Identifier
Values
[1] => [1] => [[1]] => [1] => 1
[1,1] => [1,1] => [[1],[2]] => [1,1] => 2
[2] => [2] => [[1,2]] => [2] => 1
[1,1,1] => [1,1,1] => [[1],[2],[3]] => [1,1,1] => 3
[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] => 1
[1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => [1,1,1,1] => 4
[1,1,2] => [2,1,1] => [[1,2],[3],[4]] => [2,1,1] => 2
[1,2,1] => [2,1,1] => [[1,2],[3],[4]] => [2,1,1] => 2
[1,3] => [3,1] => [[1,2,3],[4]] => [3,1] => 1
[2,1,1] => [2,1,1] => [[1,2],[3],[4]] => [2,1,1] => 2
[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] => 1
[1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [1,1,1,1,1] => 5
[1,1,1,2] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [2,1,1,1] => 3
[1,1,2,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [2,1,1,1] => 3
[1,1,3] => [3,1,1] => [[1,2,3],[4],[5]] => [3,1,1] => 2
[1,2,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [2,1,1,1] => 3
[1,2,2] => [2,2,1] => [[1,2],[3,4],[5]] => [2,2,1] => 2
[1,3,1] => [3,1,1] => [[1,2,3],[4],[5]] => [3,1,1] => 2
[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] => 3
[2,1,2] => [2,2,1] => [[1,2],[3,4],[5]] => [2,2,1] => 2
[2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => [2,2,1] => 2
[2,3] => [3,2] => [[1,2,3],[4,5]] => [3,2] => 1
[3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => [3,1,1] => 2
[3,2] => [3,2] => [[1,2,3],[4,5]] => [3,2] => 1
[4,1] => [4,1] => [[1,2,3,4],[5]] => [4,1] => 1
[5] => [5] => [[1,2,3,4,5]] => [5] => 1
[1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => 6
[1,1,1,1,2] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 4
[1,1,1,2,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 4
[1,1,1,3] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => 3
[1,1,2,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 4
[1,1,2,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 2
[1,1,3,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => 3
[1,1,4] => [4,1,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 2
[1,2,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 4
[1,2,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 2
[1,2,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 2
[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] => 3
[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] => 2
[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] => 4
[2,1,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 2
[2,1,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 2
[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] => 2
[2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => [2,2,2] => 3
[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] => 1
[3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => 3
[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] => 2
[4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 2
[4,2] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 1
[5,1] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 1
[6] => [6] => [[1,2,3,4,5,6]] => [6] => 1
[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] => 7
[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] => 5
[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] => 5
[1,1,1,1,3] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => 4
[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] => 5
[1,1,1,2,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 3
[1,1,1,3,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => 4
[1,1,1,4] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => 3
[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] => 5
[1,1,2,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 3
[1,1,2,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 3
[1,1,2,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 2
[1,1,3,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => 4
[1,1,3,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 2
[1,1,4,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => 3
[1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [5,1,1] => 2
[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] => 5
[1,2,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 3
[1,2,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 3
[1,2,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 2
[1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 3
[1,2,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => 3
[1,2,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 2
[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] => 4
[1,3,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 2
[1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 2
[1,3,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [3,3,1] => 2
[1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => 3
[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] => 2
[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] => 5
[2,1,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 3
[2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 3
[2,1,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 2
[2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 3
[2,1,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => 3
>>> Load all 511 entries. <<<
[2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 2
[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] => 3
[2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => 3
[2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => 3
[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] => 2
[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] => 1
[3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => 4
[3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 2
[3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 2
[3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [3,3,1] => 2
[3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 2
[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] => 2
[3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => [4,3] => 1
[4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => 3
[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] => 1
[5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [5,1,1] => 2
[5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => [5,2] => 1
[6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => [6,1] => 1
[7] => [7] => [[1,2,3,4,5,6,7]] => [7] => 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]] => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => 6
[1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => 6
[1,1,1,1,1,3] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => 5
[1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => 6
[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] => 4
[1,1,1,1,3,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => 5
[1,1,1,1,4] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [4,1,1,1,1] => 4
[1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => 6
[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] => 4
[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] => 4
[1,1,1,2,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => 5
[1,1,1,3,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[1,1,1,4,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [4,1,1,1,1] => 4
[1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => 3
[1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => 6
[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] => 4
[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] => 4
[1,1,2,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[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] => 4
[1,1,2,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 3
[1,1,2,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[1,1,2,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 2
[1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => 5
[1,1,3,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[1,1,3,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[1,1,3,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 2
[1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [4,1,1,1,1] => 4
[1,1,4,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 2
[1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => 3
[1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [6,1,1] => 2
[1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => 6
[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] => 4
[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] => 4
[1,2,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[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] => 4
[1,2,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 3
[1,2,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[1,2,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 2
[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] => 4
[1,2,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 3
[1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 3
[1,2,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 2
[1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[1,2,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 2
[1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 2
[1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [5,2,1] => 1
[1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => 5
[1,3,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[1,3,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 2
[1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[1,3,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 2
[1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 2
[1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [4,3,1] => 1
[1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [4,1,1,1,1] => 4
[1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 2
[1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 2
[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] => 3
[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] => 2
[1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [7,1] => 1
[2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => 6
[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] => 4
[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] => 4
[2,1,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[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] => 4
[2,1,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 3
[2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[2,1,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 2
[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] => 4
[2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 3
[2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 3
[2,1,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 2
[2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 2
[2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 2
[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] => 4
[2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 3
[2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 3
[2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 2
[2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 3
[2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => [2,2,2,2] => 4
[2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 2
[2,2,4] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [4,2,2] => 2
[2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 2
[2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 2
[2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [3,3,2] => 2
[2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 2
[2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [4,2,2] => 2
[2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [5,2,1] => 1
[2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [6,2] => 1
[3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => 5
[3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 2
[3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 2
[3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 2
[3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [4,3,1] => 1
[3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 3
[3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 2
[3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 2
[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] => 2
[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
[3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [5,3] => 1
[4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [4,1,1,1,1] => 4
[4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 2
[4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 2
[4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [4,3,1] => 1
[4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 2
[4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [4,2,2] => 2
[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] => 2
[5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => 3
[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
[5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [5,3] => 1
[6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [6,1,1] => 2
[6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [6,2] => 1
[7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [7,1] => 1
[8] => [8] => [[1,2,3,4,5,6,7,8]] => [8] => 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]] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1] => 6
[1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1] => 7
[1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1] => 6
[1,1,1,1,1,4] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [4,1,1,1,1,1] => 5
[1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1] => 7
[1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,1,1,1,2,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1] => 6
[1,1,1,1,3,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [4,1,1,1,1,1] => 5
[1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [5,1,1,1,1] => 4
[1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1] => 7
[1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,1,1,2,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,1,1,2,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[1,1,1,2,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,1,1,2,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1] => 6
[1,1,1,3,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,1,1,3,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,1,1,3,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => 3
[1,1,1,4,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [4,1,1,1,1,1] => 5
[1,1,1,4,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[1,1,1,5,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [5,1,1,1,1] => 4
[1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [6,1,1,1] => 3
[1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1] => 7
[1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,1,2,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,1,2,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[1,1,2,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,1,2,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,1,2,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[1,1,2,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[1,1,2,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[1,1,2,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,1,2,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[1,1,2,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[1,1,2,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => 2
[1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1] => 6
[1,1,3,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,1,3,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,1,3,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => 3
[1,1,3,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,1,3,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[1,1,3,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => 3
[1,1,3,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => 2
[1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [4,1,1,1,1,1] => 5
[1,1,4,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[1,1,4,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[1,1,4,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => 2
[1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [5,1,1,1,1] => 4
[1,1,5,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => 2
[1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [6,1,1,1] => 3
[1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [7,1,1] => 2
[1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1] => 7
[1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,2,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,2,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[1,2,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,2,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,2,1,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[1,2,1,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[1,2,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[1,2,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,2,1,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[1,2,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[1,2,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => 2
[1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[1,2,2,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[1,2,2,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[1,2,2,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[1,2,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[1,2,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [2,2,2,2,1] => 4
[1,2,2,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[1,2,2,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => 2
[1,2,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,2,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[1,2,3,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[1,2,3,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => 2
[1,2,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[1,2,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => 2
[1,2,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => 2
[1,2,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [6,2,1] => 1
[1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1] => 6
[1,3,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,3,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,3,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => 3
[1,3,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,3,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[1,3,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => 3
[1,3,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => 2
[1,3,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[1,3,2,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[1,3,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[1,3,2,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => 2
[1,3,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => 3
[1,3,3,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => 2
[1,3,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => 2
[1,3,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [5,3,1] => 1
[1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [4,1,1,1,1,1] => 5
[1,4,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[1,4,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[1,4,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => 2
[1,4,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[1,4,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => 2
[1,4,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => 2
[1,4,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [4,4,1] => 2
[1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [5,1,1,1,1] => 4
[1,5,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => 2
[1,5,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => 2
[1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [5,3,1] => 1
[1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [6,1,1,1] => 3
[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] => 2
[1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [8,1] => 1
[2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1] => 7
[2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[2,1,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[2,1,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[2,1,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[2,1,1,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[2,1,1,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[2,1,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[2,1,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[2,1,1,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[2,1,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[2,1,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => 2
[2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[2,1,2,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[2,1,2,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[2,1,2,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[2,1,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[2,1,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [2,2,2,2,1] => 4
[2,1,2,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[2,1,2,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => 2
[2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[2,1,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[2,1,3,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[2,1,3,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => 2
[2,1,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[2,1,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => 2
[2,1,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => 2
[2,1,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [6,2,1] => 1
[2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => 5
[2,2,1,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[2,2,1,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[2,2,1,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[2,2,1,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[2,2,1,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [2,2,2,2,1] => 4
[2,2,1,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[2,2,1,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => 2
[2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => 3
[2,2,2,1,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [2,2,2,2,1] => 4
[2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [2,2,2,2,1] => 4
[2,2,2,3] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [3,2,2,2] => 3
[2,2,3,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[2,2,3,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [3,2,2,2] => 3
[2,2,4,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => 2
[2,2,5] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [5,2,2] => 2
[2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[2,3,1,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[2,3,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[2,3,1,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => 2
[2,3,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[2,3,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [3,2,2,2] => 3
[2,3,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => 2
[2,3,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [4,3,2] => 1
[2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[2,4,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => 2
[2,4,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => 2
[2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [4,3,2] => 1
[2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => 2
[2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [5,2,2] => 2
[2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [6,2,1] => 1
[2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [7,2] => 1
[3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1] => 6
[3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[3,1,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => 3
[3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[3,1,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[3,1,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => 3
[3,1,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => 2
[3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[3,1,2,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[3,1,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[3,1,2,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => 2
[3,1,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => 3
[3,1,3,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => 2
[3,1,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => 2
[3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [5,3,1] => 1
[3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => 4
[3,2,1,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[3,2,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[3,2,1,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => 2
[3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => 2
[3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [3,2,2,2] => 3
[3,2,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => 2
[3,2,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [4,3,2] => 1
[3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => 3
[3,3,1,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => 2
[3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => 2
[3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [3,3,3] => 3
[3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => 2
[3,4,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [4,3,2] => 1
[3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [5,3,1] => 1
[3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [6,3] => 1
[4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [4,1,1,1,1,1] => 5
[4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[4,1,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => 2
[4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[4,1,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => 2
[4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => 2
[4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [4,4,1] => 2
[4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => 3
[4,2,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => 2
[4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => 2
[4,2,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [4,3,2] => 1
[4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => 2
[4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [4,3,2] => 1
[4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [4,4,1] => 2
[4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [5,4] => 1
[5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [5,1,1,1,1] => 4
[5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => 2
[5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => 2
[5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [5,3,1] => 1
[5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => 2
[5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [5,2,2] => 2
[5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [5,3,1] => 1
[5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [5,4] => 1
[6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [6,1,1,1] => 3
[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
[6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => [6,3] => 1
[7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [7,1,1] => 2
[7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => [7,2] => 1
[8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [8,1] => 1
[9] => [9] => [[1,2,3,4,5,6,7,8,9]] => [9] => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The length of the longest weakly inreasing subsequence of parts of an integer composition.
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.