Processing math: 100%

Values
[1] => [1] => [[1]] => [1] => 1
[1,1] => [1,1] => [[1],[2]] => [1,1] => 1
[2] => [2] => [[1,2]] => [2] => 2
[1,1,1] => [1,1,1] => [[1],[2],[3]] => [1,1,1] => 1
[1,2] => [2,1] => [[1,2],[3]] => [2,1] => 1
[2,1] => [2,1] => [[1,2],[3]] => [2,1] => 1
[3] => [3] => [[1,2,3]] => [3] => 3
[1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [1,1,1,1] => 1
[1,1,2] => [2,1,1] => [[1,2],[3],[4]] => [2,1,1] => 1
[1,2,1] => [2,1,1] => [[1,2],[3],[4]] => [2,1,1] => 1
[1,3] => [3,1] => [[1,2,3],[4]] => [3,1] => 1
[2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [2,1,1] => 1
[2,2] => [2,2] => [[1,2],[3,4]] => [2,2] => 2
[3,1] => [3,1] => [[1,2,3],[4]] => [3,1] => 1
[4] => [4] => [[1,2,3,4]] => [4] => 4
[1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [1,1,1,1,1] => 1
[1,1,1,2] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [2,1,1,1] => 1
[1,1,2,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [2,1,1,1] => 1
[1,1,3] => [3,1,1] => [[1,2,3],[4],[5]] => [3,1,1] => 1
[1,2,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [2,1,1,1] => 1
[1,2,2] => [2,2,1] => [[1,2],[3,4],[5]] => [2,2,1] => 1
[1,3,1] => [3,1,1] => [[1,2,3],[4],[5]] => [3,1,1] => 1
[1,4] => [4,1] => [[1,2,3,4],[5]] => [4,1] => 1
[2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [2,1,1,1] => 1
[2,1,2] => [2,2,1] => [[1,2],[3,4],[5]] => [2,2,1] => 1
[2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [2,2,1] => 1
[2,3] => [3,2] => [[1,2,3],[4,5]] => [3,2] => 2
[3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [3,1,1] => 1
[3,2] => [3,2] => [[1,2,3],[4,5]] => [3,2] => 2
[4,1] => [4,1] => [[1,2,3,4],[5]] => [4,1] => 1
[5] => [5] => [[1,2,3,4,5]] => [5] => 5
[1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => 1
[1,1,1,1,2] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 1
[1,1,1,2,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 1
[1,1,1,3] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => 1
[1,1,2,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 1
[1,1,2,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 1
[1,1,3,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => 1
[1,1,4] => [4,1,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 1
[1,2,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 1
[1,2,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 1
[1,2,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 1
[1,2,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => [3,2,1] => 1
[1,3,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => 1
[1,3,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => [3,2,1] => 1
[1,4,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 1
[1,5] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 1
[2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 1
[2,1,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 1
[2,1,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 1
[2,1,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => [3,2,1] => 1
[2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 1
[2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [2,2,2] => 2
[2,3,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => [3,2,1] => 1
[2,4] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 2
[3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => 1
[3,1,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => [3,2,1] => 1
[3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => [3,2,1] => 1
[3,3] => [3,3] => [[1,2,3],[4,5,6]] => [3,3] => 3
[4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 1
[4,2] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 2
[5,1] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 1
[6] => [6] => [[1,2,3,4,5,6]] => [6] => 6
[1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 1
[1,1,1,1,2,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 1
[1,1,1,1,3] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => 1
[1,1,1,2,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 1
[1,1,1,2,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 1
[1,1,1,3,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => 1
[1,1,1,4] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => 1
[1,1,2,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 1
[1,1,2,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 1
[1,1,2,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 1
[1,1,2,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 1
[1,1,3,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => 1
[1,1,3,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 1
[1,1,4,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => 1
[1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [5,1,1] => 1
[1,2,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 1
[1,2,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 1
[1,2,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 1
[1,2,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 1
[1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 1
[1,2,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => 1
[1,2,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 1
[1,2,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [4,2,1] => 1
[1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => 1
[1,3,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 1
[1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 1
[1,3,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [3,3,1] => 1
[1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => 1
[1,4,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [4,2,1] => 1
[1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [5,1,1] => 1
[1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => [6,1] => 1
[2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 1
[2,1,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 1
[2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 1
[2,1,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 1
[2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 1
[2,1,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => 1
>>> Load all 320 entries. <<<
[2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 1
[2,1,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [4,2,1] => 1
[2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 1
[2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => 1
[2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => 1
[2,2,3] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [3,2,2] => 2
[2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 1
[2,3,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [3,2,2] => 2
[2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [4,2,1] => 1
[2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => [5,2] => 2
[3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => 1
[3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 1
[3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 1
[3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [3,3,1] => 1
[3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 1
[3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [3,2,2] => 2
[3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [3,3,1] => 1
[3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => [4,3] => 3
[4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => 1
[4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [4,2,1] => 1
[4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [4,2,1] => 1
[4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => [4,3] => 3
[5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [5,1,1] => 1
[5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [5,2] => 2
[6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => [6,1] => 1
[7] => [7] => [[1,2,3,4,5,6,7]] => [7] => 7
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[1,1,1,2,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[1,1,1,2,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => 1
[1,1,2,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[1,1,2,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 1
[1,1,3,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 1
[1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => 1
[1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [6,1,1] => 1
[1,2,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[1,2,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 1
[1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[1,2,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 1
[1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 1
[1,2,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 1
[1,2,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 1
[1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [5,2,1] => 1
[1,3,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 1
[1,3,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 1
[1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 1
[1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [4,3,1] => 1
[1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [4,3,1] => 1
[1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => 1
[1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [5,2,1] => 1
[1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [6,1,1] => 1
[1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [7,1] => 1
[2,1,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[2,1,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 1
[2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 1
[2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 1
[2,1,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 1
[2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 1
[2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [5,2,1] => 1
[2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 1
[2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 1
[2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 1
[2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 1
[2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 1
[2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [2,2,2,2] => 2
[2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 1
[2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 1
[2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 1
[2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [3,3,2] => 2
[2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [5,2,1] => 1
[3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 1
[3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 1
[3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 1
[3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [4,3,1] => 1
[3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 1
[3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 1
[3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [3,3,2] => 2
[3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 1
[3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [3,3,2] => 2
[3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [4,3,1] => 1
[4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [4,3,1] => 1
[4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [4,3,1] => 1
[4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [4,4] => 4
[5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => 1
[5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [5,2,1] => 1
[5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [5,2,1] => 1
[6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [6,1,1] => 1
[7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [7,1] => 1
[1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [7,1,1] => 1
[1,2,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [6,2,1] => 1
[1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [6,2,1] => 1
[1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [7,1,1] => 1
[1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [8,1] => 1
[2,1,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [6,2,1] => 1
[2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [6,2,1] => 1
[6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [6,2,1] => 1
[6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [6,2,1] => 1
[7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [7,1,1] => 1
[8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [8,1] => 1
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,3,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,3,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[1,1,1,3,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,1,2,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[1,1,3,1,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[1,1,3,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[1,1,3,3,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[1,1,4,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [4,4,1,1] => 1
[1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [8,1,1] => 1
[1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,2,1,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[1,2,2,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[1,2,2,2,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[1,3,1,1,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[1,3,1,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[1,3,1,3,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[1,3,3,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[1,4,1,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [4,4,1,1] => 1
[1,4,4,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [4,4,1,1] => 1
[1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [8,1,1] => 1
[1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1] => 1
[2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[2,1,1,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[2,1,2,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[2,1,2,2,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[2,1,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => 1
[2,2,1,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[2,2,1,2,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[2,2,1,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[2,2,2,1,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[2,2,2,1,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => 1
[2,2,3,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [3,3,2,2] => 2
[2,3,2,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [3,3,2,2] => 2
[2,3,3,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [3,3,2,2] => 2
[3,1,1,1,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[3,1,1,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[3,1,1,3,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[3,1,3,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[3,2,2,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [3,3,2,2] => 2
[3,2,3,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [3,3,2,2] => 2
[3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => 1
[3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [3,3,2,2] => 2
[4,1,1,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [4,4,1,1] => 1
[4,1,4,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [4,4,1,1] => 1
[4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [4,4,1,1] => 1
[5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [5,5] => 5
[8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [8,1,1] => 1
[9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,2,2,3,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[1,1,3,3,2,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[1,1,3,2,2,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[2,2,1,1,3,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [2,2,2,2,2,2] => 2
[2,2,3,3,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[2,2,3,1,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[2,2,4,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => [4,4,2,2] => 2
[2,1,1,2,3,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[2,1,3,3,1,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[2,1,3,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[3,3,1,1,2,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[3,3,2,2,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[3,3,2,1,1,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[3,2,1,1,2,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[3,2,2,3,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[3,2,2,1,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[3,1,1,3,2,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[3,1,1,2,2,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[3,1,2,3,1,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[4,4,2,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => [4,4,2,2] => 2
[4,2,2,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => [4,4,2,2] => 2
[6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [6,6] => 6
[1,2,2,3,3,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[1,2,3,3,2,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[1,2,3,2,3,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[1,3,3,2,2,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[1,3,2,3,2,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[1,3,2,2,3,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
[2,4,4,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => [4,4,2,2] => 2
[2,4,2,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => [4,4,2,2] => 2
[4,2,4,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => [4,4,2,2] => 2
[1,1,2,3,2,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => [3,3,2,2,1,1] => 1
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Description
The last part of an integer composition.
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to partition
Description
Sends a composition to the partition obtained by sorting the entries.
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initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers 1 through n row by row.
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horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau T the composition (c1,,ck), such that k is minimal and the numbers c1++ci+1,,c1++ci+1 form a horizontal strip in T for all i.