Processing math: 100%

Identifier
Values
[1] => [1,0] => [1] => [[1]] => 1
[1,1] => [1,0,1,0] => [2,1] => [[1],[2]] => 2
[2] => [1,1,0,0] => [1,2] => [[1,2]] => 1
[1,1,1] => [1,0,1,0,1,0] => [3,2,1] => [[1],[2],[3]] => 3
[1,2] => [1,0,1,1,0,0] => [2,3,1] => [[1,2],[3]] => 1
[2,1] => [1,1,0,0,1,0] => [3,1,2] => [[1,3],[2]] => 2
[3] => [1,1,1,0,0,0] => [1,2,3] => [[1,2,3]] => 1
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => [[1],[2],[3],[4]] => 4
[1,1,2] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => [[1,2],[3],[4]] => 1
[1,2,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => [[1,3],[2],[4]] => 2
[1,3] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => [[1,2,3],[4]] => 1
[2,1,1] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => [[1,4],[2],[3]] => 3
[2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => [[1,2],[3,4]] => 1
[3,1] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => [[1,3,4],[2]] => 2
[4] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => [[1,2,3,4]] => 1
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]] => 5
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [[1,2],[3],[4],[5]] => 1
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [[1,3],[2],[4],[5]] => 2
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [[1,2,3],[4],[5]] => 1
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [[1,4],[2],[3],[5]] => 3
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [[1,2],[3,4],[5]] => 1
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [[1,3,4],[2],[5]] => 2
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[1,2,3,4],[5]] => 1
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [[1,5],[2],[3],[4]] => 4
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [[1,2],[3,5],[4]] => 1
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [[1,3],[2,5],[4]] => 2
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [[1,2,3],[4,5]] => 1
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [[1,4,5],[2],[3]] => 3
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [[1,2,5],[3,4]] => 1
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [[1,3,4,5],[2]] => 2
[5] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [[1,2,3,4,5]] => 1
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => 6
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [[1,2],[3],[4],[5],[6]] => 1
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [[1,3],[2],[4],[5],[6]] => 2
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [[1,2,3],[4],[5],[6]] => 1
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [[1,4],[2],[3],[5],[6]] => 3
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [[1,2],[3,4],[5],[6]] => 1
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [[1,3,4],[2],[5],[6]] => 2
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [[1,2,3,4],[5],[6]] => 1
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [[1,5],[2],[3],[4],[6]] => 4
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [[1,2],[3,5],[4],[6]] => 1
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [[1,3],[2,5],[4],[6]] => 2
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [[1,2,3],[4,5],[6]] => 1
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [[1,4,5],[2],[3],[6]] => 3
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [[1,2,5],[3,4],[6]] => 1
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => 2
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[1,2,3,4,5],[6]] => 1
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [[1,6],[2],[3],[4],[5]] => 5
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [[1,2],[3,6],[4],[5]] => 1
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [[1,3],[2,6],[4],[5]] => 2
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [[1,2,3],[4,6],[5]] => 1
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [[1,4],[2,6],[3],[5]] => 3
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [[1,2],[3,4],[5,6]] => 1
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [[1,3,4],[2,6],[5]] => 2
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [[1,2,3,4],[5,6]] => 1
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [[1,5,6],[2],[3],[4]] => 4
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [[1,2,6],[3,5],[4]] => 1
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [[1,3,6],[2,5],[4]] => 2
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [[1,2,3],[4,5,6]] => 1
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [[1,4,5,6],[2],[3]] => 3
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [[1,2,5,6],[3,4]] => 1
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [[1,3,4,5,6],[2]] => 2
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]] => 7
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 1
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7]] => 2
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [[1,2,3],[4],[5],[6],[7]] => 1
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => 3
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [[1,2],[3,4],[5],[6],[7]] => 1
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => 2
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[1,2,3,4],[5],[6],[7]] => 1
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [[1,5],[2],[3],[4],[6],[7]] => 4
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [[1,2],[3,5],[4],[6],[7]] => 1
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [[1,3],[2,5],[4],[6],[7]] => 2
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [[1,2,3],[4,5],[6],[7]] => 1
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [[1,4,5],[2],[3],[6],[7]] => 3
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [[1,2,5],[3,4],[6],[7]] => 1
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [[1,3,4,5],[2],[6],[7]] => 2
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [[1,2,3,4,5],[6],[7]] => 1
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [[1,6],[2],[3],[4],[5],[7]] => 5
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [[1,2],[3,6],[4],[5],[7]] => 1
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [[1,3],[2,6],[4],[5],[7]] => 2
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [[1,2,3],[4,6],[5],[7]] => 1
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [[1,4],[2,6],[3],[5],[7]] => 3
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [[1,2],[3,4],[5,6],[7]] => 1
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [[1,3,4],[2,6],[5],[7]] => 2
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [[1,2,3,4],[5,6],[7]] => 1
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [[1,5,6],[2],[3],[4],[7]] => 4
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [[1,2,6],[3,5],[4],[7]] => 1
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [[1,3,6],[2,5],[4],[7]] => 2
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [[1,2,3],[4,5,6],[7]] => 1
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [[1,4,5,6],[2],[3],[7]] => 3
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [[1,2,5,6],[3,4],[7]] => 1
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => 2
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[1,2,3,4,5,6],[7]] => 1
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [[1,7],[2],[3],[4],[5],[6]] => 6
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [[1,2],[3,7],[4],[5],[6]] => 1
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [[1,3],[2,7],[4],[5],[6]] => 2
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [[1,2,3],[4,7],[5],[6]] => 1
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [[1,4],[2,7],[3],[5],[6]] => 3
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [[1,2],[3,4],[5,7],[6]] => 1
>>> Load all 324 entries. <<<
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [[1,3,4],[2,7],[5],[6]] => 2
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [[1,2,3,4],[5,7],[6]] => 1
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [[1,5],[2,7],[3],[4],[6]] => 4
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [[1,2],[3,5],[4,7],[6]] => 1
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [[1,3],[2,5],[4,7],[6]] => 2
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [[1,2,3],[4,5],[6,7]] => 1
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [[1,4,5],[2,7],[3],[6]] => 3
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [[1,2,5],[3,4],[6,7]] => 1
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [[1,3,4,5],[2,7],[6]] => 2
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [[1,2,3,4,5],[6,7]] => 1
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [[1,6,7],[2],[3],[4],[5]] => 5
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [[1,2,7],[3,6],[4],[5]] => 1
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [[1,3,7],[2,6],[4],[5]] => 2
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [[1,2,3],[4,6,7],[5]] => 1
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [[1,4,7],[2,6],[3],[5]] => 3
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [[1,2,7],[3,4],[5,6]] => 1
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [[1,3,4],[2,6,7],[5]] => 2
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[1,2,3,4],[5,6,7]] => 1
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [[1,5,6,7],[2],[3],[4]] => 4
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [[1,2,6,7],[3,5],[4]] => 1
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [[1,3,6,7],[2,5],[4]] => 2
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [[1,2,3,7],[4,5,6]] => 1
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [[1,4,5,6,7],[2],[3]] => 3
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [[1,2,5,6,7],[3,4]] => 1
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [[1,3,4,5,6,7],[2]] => 2
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 8
[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 1
[1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 1
[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => 3
[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 1
[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 2
[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 1
[1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 4
[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 1
[1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 2
[1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 3
[1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => 2
[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [[1,2,3,4,5],[6],[7],[8]] => 1
[1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 5
[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 1
[1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 2
[1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 3
[1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [[1,2],[3,4],[5,6],[7],[8]] => 1
[1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => 2
[1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [[1,2,3,4],[5,6],[7],[8]] => 1
[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 4
[1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => 1
[1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [[1,3,6],[2,5],[4],[7],[8]] => 2
[1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [[1,2,3],[4,5,6],[7],[8]] => 1
[1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 3
[1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [[1,2,5,6],[3,4],[7],[8]] => 1
[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [[1,3,4,5,6],[2],[7],[8]] => 2
[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [[1,2,3,4,5,6],[7],[8]] => 1
[1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 6
[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 1
[1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 2
[1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 3
[1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [[1,3,4],[2,7],[5],[6],[8]] => 2
[1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [[1,2,3,4],[5,7],[6],[8]] => 1
[1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 4
[1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [[1,3],[2,5],[4,7],[6],[8]] => 2
[1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => [[1,4,5],[2,7],[3],[6],[8]] => 3
[1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [[1,2,5],[3,4],[6,7],[8]] => 1
[1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [[1,3,4,5],[2,7],[6],[8]] => 2
[1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [[1,2,3,4,5],[6,7],[8]] => 1
[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 5
[1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [[1,3,7],[2,6],[4],[5],[8]] => 2
[1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [[1,2,3],[4,6,7],[5],[8]] => 1
[1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [[1,4,7],[2,6],[3],[5],[8]] => 3
[1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => [[1,2,7],[3,4],[5,6],[8]] => 1
[1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [[1,3,4],[2,6,7],[5],[8]] => 2
[1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [[1,2,3,4],[5,6,7],[8]] => 1
[1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [[1,5,6,7],[2],[3],[4],[8]] => 4
[1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => [[1,2,6,7],[3,5],[4],[8]] => 1
[1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [[1,3,6,7],[2,5],[4],[8]] => 2
[1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [[1,2,3,7],[4,5,6],[8]] => 1
[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [[1,4,5,6,7],[2],[3],[8]] => 3
[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [[1,2,5,6,7],[3,4],[8]] => 1
[1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => 2
[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [[1,2,3,4,5,6,7],[8]] => 1
[2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [[1,8],[2],[3],[4],[5],[6],[7]] => 7
[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [[1,2],[3,8],[4],[5],[6],[7]] => 1
[2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [[1,3],[2,8],[4],[5],[6],[7]] => 2
[2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [[1,2,3],[4,8],[5],[6],[7]] => 1
[2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [[1,4],[2,8],[3],[5],[6],[7]] => 3
[2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [[1,2],[3,4],[5,8],[6],[7]] => 1
[2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [[1,2,3,4],[5,8],[6],[7]] => 1
[2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [[1,5],[2,8],[3],[4],[6],[7]] => 4
[2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [[1,2],[3,5],[4,8],[6],[7]] => 1
[2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [[1,3],[2,5],[4,8],[6],[7]] => 2
[2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => [[1,2,3],[4,5],[6,8],[7]] => 1
[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [[1,2,3,4,5],[6,8],[7]] => 1
[2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
[2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => 1
[2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [[1,2,3],[4,6],[5,8],[7]] => 1
[2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => 3
[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8]] => 1
[2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 2
[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [[1,2,3,4],[5,6],[7,8]] => 1
[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 4
[2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [[1,3,6],[2,5],[4,8],[7]] => 2
[2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 3
[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [[1,2,5,6],[3,4],[7,8]] => 1
[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [[1,3,4,5,6],[2,8],[7]] => 2
[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [[1,2,3,4,5,6],[7,8]] => 1
[3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [[1,7,8],[2],[3],[4],[5],[6]] => 6
[3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [[1,2,8],[3,7],[4],[5],[6]] => 1
[3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [[1,2,3],[4,7,8],[5],[6]] => 1
[3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [[1,2,8],[3,4],[5,7],[6]] => 1
[3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [[1,3,4],[2,7,8],[5],[6]] => 2
[3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [[1,2,3,4],[5,7,8],[6]] => 1
[3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [[1,5,8],[2,7],[3],[4],[6]] => 4
[3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [[1,3,8],[2,5],[4,7],[6]] => 2
[3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => [[1,2,3],[4,5,8],[6,7]] => 1
[3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => 3
[3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [[1,2,5],[3,4,8],[6,7]] => 1
[3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [[1,3,4,5],[2,7,8],[6]] => 2
[3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [[1,2,3,4,5],[6,7,8]] => 1
[4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [[1,6,7,8],[2],[3],[4],[5]] => 5
[4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [[1,2,7,8],[3,6],[4],[5]] => 1
[4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [[1,3,7,8],[2,6],[4],[5]] => 2
[4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [[1,2,3,8],[4,6,7],[5]] => 1
[4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [[1,4,7,8],[2,6],[3],[5]] => 3
[4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [[1,2,7,8],[3,4],[5,6]] => 1
[4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [[1,3,4,8],[2,6,7],[5]] => 2
[4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [[1,2,3,4],[5,6,7,8]] => 1
[5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [[1,5,6,7,8],[2],[3],[4]] => 4
[5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [[1,2,6,7,8],[3,5],[4]] => 1
[5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [[1,3,6,7,8],[2,5],[4]] => 2
[5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [[1,2,3,7,8],[4,5,6]] => 1
[6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [[1,4,5,6,7,8],[2],[3]] => 3
[6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [[1,2,5,6,7,8],[3,4]] => 1
[7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [[1,3,4,5,6,7,8],[2]] => 2
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 1
[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] => [9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 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] => [8,9,7,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 1
[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] => [7,8,9,6,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 1
[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] => [8,9,6,7,5,4,3,2,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 1
[1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 1
[1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 1
[1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 1
[1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => [[1,2,3,4,5,6,7],[8],[9]] => 1
[1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,2,3,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 1
[1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => [[1,2,3,4,5,6],[7,8],[9]] => 1
[1,4,4] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,5,1] => [[1,2,3,4],[5,6,7,8],[9]] => 1
[1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2],[9]] => 2
[1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [[1,2,3,4,5,6,7,8],[9]] => 1
[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] => [9,8,7,6,5,4,3,1,2] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 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] => [9,8,7,6,5,3,4,1,2] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
[2,2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
[2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => [[1,3],[2,5],[4,7],[6,9],[8]] => 2
[2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [[1,2,3,4,5,6,7],[8,9]] => 1
[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] => [9,8,7,6,5,4,1,2,3] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 7
[3,2,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
[3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => [[1,2,9],[3,4],[5,6],[7,8]] => 1
[3,3,1,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => [[1,2,3],[4,5,6],[7,8,9]] => 1
[3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [[1,2,3,4,5,6],[7,8,9]] => 1
[4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 6
[4,2,1,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
[4,2,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => [[1,3,8,9],[2,5],[4,7],[6]] => 2
[4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
[4,3,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => [[1,2,5,9],[3,4,8],[6,7]] => 1
[4,4,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => [[1,3,4,5],[2,7,8,9],[6]] => 2
[4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [[1,2,3,4,5],[6,7,8,9]] => 1
[5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => [[1,6,7,8,9],[2],[3],[4],[5]] => 5
[5,2,1,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
[5,3,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => [[1,3,4,8,9],[2,6,7],[5]] => 2
[5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [[1,2,3,4,9],[5,6,7,8]] => 1
[6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => [[1,5,6,7,8,9],[2],[3],[4]] => 4
[6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => [[1,3,6,7,8,9],[2,5],[4]] => 2
[6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [[1,2,3,7,8,9],[4,5,6]] => 1
[7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => [[1,4,5,6,7,8,9],[2],[3]] => 3
[7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [[1,2,5,6,7,8,9],[3,4]] => 1
[8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [[1,3,4,5,6,7,8,9],[2]] => 2
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 1
[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] => [10,9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 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] => [9,10,8,7,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 1
[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] => [8,9,10,7,6,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 1
[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] => [7,8,9,10,6,5,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 1
[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] => [6,7,8,9,10,5,4,3,2,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 1
[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] => [5,6,7,8,9,10,4,3,2,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 1
[1,1,1,7] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 1
[1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 1
[1,2,7] => [1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,2,3,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 1
[1,3,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,2,3,4,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 1
[1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[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] => [10,9,8,7,6,5,4,3,1,2] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 9
[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] => [10,9,8,7,6,5,3,4,1,2] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 7
[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] => [10,9,8,7,5,6,3,4,1,2] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 5
[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] => [10,9,7,8,5,6,3,4,1,2] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 3
[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] => [9,10,7,8,5,6,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 1
[2,2,2,4] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,5,6,3,4,1,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 1
[2,4,4] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,3,4,5,6,1,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 1
[2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 1
[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] => [10,9,8,7,6,5,4,1,2,3] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 8
[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] => [10,9,8,7,6,4,5,1,2,3] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
[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] => [10,8,9,6,7,4,5,1,2,3] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 2
[3,3,2,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 1
[3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 1
[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] => [10,9,8,7,6,5,1,2,3,4] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 7
[4,2,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 1
[4,3,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1
[4,4,1,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 3
[4,4,2] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => [[1,2,5,6],[3,4,9,10],[7,8]] => 1
[4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 1
[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] => [10,9,8,7,6,1,2,3,4,5] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 6
[5,2,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 2
[5,4,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => [[1,3,4,5,10],[2,7,8,9],[6]] => 2
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 1
[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] => [10,9,8,7,1,2,3,4,5,6] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 5
[6,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => [[1,3,4,8,9,10],[2,6,7],[5]] => 2
[6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [[1,2,3,4,9,10],[5,6,7,8]] => 1
[7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 4
[7,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => [[1,3,6,7,8,9,10],[2,5],[4]] => 2
[7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [[1,2,3,7,8,9,10],[4,5,6]] => 1
[8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [[1,4,5,6,7,8,9,10],[2],[3]] => 3
[8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [[1,2,5,6,7,8,9,10],[3,4]] => 1
[9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9,10],[2]] => 2
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[2,2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [11,12,9,10,7,8,5,6,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 1
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Description
The index of the last row whose first entry is the row number in a standard Young tableau.
Map
bounce path
Description
The bounce path determined by an integer composition.
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.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].