Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Images
[1] => [1,0] => [1] => [[1]]
[1,1] => [1,0,1,0] => [1,2] => [[1,2]]
[2] => [1,1,0,0] => [2,1] => [[1],[2]]
[1,1,1] => [1,0,1,0,1,0] => [1,2,3] => [[1,2,3]]
[1,2] => [1,0,1,1,0,0] => [1,3,2] => [[1,2],[3]]
[2,1] => [1,1,0,0,1,0] => [2,1,3] => [[1,3],[2]]
[3] => [1,1,1,0,0,0] => [3,2,1] => [[1],[2],[3]]
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => [[1,2,3,4]]
[1,1,2] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => [[1,2,3],[4]]
[1,2,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => [[1,2,4],[3]]
[1,3] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => [[1,2],[3],[4]]
[2,1,1] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => [[1,3,4],[2]]
[2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => [[1,3],[2,4]]
[3,1] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => [[1,4],[2],[3]]
[4] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => [[1],[2],[3],[4]]
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [[1,2,3,4,5]]
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [[1,2,3,4],[5]]
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [[1,2,3,5],[4]]
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [[1,2,3],[4],[5]]
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [[1,2,4,5],[3]]
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [[1,2,4],[3,5]]
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [[1,2,5],[3],[4]]
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [[1,2],[3],[4],[5]]
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [[1,3,4,5],[2]]
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [[1,3,4],[2,5]]
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [[1,3,5],[2,4]]
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [[1,3],[2,4],[5]]
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [[1,4,5],[2],[3]]
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [[1,4],[2,5],[3]]
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [[1,5],[2],[3],[4]]
[5] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]]
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]]
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]]
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]]
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [[1,2,3,4],[5],[6]]
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]]
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [[1,2,3,5],[4,6]]
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [[1,2,3,6],[4],[5]]
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [[1,2,3],[4],[5],[6]]
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]]
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [[1,2,4,5],[3,6]]
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [[1,2,4,6],[3,5]]
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [[1,2,4],[3,5],[6]]
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [[1,2,5,6],[3],[4]]
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [[1,2,5],[3,6],[4]]
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [[1,2,6],[3],[4],[5]]
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]]
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]]
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [[1,3,4,5],[2,6]]
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [[1,3,4,6],[2,5]]
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [[1,3,4],[2,5],[6]]
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]]
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]]
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [[1,3,6],[2,4],[5]]
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]]
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [[1,4,5,6],[2],[3]]
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [[1,4,5],[2,6],[3]]
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [[1,4,6],[2,5],[3]]
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]]
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]]
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]]
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]]
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]]
[1,1,1,1,1,1,1] => [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]]
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]]
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]]
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [[1,2,3,4,5],[6],[7]]
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]]
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [[1,2,3,4,6],[5,7]]
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [[1,2,3,4,7],[5],[6]]
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [[1,2,3,4],[5],[6],[7]]
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]]
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]]
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [[1,2,3,5,7],[4,6]]
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [[1,2,3,5],[4,6],[7]]
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [[1,2,3,6,7],[4],[5]]
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [[1,2,3,6],[4,7],[5]]
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [[1,2,3,7],[4],[5],[6]]
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7]]
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]]
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]]
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [[1,2,4,5,7],[3,6]]
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [[1,2,4,5],[3,6],[7]]
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [[1,2,4,6,7],[3,5]]
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [[1,2,4,6],[3,5,7]]
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [[1,2,4,7],[3,5],[6]]
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [[1,2,4],[3,5],[6],[7]]
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [[1,2,5,6,7],[3],[4]]
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [[1,2,5,6],[3,7],[4]]
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [[1,2,5,7],[3,6],[4]]
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [[1,2,5],[3,6],[4,7]]
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [[1,2,6,7],[3],[4],[5]]
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [[1,2,6],[3,7],[4],[5]]
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [[1,2,7],[3],[4],[5],[6]]
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]]
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]]
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]]
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [[1,3,4,5,7],[2,6]]
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [[1,3,4,5],[2,6],[7]]
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [[1,3,4,6,7],[2,5]]
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [[1,3,4,6],[2,5,7]]
>>> Load all 373 entries. <<<
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [[1,3,4,7],[2,5],[6]]
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [[1,3,4],[2,5],[6],[7]]
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[1,3,5,6,7],[2,4]]
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [[1,3,5,6],[2,4,7]]
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [[1,3,5,7],[2,4,6]]
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [[1,3,5],[2,4,6],[7]]
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [[1,3,6,7],[2,4],[5]]
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [[1,3,6],[2,4,7],[5]]
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [[1,3,7],[2,4],[5],[6]]
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]]
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]]
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [[1,4,5,6],[2,7],[3]]
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [[1,4,5,7],[2,6],[3]]
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [[1,4,5],[2,6],[3,7]]
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [[1,4,6,7],[2,5],[3]]
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [[1,4,6],[2,5,7],[3]]
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [[1,4,7],[2,5],[3,6]]
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]]
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [[1,5,6,7],[2],[3],[4]]
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [[1,5,6],[2,7],[3],[4]]
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [[1,5,7],[2,6],[3],[4]]
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]]
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5]]
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [[1,6],[2,7],[3],[4],[5]]
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6]]
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,1,1,1] => [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]]
[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]]
[1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [[1,2,3,4,5,6,8],[7]]
[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [[1,2,3,4,5,6],[7],[8]]
[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]]
[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [[1,2,3,4,5,7],[6,8]]
[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [[1,2,3,4,5,8],[6],[7]]
[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8]]
[1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [[1,2,3,4,6,7,8],[5]]
[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [[1,2,3,4,6,7],[5,8]]
[1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [[1,2,3,4,6,8],[5,7]]
[1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [[1,2,3,4,6],[5,7],[8]]
[1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [[1,2,3,4,7,8],[5],[6]]
[1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [[1,2,3,4,7],[5,8],[6]]
[1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [[1,2,3,4,8],[5],[6],[7]]
[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8]]
[1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]]
[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]]
[1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]]
[1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]]
[1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]]
[1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [[1,2,3,5,7],[4,6,8]]
[1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]]
[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [[1,2,3,6,7,8],[4],[5]]
[1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [[1,2,3,6,7],[4,8],[5]]
[1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [[1,2,3,6],[4,7],[5,8]]
[1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [[1,2,3,7,8],[4],[5],[6]]
[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [[1,2,3,8],[4],[5],[6],[7]]
[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8]]
[1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]]
[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]]
[1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]]
[1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [[1,2,4,5,6],[3,7],[8]]
[1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [[1,2,4,5,7,8],[3,6]]
[1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]]
[1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [[1,2,4,5,8],[3,6],[7]]
[1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]]
[1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]]
[1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]]
[1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [[1,2,4,6],[3,5,7],[8]]
[1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]]
[1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]]
[1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [[1,2,4,8],[3,5],[6],[7]]
[1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]]
[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]]
[1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [[1,2,5,6,7],[3,8],[4]]
[1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [[1,2,5,6,8],[3,7],[4]]
[1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]]
[1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [[1,2,5,8],[3,6],[4,7]]
[1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]]
[1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [[1,2,6,7,8],[3],[4],[5]]
[1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [[1,2,6,8],[3,7],[4],[5]]
[1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [[1,2,6],[3,7],[4,8],[5]]
[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [[1,2,7,8],[3],[4],[5],[6]]
[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [[1,2,7],[3,8],[4],[5],[6]]
[1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [[1,2,8],[3],[4],[5],[6],[7]]
[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]]
[2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]]
[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]]
[2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]]
[2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [[1,3,4,5,6],[2,7],[8]]
[2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [[1,3,4,5,7,8],[2,6]]
[2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]]
[2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [[1,3,4,5],[2,6],[7],[8]]
[2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [[1,3,4,6,7],[2,5,8]]
[2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [[1,3,4,6],[2,5,7],[8]]
[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [[1,3,4],[2,5],[6],[7],[8]]
[2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4]]
[2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [[1,3,5,6,7],[2,4,8]]
[2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [[1,3,5,6],[2,4,7],[8]]
[2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [[1,3,5,7,8],[2,4,6]]
[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]]
[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8]]
[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [[1,3,6,7,8],[2,4],[5]]
[2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [[1,3,6,8],[2,4,7],[5]]
[2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [[1,3,6],[2,4,7],[5,8]]
[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [[1,3,7],[2,4,8],[5],[6]]
[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [[1,3,8],[2,4],[5],[6],[7]]
[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]]
[3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]]
[3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]]
[3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]]
[3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]]
[3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [[1,4,5],[2,6],[3,7],[8]]
[3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [[1,4,6,7,8],[2,5],[3]]
[3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [[1,4,6,8],[2,5,7],[3]]
[3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [[1,4,7,8],[2,5],[3,6]]
[3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [[1,4,7],[2,5,8],[3,6]]
[3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [[1,4,8],[2,5],[3,6],[7]]
[3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]]
[4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [[1,5,6,7,8],[2],[3],[4]]
[4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [[1,5,6,7],[2,8],[3],[4]]
[4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [[1,5,6,8],[2,7],[3],[4]]
[4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [[1,5,6],[2,7],[3,8],[4]]
[4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [[1,5,7,8],[2,6],[3],[4]]
[4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [[1,5,7],[2,6,8],[3],[4]]
[4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [[1,5,8],[2,6],[3,7],[4]]
[4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]]
[5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [[1,6,7,8],[2],[3],[4],[5]]
[5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [[1,6,7],[2,8],[3],[4],[5]]
[5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [[1,6,8],[2,7],[3],[4],[5]]
[5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]]
[6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [[1,7,8],[2],[3],[4],[5],[6]]
[6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [[1,7],[2,8],[3],[4],[5],[6]]
[7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [[1,8],[2],[3],[4],[5],[6],[7]]
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,1,1] => [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]]
[1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [[1,2,3,4,5,6,7,8],[9]]
[1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [[1,2,3,4,5,6,7,9],[8]]
[1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [[1,2,3,4,5,6,7],[8],[9]]
[1,1,1,1,1,2,1,1] => [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] => [[1,2,3,4,5,6,8,9],[7]]
[1,1,1,1,1,2,2] => [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] => [[1,2,3,4,5,6,8],[7,9]]
[1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [[1,2,3,4,5,6],[7],[8],[9]]
[1,1,1,1,2,1,1,1] => [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] => [[1,2,3,4,5,7,8,9],[6]]
[1,1,1,1,2,2,1] => [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] => [[1,2,3,4,5,7,9],[6,8]]
[1,1,1,1,2,3] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,9,8,7] => [[1,2,3,4,5,7],[6,8],[9]]
[1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8],[9]]
[1,1,1,2,1,1,1,1] => [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] => [[1,2,3,4,6,7,8,9],[5]]
[1,1,1,2,2,2] => [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] => [[1,2,3,4,6,8],[5,7,9]]
[1,1,1,2,4] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,9,8,7,6] => [[1,2,3,4,6],[5,7],[8],[9]]
[1,1,1,3,3] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,3,6,5,4,9,8,7] => [[1,2,3,4,7],[5,8],[6,9]]
[1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8],[9]]
[1,1,2,1,1,1,1,1] => [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] => [[1,2,3,5,6,7,8,9],[4]]
[1,1,2,2,2,1] => [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] => [[1,2,3,5,7,9],[4,6,8]]
[1,1,2,2,3] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,9,8,7] => [[1,2,3,5,7],[4,6,8],[9]]
[1,1,2,5] => [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,9,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8],[9]]
[1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8],[9]]
[1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]]
[1,2,1,1,1,1,2] => [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] => [[1,2,4,5,6,7,8],[3,9]]
[1,2,1,1,1,3] => [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] => [[1,2,4,5,6,7],[3,8],[9]]
[1,2,2,1,1,1,1] => [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] => [[1,2,4,6,7,8,9],[3,5]]
[1,2,2,2,2] => [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] => [[1,2,4,6,8],[3,5,7,9]]
[1,2,2,4] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,9,8,7,6] => [[1,2,4,6],[3,5,7],[8],[9]]
[1,2,3,3] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4,9,8,7] => [[1,2,4,7],[3,5,8],[6,9]]
[1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,9,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8],[9]]
[1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3],[4]]
[1,3,5] => [1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,4,3,2,9,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8],[9]]
[1,4,4] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2,9,8,7,6] => [[1,2,6],[3,7],[4,8],[5,9]]
[1,6,2] => [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] => [[1,2,8],[3,9],[4],[5],[6],[7]]
[1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]]
[1,8] => [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] => [[1,2],[3],[4],[5],[6],[7],[8],[9]]
[2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]]
[2,1,1,1,1,1,2] => [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] => [[1,3,4,5,6,7,8],[2,9]]
[2,1,1,1,1,2,1] => [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] => [[1,3,4,5,6,7,9],[2,8]]
[2,2,1,1,1,1,1] => [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] => [[1,3,5,6,7,8,9],[2,4]]
[2,2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => [[1,3,5,7,8,9],[2,4,6]]
[2,2,2,2,1] => [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] => [[1,3,5,7,9],[2,4,6,8]]
[2,2,2,3] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,9,8,7] => [[1,3,5,7],[2,4,6,8],[9]]
[2,2,5] => [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] => [[1,3,5],[2,4,6],[7],[8],[9]]
[2,3,4] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,5,4,3,9,8,7,6] => [[1,3,6],[2,4,7],[5,8],[9]]
[2,6,1] => [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] => [[1,3,9],[2,4],[5],[6],[7],[8]]
[2,7] => [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] => [[1,3],[2,4],[5],[6],[7],[8],[9]]
[3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]]
[3,2,1,1,1,1] => [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] => [[1,4,6,7,8,9],[2,5],[3]]
[3,2,2,2] => [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] => [[1,4,6,8],[2,5,7,9],[3]]
[3,3,1,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,6,5,4,7,8,9] => [[1,4,7,8,9],[2,5],[3,6]]
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4,9,8,7] => [[1,4,7],[2,5,8],[3,6,9]]
[3,6] => [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] => [[1,4],[2,5],[3,6],[7],[8],[9]]
[4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [[1,5,6,7,8,9],[2],[3],[4]]
[4,2,1,1,1] => [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] => [[1,5,7,8,9],[2,6],[3],[4]]
[4,2,2,1] => [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] => [[1,5,7,9],[2,6,8],[3],[4]]
[4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,3,2,1,7,6,5,8,9] => [[1,5,8,9],[2,6],[3,7],[4]]
[4,3,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2,1,7,6,5,9,8] => [[1,5,8],[2,6,9],[3,7],[4]]
[4,4,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,8,7,6,5,9] => [[1,5,9],[2,6],[3,7],[4,8]]
[4,5] => [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] => [[1,5],[2,6],[3,7],[4,8],[9]]
[5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [[1,6,7,8,9],[2],[3],[4],[5]]
[5,2,1,1] => [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] => [[1,6,8,9],[2,7],[3],[4],[5]]
[5,3,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,4,3,2,1,8,7,6,9] => [[1,6,9],[2,7],[3,8],[4],[5]]
[5,4] => [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] => [[1,6],[2,7],[3,8],[4,9],[5]]
[6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [[1,7,8,9],[2],[3],[4],[5],[6]]
[6,2,1] => [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] => [[1,7,9],[2,8],[3],[4],[5],[6]]
[6,3] => [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] => [[1,7],[2,8],[3,9],[4],[5],[6]]
[7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]]
[7,2] => [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] => [[1,8],[2,9],[3],[4],[5],[6],[7]]
[8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [[1,9],[2],[3],[4],[5],[6],[7],[8]]
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,1,1,1,1] => [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]]
[1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [[1,2,3,4,5,6,7,8,9],[10]]
[1,1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [[1,2,3,4,5,6,7,8,10],[9]]
[1,1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [[1,2,3,4,5,6,7,8],[9],[10]]
[1,1,1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [[1,2,3,4,5,6,7,9,10],[8]]
[1,1,1,1,1,1,2,2] => [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] => [[1,2,3,4,5,6,7,9],[8,10]]
[1,1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [[1,2,3,4,5,6,7],[8],[9],[10]]
[1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]]
[1,1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [[1,2,3,4,5,6],[7],[8],[9],[10]]
[1,1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]]
[1,1,1,1,2,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7,10,9] => [[1,2,3,4,5,7,9],[6,8,10]]
[1,1,1,1,6] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8],[9],[10]]
[1,1,1,2,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]]
[1,1,1,2,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]]
[1,1,1,7] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]]
[1,1,2,1,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]]
[1,1,2,2,2,2] => [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] => [[1,2,3,5,7,9],[4,6,8,10]]
[1,1,4,4] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3,10,9,8,7] => [[1,2,3,7],[4,8],[5,9],[6,10]]
[1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]]
[1,2,1,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]]
[1,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]]
[1,2,2,2,3] => [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] => [[1,2,4,6,8],[3,5,7,9],[10]]
[1,2,3,4] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,2,6,5,4,10,9,8,7] => [[1,2,4,7],[3,5,8],[6,9],[10]]
[1,2,7] => [1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,10,9,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8],[9],[10]]
[1,3,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5,10,9,8] => [[1,2,5,8],[3,6,9],[4,7,10]]
[1,3,6] => [1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,4,3,2,10,9,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8],[9],[10]]
[1,4,5] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,5,4,3,2,10,9,8,7,6] => [[1,2,6],[3,7],[4,8],[5,9],[10]]
[1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]]
[1,9] => [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] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]
[2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]]
[2,1,1,1,1,1,1,2] => [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] => [[1,3,4,5,6,7,8,9],[2,10]]
[2,2,1,1,1,1,1,1] => [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] => [[1,3,5,6,7,8,9,10],[2,4]]
[2,2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9,10] => [[1,3,5,7,8,9,10],[2,4,6]]
[2,2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => [[1,3,5,7,9,10],[2,4,6,8]]
[2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]]
[2,2,2,4] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => [[1,3,5,7],[2,4,6,8],[9],[10]]
[2,2,3,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5,10,9,8] => [[1,3,5,8],[2,4,6,9],[7,10]]
[2,4,4] => [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] => [[1,3,7],[2,4,8],[5,9],[6,10]]
[2,8] => [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] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]]
[3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [[1,4,5,6,7,8,9,10],[2],[3]]
[3,2,1,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9,10] => [[1,4,6,7,8,9,10],[2,5],[3]]
[3,2,2,2,1] => [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] => [[1,4,6,8,10],[2,5,7,9],[3]]
[3,3,2,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7,10,9] => [[1,4,7,9],[2,5,8,10],[3,6]]
[3,3,4] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,6,5,4,10,9,8,7] => [[1,4,7],[2,5,8],[3,6,9],[10]]
[3,7] => [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] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]]
[4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [[1,5,6,7,8,9,10],[2],[3],[4]]
[4,2,2,2] => [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] => [[1,5,7,9],[2,6,8,10],[3],[4]]
[4,3,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5,10,9,8] => [[1,5,8],[2,6,9],[3,7,10],[4]]
[4,4,1,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,8,7,6,5,9,10] => [[1,5,9,10],[2,6],[3,7],[4,8]]
[4,4,2] => [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] => [[1,5,9],[2,6,10],[3,7],[4,8]]
[4,6] => [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] => [[1,5],[2,6],[3,7],[4,8],[9],[10]]
[5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [[1,6,7,8,9,10],[2],[3],[4],[5]]
[5,2,2,1] => [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] => [[1,6,8,10],[2,7,9],[3],[4],[5]]
[5,4,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,3,2,1,9,8,7,6,10] => [[1,6,10],[2,7],[3,8],[4,9],[5]]
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5,10]]
[6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [[1,7,8,9,10],[2],[3],[4],[5],[6]]
[6,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,5,4,3,2,1,9,8,7,10] => [[1,7,10],[2,8],[3,9],[4],[5],[6]]
[6,4] => [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] => [[1,7],[2,8],[3,9],[4,10],[5],[6]]
[7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]]
[7,2,1] => [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] => [[1,8,10],[2,9],[3],[4],[5],[6],[7]]
[7,3] => [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] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]]
[8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]]
[8,2] => [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] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]]
[9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
[1,10] => [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] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10],[11]]
[10,1] => [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] => [[1,11],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
[2,2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[1,3,5,7,9,11],[2,4,6,8,10,12]]
[1,1,1,1,1,1,1,1,1,2] => [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] => [[1,2,3,4,5,6,7,8,9,10],[11]]
[1,2,2,2,2,2] => [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] => [[1,2,4,6,8,10],[3,5,7,9,11]]
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
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.