3],[4]]

[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,7,5,6,1,8,4] => [[1,3,4,6,8],[2,5],[7]] => [[1,2,4,6,7],[3,8],[5]]

[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,8,4,5,6,1,3,7] => [[1,3,5,6,7],[2,4],[8]] => [[1,3,4,5,7],[2,8],[6]]

[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,8,4,5,7,1,3,6] => [[1,3,5,6],[2,4,7],[8]] => [[1,4,5,7],[2,6,8],[3]]

[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,4,7,6,1,3,5] => [[1,3,5],[2,4,6],[7],[8]] => [[1,5,7],[2,6,8],[3],[4]]

[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [[1,3,4],[2,5,6],[7],[8]] => [[1,4,7],[2,6,8],[3],[5]]

[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7,4,5,6,1,8,3] => [[1,3,5,6,8],[2,4],[7]] => [[1,2,4,5,7],[3,8],[6]]

[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [[1,2,5,6,7],[3,4],[8]] => [[1,3,4,5,6],[2,8],[7]]

[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8,3,4,5,7,1,2,6] => [[1,2,5,6],[3,4,7],[8]] => [[1,4,5,6],[2,7,8],[3]]

[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8,3,4,7,6,1,2,5] => [[1,2,5],[3,4,6],[7],[8]] => [[1,5,6],[2,7,8],[3],[4]]

[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8,3,7,5,6,1,2,4] => [[1,2,4],[3,5,6],[7],[8]] => [[1,4,6],[2,7,8],[3],[5]]

[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,7,4,5,6,1,2,3] => [[1,2,3],[4,5,6],[7],[8]] => [[1,4,5],[2,7,8],[3],[6]]

[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,3,4,5,6,1,8,2] => [[1,2,5,6,8],[3,4],[7]] => [[1,2,4,5,6],[3,8],[7]]

[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => [[1,3,4,5,6,7],[2,8]] => [[1,3,4,5,6,7],[2,8]]

[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,4,5,8,7,1,6] => [[1,3,4,5,6],[2,7],[8]] => [[1,4,5,6,7],[2,8],[3]]

[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,8,6,7,1,5] => [[1,3,4,5,7],[2,6],[8]] => [[1,3,5,6,7],[2,8],[4]]

[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,8,5,6,7,1,4] => [[1,3,4,6,7],[2,5],[8]] => [[1,3,4,6,7],[2,8],[5]]

[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,4,5,6,7,1,3] => [[1,3,5,6,7],[2,4],[8]] => [[1,3,4,5,7],[2,8],[6]]

[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8,3,4,5,6,7,1,2] => [[1,2,5,6,7],[3,4],[8]] => [[1,3,4,5,6],[2,8],[7]]

[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2]] => [[1,2,3,4,5,6,7],[8]]

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9]] => [[1,3,4,5,6,7,8,9],[2]]

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => [[1,2,3,4,5,6,7],[8,9]] => [[1,2,5,6,7,8,9],[3,4]]

[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => [[1,2,3,4,5,6,8],[7,9]] => [[1,3,5,6,7,8,9],[2,4]]

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]]

[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => [[1,2,3,4,5,6,9],[7,8]] => [[1,2,3,6,7,8,9],[4,5]]

[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,1,2,3,4,8,5,9,7] => [[1,2,3,4,5,7],[6,8,9]] => [[1,2,4,7,8,9],[3,5,6]]

[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [9,1,2,3,4,7,5,6,8] => [[1,2,3,4,5,6,8],[7],[9]] => [[1,3,5,6,7,8,9],[2],[4]]

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,1,2,3,4,8,5,6,7] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]]

[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [8,1,2,3,4,7,5,9,6] => [[1,2,3,4,5,6],[7,9],[8]] => [[1,2,6,7,8,9],[3,5],[4]]

[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,1,2,3,4,9,8,5,7] => [[1,2,3,4,5,7],[6,8],[9]] => [[1,4,6,7,8,9],[2,5],[3]]

[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [9,1,2,3,4,7,8,5,6] => [[1,2,3,4,5,6],[7,8],[9]] => [[1,3,6,7,8,9],[2,5],[4]]

[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => [[1,2,3,4,5,8,9],[6,7]] => [[1,2,3,4,7,8,9],[5,6]]

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,1,2,3,9,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [[1,2,5,6,7,8,9],[3,4]]

[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [9,1,2,3,6,8,4,5,7] => [[1,2,3,4,5,7],[6,8],[9]] => [[1,4,6,7,8,9],[2,5],[3]]

[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,6,7,8,9,4] => [[1,2,3,4,7,8,9],[5,6]] => [[1,2,3,4,5,8,9],[6,7]]

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,1,2,8,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]]

[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [7,1,2,8,3,4,5,9,6] => [[1,2,3,4,5,6],[7,8,9]] => [[1,2,3,7,8,9],[4,5,6]]

[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [8,1,2,9,6,3,4,5,7] => [[1,2,3,4,5,7],[6,9],[8]] => [[1,2,6,7,8,9],[3,4],[5]]

[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [9,1,2,8,6,7,3,4,5] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,4,7,8,9],[2,6],[3],[5]]

[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [9,1,2,5,6,7,8,3,4] => [[1,2,3,4,7,8],[5,6],[9]] => [[1,3,4,5,8,9],[2,7],[6]]

[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,9,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3,9]] => [[1,3,4,5,6,7,9],[2,8]]

[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,8,2,4,5,6,9,7] => [[1,2,4,5,6,7],[3,8,9]] => [[1,2,5,6,7,9],[3,4,8]]

[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [8,1,4,2,3,5,6,9,7] => [[1,2,3,5,6,7],[4,9],[8]] => [[1,2,5,6,8,9],[3,4],[7]]

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,8,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]]

[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,1,7,2,3,4,5,9,6] => [[1,2,3,4,5,6],[7,9],[8]] => [[1,2,6,7,8,9],[3,5],[4]]

[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,4,9,2,5,8,6,7] => [[1,2,5,6,7],[3,4,8],[9]] => [[1,4,5,6,7],[2,8,9],[3]]

[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1,9,6,2,3,4,5,8] => [[1,2,3,4,5,8],[6,9],[7]] => [[1,3,6,7,8,9],[2,4],[5]]

[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [9,1,8,6,2,3,4,5,7] => [[1,2,3,4,5,7],[6],[8],[9]] => [[1,4,6,7,8,9],[2],[3],[5]]

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,1,8,9,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9]] => [[1,2,3,7,8,9],[4,5,6]]

[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [8,1,9,7,6,2,3,4,5] => [[1,2,3,4,5],[6,9],[7],[8]] => [[1,2,7,8,9],[3,6],[4],[5]]

[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,1,4,5,6,2,8,9,3] => [[1,2,3,6,8,9],[4,5],[7]] => [[1,2,3,5,6,9],[4,8],[7]]

[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [9,1,8,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7],[8],[9]] => [[1,4,5,9],[2,7,8],[3],[6]]

[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [[1,2,5,6,7,8,9],[3,4]] => [[1,2,3,4,5,6,7],[8,9]]

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,9,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [[1,3,4,5,6,7,8],[2,9]]

[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,5,1,3,6,7,8,9,4] => [[1,3,4,7,8,9],[2,5,6]] => [[1,2,3,4,5,8],[6,7,9]]

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [[1,3,5,7,9],[2,4,6,8]] => [[1,2,4,6,8],[3,5,7,9]]

[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,5,9,3,6,7,8] => [[1,3,5,6,7,8],[2,4,9]] => [[1,3,4,5,6,8],[2,7,9]]

[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,8,9,3,5,6,7] => [[1,3,5,6,7],[2,4,8,9]] => [[1,2,5,6,8],[3,4,7,9]]

[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1,5,6,7,9,3,8] => [[1,3,5,6,7,8],[2,4,9]] => [[1,3,4,5,6,8],[2,7,9]]

[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [[1,3,5,6,7,8,9],[2,4]] => [[1,2,3,4,5,6,8],[7,9]]

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,3,1,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3],[9]] => [[1,3,4,5,6,7,9],[2],[8]]

[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [8,3,1,2,4,5,6,9,7] => [[1,2,4,5,6,7],[3,9],[8]] => [[1,2,5,6,7,9],[3,4],[8]]

[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [6,3,1,2,4,7,8,9,5] => [[1,2,4,5,8,9],[3,7],[6]] => [[1,2,3,4,7,9],[5,6],[8]]

[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,4,1,2,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4],[9]] => [[1,3,4,5,6,8,9],[2],[7]]

[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [7,4,1,2,3,5,8,9,6] => [[1,2,3,5,6,9],[4,8],[7]] => [[1,2,3,6,8,9],[4,5],[7]]

[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,6,1,2,3,4,5,9,7] => [[1,2,3,4,5,7],[6,9],[8]] => [[1,2,6,7,8,9],[3,4],[5]]

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [[1,2,3,4,5,6,8],[7],[9]] => [[1,3,5,6,7,8,9],[2],[4]]

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,9,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => [[1,2,5,6,7,8,9],[3,4]]

[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,7,1,2,3,4,5,9,6] => [[1,2,3,4,5,6],[7,9],[8]] => [[1,2,6,7,8,9],[3,5],[4]]

[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,6,1,2,3,4,9,5,8] => [[1,2,3,4,5,8],[6,9],[7]] => [[1,3,6,7,8,9],[2,4],[5]]

[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [9,6,1,2,3,4,8,5,7] => [[1,2,3,4,5,7],[6,8],[9]] => [[1,4,6,7,8,9],[2,5],[3]]

[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9,7,1,2,3,4,8,5,6] => [[1,2,3,4,5,6],[7,8],[9]] => [[1,3,6,7,8,9],[2,5],[4]]

[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,6,1,2,3,9,4,7,8] => [[1,2,3,4,7,8],[5,6,9]] => [[1,3,4,5,8,9],[2,6,7]]

[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,8,1,2,3,7,4,5,6] => [[1,2,3,4,5,6],[7],[8],[9]] => [[1,5,6,7,8,9],[2],[3],[4]]

[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [9,6,1,2,3,7,8,4,5] => [[1,2,3,4,5],[6,7,8],[9]] => [[1,3,4,8,9],[2,6,7],[5]]

[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [5,4,1,2,9,3,6,7,8] => [[1,2,3,6,7,8],[4,9],[5]] => [[1,3,4,5,8,9],[2,6],[7]]

[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,4,1,2,9,3,5,6,7] => [[1,2,3,5,6,7],[4,9],[8]] => [[1,2,5,6,8,9],[3,4],[7]]

[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [5,9,1,2,6,3,4,7,8] => [[1,2,3,4,7,8],[5,6],[9]] => [[1,3,4,5,8,9],[2,7],[6]]

[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [9,8,1,2,6,7,3,4,5] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,4,7,8,9],[2,6],[3],[5]]

[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,3,1,9,2,5,6,7,8] => [[1,2,5,6,7,8],[3,9],[4]] => [[1,3,4,5,6,9],[2,7],[8]]

[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,1,9,2,3,4,5,6] => [[1,2,3,4,5,6],[7,9],[8]] => [[1,2,6,7,8,9],[3,5],[4]]

[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [8,7,1,6,2,3,4,9,5] => [[1,2,3,4,5],[6,9],[7],[8]] => [[1,2,7,8,9],[3,6],[4],[5]]

[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [9,8,1,6,2,7,3,4,5] => [[1,2,3,4,5],[6,7],[8],[9]] => [[1,4,7,8,9],[2,6],[3],[5]]

[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [9,8,1,7,6,2,3,4,5] => [[1,2,3,4,5],[6],[7],[8],[9]] => [[1,6,7,8,9],[2],[3],[4],[5]]

[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,9,1,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7],[8,9]] => [[1,2,5,9],[3,4,8],[6,7]]

[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,9,1,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [[1,3,4,5,6,7,8],[2,9]]

[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [[1,3,4,6,7,8,9],[2,5]] => [[1,2,3,4,5,7,8],[6,9]]

[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,9,4,1,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4],[9]] => [[1,3,4,5,6,8],[2,9],[7]]

[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [2,9,4,1,6,3,5,7,8] => [[1,3,5,7,8],[2,4,6],[9]] => [[1,3,4,6,8],[2,7,9],[5]]

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,9,4,1,6,3,8,5,7] => [[1,3,5,7],[2,4,6,8],[9]] => [[1,4,6,8],[2,5,7,9],[3]]

[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [9,5,4,1,2,3,6,7,8] => [[1,2,3,6,7,8],[4],[5],[9]] => [[1,3,4,5,8,9],[2],[6],[7]]

[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [8,5,4,1,2,3,6,9,7] => [[1,2,3,6,7],[4,9],[5],[8]] => [[1,2,5,8,9],[3,4],[6],[7]]

[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,9,8,1,2,3,4,5,7] => [[1,2,3,4,5,7],[6,8],[9]] => [[1,4,6,7,8,9],[2,5],[3]]

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,7,8,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8],[9]] => [[1,3,6,7,8,9],[2,5],[4]]

[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,8,1,2,3,4,9,5] => [[1,2,3,4,5],[6,7,8,9]] => [[1,2,3,4,9],[5,6,7,8]]

[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,9,1,5,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [[1,3,4,5,6,7,8],[2,9]]

[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,6,1,7,8,9,5] => [[1,3,4,5,7,8,9],[2,6]] => [[1,2,3,4,6,7,8],[5,9]]

[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [2,9,4,5,1,3,6,7,8] => [[1,3,5,6,7,8],[2,4],[9]] => [[1,3,4,5,6,8],[2,9],[7]]

[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [2,7,4,5,1,3,8,9,6] => [[1,3,5,6,9],[2,4,8],[7]] => [[1,2,3,6,8],[4,5,9],[7]]

[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [9,3,4,8,1,2,5,6,7] => [[1,2,5,6,7],[3,4,8],[9]] => [[1,4,5,6,7],[2,8,9],[3]]

[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,9,1,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [[1,3,4,5,6,7,8],[2,9]]

[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [[1,3,4,5,6,8,9],[2,7]] => [[1,2,3,5,6,7,8],[4,9]]

[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [9,3,4,5,6,1,8,2,7] => [[1,2,5,6,7],[3,4,8],[9]] => [[1,4,5,6,7],[2,8,9],[3]]

[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,9,1,7,8] => [[1,3,4,5,6,7,8],[2,9]] => [[1,3,4,5,6,7,8],[2,9]]

[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [2,9,4,5,6,7,1,3,8] => [[1,3,5,6,7,8],[2,4],[9]] => [[1,3,4,5,6,8],[2,9],[7]]

[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [9,3,4,5,6,8,1,2,7] => [[1,2,5,6,7],[3,4,8],[9]] => [[1,4,5,6,7],[2,8,9],[3]]

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => [[1,3,4,5,6,7,8],[2,9]] => [[1,3,4,5,6,7,8],[2,9]]

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,9,4,5,6,7,8,1,3] => [[1,3,5,6,7,8],[2,4],[9]] => [[1,3,4,5,6,8],[2,9],[7]]

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2]] => [[1,2,3,4,5,6,7,8],[9]]

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,10,1,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [[1,3,4,5,6,7,8,9],[2,10]]

[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [[1,2,5,6,7,8,9,10],[3,4]] => [[1,2,3,4,5,6,7,8],[9,10]]

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [2,10,4,5,6,7,8,1,3,9] => [[1,3,5,6,7,8,9],[2,4],[10]] => [[1,3,4,5,6,7,9],[2,10],[8]]

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,9,1,10,8] => [[1,3,4,5,6,7,8,10],[2,9]] => [[1,2,4,5,6,7,8,9],[3,10]]

[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [[1,3,5,6,7,8,9,10],[2,4]] => [[1,2,3,4,5,6,7,9],[8,10]]

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,7,10,1,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [[1,3,4,5,6,7,8,9],[2,10]]

[] => [1] => [[1]] => [[1]]

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]]

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,10,7] => [[1,2,3,4,5,6,7],[8,9,10]] => [[1,2,3,7,8,9,10],[4,5,6]]

[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [10,7,1,2,3,4,5,9,6,8] => [[1,2,3,4,5,6,8],[7,9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]]

[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,10,1,2,3,4,5,9,6,7] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[1,3,6,7,8,9,10],[2,5],[4]]

[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [10,7,1,2,3,4,9,5,6,8] => [[1,2,3,4,5,6,8],[7,9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]]

[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,10,1,2,3,4,8,5,6,7] => [[1,2,3,4,5,6,7],[8,10],[9]] => [[1,2,6,7,8,9,10],[3,5],[4]]

[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,6,1,2,3,4,10,9,5,8] => [[1,2,3,4,5,8],[6,9],[7,10]] => [[1,4,7,8,9,10],[2,5],[3,6]]

[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [10,7,1,2,3,4,8,9,5,6] => [[1,2,3,4,5,6],[7,8,9],[10]] => [[1,3,4,8,9,10],[2,6,7],[5]]

[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [10,9,1,2,3,7,8,4,5,6] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,4,7,8,9,10],[2,6],[3],[5]]

[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [10,9,1,2,8,7,3,4,5,6] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [[1,6,7,8,9,10],[2],[3],[4],[5]]

[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,8,1,9,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[1,3,6,7,8,9,10],[2,5],[4]]

[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,8,1,10,7,2,3,4,5,6] => [[1,2,3,4,5,6],[7,10],[8],[9]] => [[1,2,7,8,9,10],[3,6],[4],[5]]

[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,3,10,1,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3,10],[9]] => [[1,2,5,6,7,8,10],[3,4],[9]]

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,7,9,1,2,3,4,5,6,8] => [[1,2,3,4,5,6,8],[7,9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]]

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,9,8,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,5,6,7,8,9,10],[2],[3],[4]]

[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [2,7,8,9,1,3,4,5,10,6] => [[1,3,4,5,6],[2,7,8,9,10]] => [[1,2,3,4,9],[5,6,7,8,10]]

[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [10,8,4,9,1,2,3,5,6,7] => [[1,2,3,5,6,7],[4,9],[8],[10]] => [[1,3,6,7,9,10],[2,5],[4],[8]]

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => [[1,2,3,4,9,10],[5,6,7,8]]

[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [8,9,7,5,6,1,2,3,10,4] => [[1,2,3,4],[5,6,10],[7,9],[8]] => [[1,2,3,10],[4,6,9],[5,8],[7]]

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [10,3,4,5,6,7,1,9,2,8] => [[1,2,5,6,7,8],[3,4,9],[10]] => [[1,4,5,6,7,8],[2,9,10],[3]]

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [10,3,4,5,6,7,9,1,2,8] => [[1,2,5,6,7,8],[3,4,9],[10]] => [[1,4,5,6,7,8],[2,9,10],[3]]

[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,10,4,5,6,7,8,9,1,3] => [[1,3,5,6,7,8,9],[2,4],[10]] => [[1,3,4,5,6,7,9],[2,10],[8]]

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9,10],[2]] => [[1,2,3,4,5,6,7,8,9],[10]]

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10]] => [[1,3,4,5,6,7,8,9,10],[2]]

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [[1,2,5,6,7,8,9,10],[3,4]]

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,1,2,3,4,5,6,9,7,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]]

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [10,1,2,3,4,5,9,6,7,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]]

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,1,2,3,4,10,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [[1,2,5,6,7,8,9,10],[3,4]]

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,3,9,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]]

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,9,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]]

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,10,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => [[1,2,5,6,7,8,9,10],[3,4]]

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10],[11]] => [[1,3,4,5,6,7,8,9,10,11],[2]]

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,1,2,3,4,5,6,7,8,11,9] => [[1,2,3,4,5,6,7,8,9],[10,11]] => [[1,2,5,6,7,8,9,10,11],[3,4]]

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,1,2,3,4,5,6,9,10,7] => [[1,2,3,4,5,6,7,10],[8,9]] => [[1,2,3,6,7,8,9,10],[4,5]]

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [11,1,2,3,4,5,6,7,10,8,9] => [[1,2,3,4,5,6,7,8,9],[10],[11]] => [[1,4,5,6,7,8,9,10,11],[2],[3]]

[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,1,2,3,4,5,10,9,6,8] => [[1,2,3,4,5,6,8],[7,9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]]

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [11,1,2,3,4,5,6,10,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10],[11]] => [[1,4,5,6,7,8,9,10,11],[2],[3]]

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [10,1,2,3,4,5,11,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10,11]] => [[1,2,5,6,7,8,9,10,11],[3,4]]

[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,1,2,3,9,10,4,6,7,8] => [[1,2,3,4,6,7,8],[5,9,10]] => [[1,2,5,6,8,9,10],[3,4,7]]

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [11,1,2,3,4,10,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10],[11]] => [[1,4,5,6,7,8,9,10,11],[2],[3]]

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,1,2,3,10,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10],[11]] => [[1,4,5,6,7,8,9,10,11],[2],[3]]

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,11,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10,11]] => [[1,2,5,6,7,8,9,10,11],[3,4]]

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,1,10,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10],[11]] => [[1,4,5,6,7,8,9,10,11],[2],[3]]

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,10,1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10],[11]] => [[1,4,5,6,7,8,9,10,11],[2],[3]]

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [[1,2,3,4,5,6,7,8,9,10,11],[12]] => [[1,3,4,5,6,7,8,9,10,11,12],[2]]

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [11,1,2,3,4,5,6,7,8,9,12,10] => [[1,2,3,4,5,6,7,8,9,10],[11,12]] => [[1,2,5,6,7,8,9,10,11,12],[3,4]]

[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,1,2,3,4,5,8,9,10,6] => [[1,2,3,4,5,6,9,10],[7,8]] => [[1,2,3,4,7,8,9,10],[5,6]]

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,12,1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10],[11,12]] => [[1,2,5,6,7,8,9,10,11,12],[3,4]]

[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,1,2,3,4,7,8,9,10,5] => [[1,2,3,4,5,8,9,10],[6,7]] => [[1,2,3,4,5,8,9,10],[6,7]]

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,1,10,9,2,3,4,5,6,8] => [[1,2,3,4,5,6,8],[7,9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]]

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,1,8,9,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9],[10]] => [[1,3,6,7,8,9,10],[2,5],[4]]

[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,1,2,3,6,7,8,9,10,4] => [[1,2,3,4,7,8,9,10],[5,6]] => [[1,2,3,4,5,6,9,10],[7,8]]

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [11,1,10,9,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9],[10],[11]] => [[1,5,6,7,8,9,10,11],[2],[3],[4]]

[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,1,2,3,4,5,9,6,10,8] => [[1,2,3,4,5,6,8],[7,9,10]] => [[1,2,4,7,8,9,10],[3,5,6]]

[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,10,4,6,7,8,9] => [[1,2,3,4,6,7,8,9],[5,10]] => [[1,3,4,5,6,8,9,10],[2,7]]

[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,10,3,5,6,7,8,9] => [[1,2,3,5,6,7,8,9],[4,10]] => [[1,3,4,5,6,7,9,10],[2,8]]

[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,9,2,4,5,6,7,10,8] => [[1,2,4,5,6,7,8],[3,9,10]] => [[1,2,5,6,7,8,10],[3,4,9]]

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,10,1,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [[1,3,4,5,6,7,8,9],[2,10]]

[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,6,7,8,9,10,4] => [[1,3,4,7,8,9,10],[2,5,6]] => [[1,2,3,4,5,6,9],[7,8,10]]

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [[1,3,5,7,9],[2,4,6,8,10]] => [[1,3,5,7,9],[2,4,6,8,10]]

[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,4,1,5,6,7,8,10,3,9] => [[1,3,5,6,7,8,9],[2,4,10]] => [[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] => [2,3,10,1,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [[1,3,4,5,6,7,8,9],[2,10]]

[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [[1,3,4,6,7,8,9,10],[2,5]] => [[1,2,3,4,5,6,8,9],[7,10]]

[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,10,1,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [[1,3,4,5,6,7,8,9],[2,10]]

[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,6,1,7,8,9,10,5] => [[1,3,4,5,7,8,9,10],[2,6]] => [[1,2,3,4,5,7,8,9],[6,10]]

[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,10,1,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [[1,3,4,5,6,7,8,9],[2,10]]

[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [[1,3,4,5,6,8,9,10],[2,7]] => [[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] => [2,3,4,5,6,10,1,7,8,9] => [[1,3,4,5,6,7,8,9],[2,10]] => [[1,3,4,5,6,7,8,9],[2,10]]

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [[1,3,4,5,6,7,9,10],[2,8]] => [[1,2,3,5,6,7,8,9],[4,10]]

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [[1,3,4,5,6,7,8,9,10,11],[2]] => [[1,2,3,4,5,6,7,8,9,10],[11]]

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,3,1,2,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3],[10]] => [[1,3,4,5,6,7,8,10],[2],[9]]

[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,10,1,2,3,4,6,7,8,9] => [[1,2,3,4,6,7,8,9],[5,10]] => [[1,3,4,5,6,8,9,10],[2,7]]

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,10,1,2,3,4,5,6,7,9] => [[1,2,3,4,5,6,7,9],[8,10]] => [[1,3,5,6,7,8,9,10],[2,4]]

[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,1,10,2,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3,10],[4]] => [[1,3,4,5,6,7,10],[2,8],[9]]

[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,7,1,2,3,4,5,10,6,9] => [[1,2,3,4,5,6,9],[7,10],[8]] => [[1,3,6,7,8,9,10],[2,4],[5]]

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,3,1,2,4,5,6,7,10,8] => [[1,2,4,5,6,7,8],[3,10],[9]] => [[1,2,5,6,7,8,10],[3,4],[9]]

[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [10,5,4,1,2,3,6,7,8,9] => [[1,2,3,6,7,8,9],[4],[5],[10]] => [[1,3,4,5,6,9,10],[2],[7],[8]]

[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,10,4,1,3,5,6,7,8,9] => [[1,3,5,6,7,8,9],[2,4],[10]] => [[1,3,4,5,6,7,9],[2,10],[8]]

[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,7,1,10,2,3,4,5,6,9] => [[1,2,3,4,5,6,9],[7,10],[8]] => [[1,3,6,7,8,9,10],[2,4],[5]]

[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,9,1,2,3,4,6,7,10,8] => [[1,2,3,4,6,7,8],[5,9,10]] => [[1,2,5,6,8,9,10],[3,4,7]]

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9,1,8,2,3,4,5,6,10,7] => [[1,2,3,4,5,6,7],[8,10],[9]] => [[1,2,6,7,8,9,10],[3,5],[4]]

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,7,1,2,3,4,5,6,10,8] => [[1,2,3,4,5,6,8],[7,10],[9]] => [[1,2,6,7,8,9,10],[3,4],[5]]

[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [8,6,1,2,3,4,5,9,10,7] => [[1,2,3,4,5,7,10],[6,9],[8]] => [[1,2,3,7,8,9,10],[4,5],[6]]

[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,7,1,2,3,4,8,9,10,6] => [[1,2,3,4,6,9,10],[5,7,8]] => [[1,2,3,4,6,9,10],[5,7,8]]

[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [8,11,1,2,3,4,5,9,10,6,7] => [[1,2,3,4,5,6,7],[8,9,10],[11]] => [[1,3,4,8,9,10,11],[2,6,7],[5]]

[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [10,11,1,2,3,4,8,9,5,6,7] => [[1,2,3,4,5,6,7],[8,9],[10,11]] => [[1,2,7,8,9,10,11],[3,4],[5,6]]

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [11,8,9,10,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9,10],[11]] => [[1,3,4,8,9,10,11],[2,6,7],[5]]

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,10,4,1,6,3,8,5,7,9] => [[1,3,5,7,9],[2,4,6,8],[10]] => [[1,3,5,7,9],[2,6,8,10],[4]]

Map

Ringel

Description

The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.

Map

Robinson-Schensted insertion tableau

Description

Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length

$n$ and pairs of standard Young tableaux of the same shape and of size

$n$ , see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.

Map

Schützenberger involution

Description

Sends a standard tableau to the standard tableau obtained via the Schützenberger involution.