Identifier
Values
[[1]] => [1] => [1] => [1,0,1,0] => 1
[[1,2]] => [2] => [2] => [1,1,0,0,1,0] => 1
[[1],[2]] => [2] => [2] => [1,1,0,0,1,0] => 1
[[1,2,3]] => [3] => [3] => [1,1,1,0,0,0,1,0] => 1
[[1,2],[3]] => [3] => [3] => [1,1,1,0,0,0,1,0] => 1
[[1],[2],[3]] => [3] => [3] => [1,1,1,0,0,0,1,0] => 1
[[1,2,3,4]] => [4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,4],[2]] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[1,2,3],[4]] => [4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3],[2,4]] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[1,3],[2],[4]] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[1,2],[3],[4]] => [4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1],[2],[3],[4]] => [4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,3,4,5]] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3,4],[5]] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3],[4],[5]] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2],[3],[4],[5]] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1],[2],[3],[4],[5]] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3,4,5,6]] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,2,4,5,6],[3]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,2,3,4,5],[6]] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,3,5,6],[2,4]] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[1,2,5,6],[3,4]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,2,4,5],[3,6]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,4,5,6],[2],[3]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,3,5,6],[2],[4]] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[1,2,4,5],[3],[6]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,2,3,4],[5],[6]] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,3,5],[2,4,6]] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[1,2,5],[3,4,6]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,3,6],[2,5],[4]] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[1,4,5],[2,6],[3]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,3,5],[2,6],[4]] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[1,3,5],[2,4],[6]] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[1,2,5],[3,4],[6]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,2,4],[3,5],[6]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,4,5],[2],[3],[6]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,3,5],[2],[4],[6]] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[1,2,4],[3],[5],[6]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,2,3],[4],[5],[6]] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,4],[2,5],[3,6]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,3],[2,5],[4,6]] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[1,4],[2,5],[3],[6]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,3],[2,5],[4],[6]] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[1,2],[3,4],[5],[6]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,4],[2],[3],[5],[6]] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[1,2],[3],[4],[5],[6]] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1],[2],[3],[4],[5],[6]] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,2,3,5,6,7,8],[4]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,6,7,8],[2,4]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,6,7,8],[4,5]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,4,5,7,8],[2,6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5,7,8],[4,6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5,6,7],[4,8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,6,7,8],[2],[4]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,5,6,7,8],[3],[4]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,4,5,7,8],[2],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5,7,8],[4],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5,6,7],[4],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,7,8],[2,4,6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,7,8],[4,5,6]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,4,5,8],[2,6,7]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5,8],[4,6,7]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,6,7],[2,4,8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,6,7],[4,5,8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,4,5,7],[2,6,8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5,7],[4,6,8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,6,7,8],[2,5],[4]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,6,7,8],[3,5],[4]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,7,8],[2,6],[4]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,7,8],[3,6],[4]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,7,8],[2,4],[6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,7,8],[2,5],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,7,8],[4,5],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,4,5,8],[2,7],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5,8],[4,7],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,6,7],[2,8],[4]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,5,6,7],[3,8],[4]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,4,5,7],[2,8],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5,7],[4,8],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,6,7],[2,4],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,6,7],[4,5],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,4,5,7],[2,6],[8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5,7],[4,6],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5,6],[4,7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,5,6,7,8],[2],[3],[4]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,7,8],[2],[4],[6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,7,8],[3],[4],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,4,7,8],[2],[5],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,6,7],[2],[4],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,5,6,7],[3],[4],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,4,5,7],[2],[6],[8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5,7],[4],[6],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5,6],[4],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,7],[2,4,6,8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,7],[4,5,6,8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,4,5],[2,6,7,8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5],[4,6,7,8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,8],[2,6,7],[4]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,8],[3,6,7],[4]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,8],[2,4,7],[6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
>>> Load all 377 entries. <<<
[[1,3,4,8],[2,5,7],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,8],[4,5,7],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,6,7],[2,5,8],[4]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,6,7],[3,5,8],[4]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,7],[2,6,8],[4]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,7],[3,6,8],[4]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,7],[2,4,8],[6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,7],[2,5,8],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,7],[4,5,8],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,4,5],[2,7,8],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5],[4,7,8],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,7],[2,4,6],[8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,7],[4,5,6],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,6],[2,4,7],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,6],[4,5,7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,4,5],[2,6,7],[8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5],[4,6,7],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,7,8],[2,5],[4,6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,7,8],[3,5],[4,6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,8],[2,4],[6,7]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,8],[2,5],[6,7]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,8],[4,5],[6,7]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,6,7],[2,5],[4,8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,6,7],[3,5],[4,8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,7],[2,6],[4,8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,7],[3,6],[4,8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,7],[2,4],[6,8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,7],[2,5],[6,8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,7],[4,5],[6,8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,6],[2,7],[4,8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,5,6],[3,7],[4,8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,4,5],[2,7],[6,8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5],[4,7],[6,8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5,7,8],[2,6],[3],[4]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,7,8],[2,5],[4],[6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,7,8],[3,5],[4],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,7,8],[2,4],[5],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,8],[2,7],[4],[6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,8],[3,7],[4],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,4,8],[2,7],[5],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5,6,7],[2,8],[3],[4]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,7],[2,8],[4],[6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,7],[3,8],[4],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,4,7],[2,8],[5],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,6,7],[2,5],[4],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,6,7],[3,5],[4],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,7],[2,6],[4],[8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,7],[3,6],[4],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,7],[2,4],[6],[8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4,7],[2,5],[6],[8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,7],[4,5],[6],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,6],[2,7],[4],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,5,6],[3,7],[4],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,4,5],[2,7],[6],[8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,5],[4,7],[6],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,6],[2,4],[7],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3,6],[4,5],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5],[4,6],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,5,7,8],[2],[3],[4],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,7,8],[2],[4],[5],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5,6,7],[2],[3],[4],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,7],[2],[4],[6],[8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,7],[3],[4],[6],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,4,7],[2],[5],[6],[8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5,6],[2],[4],[7],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,5,6],[3],[4],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5],[4],[6],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,7],[2,5,8],[4,6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,7],[3,5,8],[4,6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5],[2,4,8],[6,7]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4],[2,5,8],[6,7]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3],[4,5,8],[6,7]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,6],[2,5,7],[4,8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,6],[3,5,7],[4,8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5],[2,6,7],[4,8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5],[3,6,7],[4,8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5],[2,4,7],[6,8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4],[2,5,7],[6,8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3],[4,5,7],[6,8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5,7],[2,6,8],[3],[4]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,7],[2,5,8],[4],[6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,7],[3,5,8],[4],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,7],[2,4,8],[5],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5],[2,7,8],[4],[6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5],[3,7,8],[4],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,4],[2,7,8],[5],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,6],[2,5,7],[4],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,6],[3,5,7],[4],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5],[2,6,7],[4],[8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5],[3,6,7],[4],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5],[2,4,7],[6],[8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4],[2,5,7],[6],[8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3],[4,5,7],[6],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,5],[2,4,6],[7],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3],[4,5,6],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,8],[2,5],[4,7],[6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,8],[3,5],[4,7],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,8],[2,4],[5,7],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5,7],[2,6],[3,8],[4]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,7],[2,5],[4,8],[6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,7],[3,5],[4,8],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,7],[2,4],[5,8],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5,6],[2,7],[3,8],[4]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5],[2,7],[4,8],[6]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5],[3,7],[4,8],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,4],[2,7],[5,8],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,7],[2,5],[4,6],[8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,7],[3,5],[4,6],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,6],[2,5],[4,7],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,6],[3,5],[4,7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5],[2,6],[4,7],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,5],[3,6],[4,7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5],[2,4],[6,7],[8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,3,4],[2,5],[6,7],[8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3],[4,5],[6,7],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5,8],[2,7],[3],[4],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,8],[2,7],[4],[5],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5,7],[2,8],[3],[4],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,7],[2,8],[4],[5],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5,7],[2,6],[3],[4],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,7],[2,5],[4],[6],[8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,7],[3,5],[4],[6],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,7],[2,4],[5],[6],[8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5,6],[2,7],[3],[4],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5],[2,7],[4],[6],[8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5],[3,7],[4],[6],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,4],[2,7],[5],[6],[8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,6],[2,5],[4],[7],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,6],[3,5],[4],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5],[2,6],[4],[7],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,5],[3,6],[4],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5],[2,4],[6],[7],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,3],[4,5],[6],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,5,7],[2],[3],[4],[6],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3,7],[2],[4],[5],[6],[8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5,6],[2],[3],[4],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5],[2],[4],[6],[7],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,5],[3],[4],[6],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,5],[2,6],[3,7],[4,8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3],[2,5],[4,7],[6,8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2],[3,5],[4,7],[6,8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3],[2,4],[5,7],[6,8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5],[2,7],[3,8],[4],[6]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3],[2,7],[4,8],[5],[6]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5],[2,6],[3,7],[4],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3],[2,5],[4,7],[6],[8]] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2],[3,5],[4,7],[6],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3],[2,4],[5,7],[6],[8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3],[2,5],[4,6],[7],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2],[3,5],[4,6],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,5],[2,7],[3],[4],[6],[8]] => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,3],[2,7],[4],[5],[6],[8]] => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,5],[2,6],[3],[4],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3],[2,5],[4],[6],[7],[8]] => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[[1,2],[3,5],[4],[6],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,5],[2],[3],[4],[6],[7],[8]] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,7,9],[2,4,6,8,10]] => [2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1,3,5,6,7],[2,4,8,9,10]] => [2,2,4,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,3,4,5,7],[2,6,8,9,10]] => [2,4,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,2,3,5,7],[4,6,8,9,10]] => [4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,2,3,4,9],[5,6,7,8,10]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,3,5,7,8,9],[2,4,6,10,11,12]] => [2,2,2,4,2] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[[1,3,5,6,7,11],[2,4,8,9,10,12]] => [2,2,4,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,3,5,6,7,9],[2,4,8,10,11,12]] => [2,2,4,2,2] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[[1,3,4,5,9,11],[2,6,7,8,10,12]] => [2,4,4,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,3,4,5,8,9],[2,6,7,10,11,12]] => [2,4,4,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,3,4,5,7,11],[2,6,8,9,10,12]] => [2,4,2,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,3,4,5,7,9],[2,6,8,10,11,12]] => [2,4,2,2,2] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[[1,2,5,7,8,11],[3,4,6,9,10,12]] => [3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,6,7,8],[3,4,9,10,11,12]] => [3,6,3] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[[1,2,4,5,8,11],[3,6,7,9,10,12]] => [3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4,5,7,8],[3,6,9,10,11,12]] => [3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,3,7,9,11],[4,5,6,8,10,12]] => [4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,2,3,6,7,11],[4,5,8,9,10,12]] => [4,4,4] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[[1,2,3,6,7,9],[4,5,8,10,11,12]] => [4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,2,3,5,9,11],[4,6,7,8,10,12]] => [4,2,4,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,2,3,5,8,9],[4,6,7,10,11,12]] => [4,2,4,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,2,3,5,7,11],[4,6,8,9,10,12]] => [4,2,2,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,2,3,5,7,9],[4,6,8,10,11,12]] => [4,2,2,2,2] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[[1,2,3,5,6,7],[4,8,9,10,11,12]] => [4,4,4] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[[1,2,3,4,5,8],[6,7,9,10,11,12]] => [6,3,3] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[[1,2,3,4],[5,6],[7,8],[9]] => [5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,2,3,4,5],[6,7],[8,9],[10]] => [6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,2,3,4],[5,6,7,8],[9],[10]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,2,3,4],[5,6,7],[8],[9],[10]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,2,3,4],[5,6],[7],[8],[9],[10]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,2,3],[4,5],[6,7],[8,9],[10]] => [4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => [6,3,3] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => [6,3,3] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[[1,2,3,4,5],[6,7],[8,9],[10,11],[12]] => [6,2,2,2] => [6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[[1,3,6,7,8,9],[2,5],[4]] => [2,2,5] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,2,5,9],[3,4,8],[6,7]] => [3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,4,5,9],[2,7,8],[3],[6]] => [3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,6,9],[2,8],[3],[4],[5],[7]] => [5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,3,6,7,8,9,10],[2,5],[4]] => [2,2,6] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,2,3,4,9,10],[5,6,7,8]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,6,7,8,9,10],[2],[3],[4],[5]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,3,8,9,10],[2,5],[4,7],[6]] => [2,2,2,4] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,3,10],[2,5],[4,7],[6,9],[8]] => [2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1,5,10],[2,7],[3,9],[4],[6],[8]] => [4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,7,10],[2,9],[3],[4],[5],[6],[8]] => [6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,2,3,7,12],[4,5,6,11],[8,9,10]] => [4,4,4] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => [2,2,4,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,5,6,7,12],[2,9,10,11],[3],[4],[8]] => [4,4,4] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => [3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[1,4,5,12],[2,7,8],[3,10,11],[6],[9]] => [3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[1,4,7],[2,5,8],[3,6,9]] => [3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,6],[2,7],[3,8],[4,9],[5,10]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,3],[2,5],[4,7],[6,9],[8,10]] => [2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1,2,3,4,9],[5,6],[7,8]] => [5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,2,5],[3,4,8],[6,7,9]] => [3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,2,3,4,5,10],[6,7],[8,9]] => [6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,2,3,10],[4,5],[6,7],[8,9]] => [4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,3,5,6,7,8,9],[2],[4]] => [2,2,5] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,2,4,7,8,9],[3,5],[6]] => [3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,6,8,9],[2],[3],[4],[5],[7]] => [5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,2,4],[3,5,7],[6,8],[9]] => [3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,6],[2,8],[3],[4],[5],[7],[9]] => [5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,3,5,6,7,8,9,10],[2],[4]] => [2,2,6] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,2,5,7,9,10],[3,6,8],[4]] => [4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,7,9,10],[2],[3],[4],[5],[6],[8]] => [6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,3],[2,5],[4,7],[6,9],[8],[10]] => [2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1,5],[2,7],[3,9],[4],[6],[8],[10]] => [4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,7],[2,9],[3],[4],[5],[6],[8],[10]] => [6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,3,4,5,6],[2,7,8,9]] => [2,5,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,3,4,5,6],[2,8,9],[7]] => [2,5,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,3,4,5,6],[2,8],[7,9]] => [2,5,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,3,4,5,6],[2,8],[7],[9]] => [2,5,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,3],[2,5],[4],[6],[7],[8],[9]] => [2,2,5] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,3,4,5,6,7],[2,8,9,10]] => [2,6,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,3,4,5,6,7],[2,9,10],[8]] => [2,6,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,3,4,5,6,7],[2,9],[8,10]] => [2,6,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,3,4,5,6,7],[2,9],[8],[10]] => [2,6,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,3,4,5],[2,7],[6,9],[8,10]] => [2,4,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,3,4,5],[2,7],[6,9],[8],[10]] => [2,4,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,3],[2,5],[4,7],[6],[8],[9],[10]] => [2,2,2,4] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,3],[2,5],[4],[6],[7],[8],[9],[10]] => [2,2,6] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,2,3,4,7,8,9,10],[5,6]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5,7,9,10],[4,6,8]] => [4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,2,3,4,5,7,9,10],[6,8]] => [6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,2,3,4,6,7,8,9,10],[5]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,2,4,5,7,8,11,12],[3,6,9,10]] => [3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4,5,7,8,10,11,12],[3,6,9]] => [3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,4,5,6,7,8,11,12],[3,9,10]] => [3,6,3] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[[1,2,4,5,6,7,8,10,11,12],[3,9]] => [3,6,3] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[[1,2,3,5,7,9,11,12],[4,6,8,10]] => [4,2,2,2,2] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[[1,2,3,5,7,9,10,11,12],[4,6,8]] => [4,2,2,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,2,3,5,7,8,9,11,12],[4,6,10]] => [4,2,4,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,2,3,5,6,7,9,11,12],[4,8,10]] => [4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[1,2,3,5,6,7,10,11,12],[4,8,9]] => [4,4,4] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[[1,2,3,5,6,7,9,10,11,12],[4,8]] => [4,4,4] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[[1,2,3,4,5,7,8,11,12],[6,9,10]] => [6,3,3] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[[1,2,3,4,5,7,9,11,12],[6,8,10]] => [6,2,2,2] => [6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[[1,2,3,4,5,8,10,11,12],[6,7,9]] => [6,3,3] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[[1,2,3,4,5,7,8,10,11,12],[6,9]] => [6,3,3] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[[1,3,6,7,8],[2,5],[4,9]] => [2,2,5] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,3,6,7,8],[2,5],[4],[9]] => [2,2,5] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,2,5],[3,4,8],[6,7],[9]] => [3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,4,5],[2,7,8],[3],[6],[9]] => [3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,3,6,7,8,9],[2,5],[4,10]] => [2,2,6] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,3,6,7,8,9],[2,5],[4],[10]] => [2,2,6] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,2,3,4,9],[5,6,7,8],[10]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,6,7,8,9],[2],[3],[4],[5],[10]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,3,8,9],[2,5],[4,7],[6,10]] => [2,2,2,4] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,3,8,9],[2,5],[4,7],[6],[10]] => [2,2,2,4] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,2,4,5,9],[3,7,8],[6]] => [3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,2,6,9],[3,8],[4],[5],[7]] => [5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,2],[3,6],[4,8],[5],[7],[9]] => [5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[1,2,3,4,8,9,10],[5,6,7]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,2,6,7,8,9,10],[3],[4],[5]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[1,2,5,10],[3,7],[4,9],[6],[8]] => [4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,2,7,10],[3,9],[4],[5],[6],[8]] => [6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,2],[3,5],[4,7],[6,9],[8],[10]] => [4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[1,2],[3,7],[4,9],[5],[6],[8],[10]] => [6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[[1,2,4,5,8,9],[3,7],[6]] => [3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,2,6,7,8,9],[3],[4],[5],[10]] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
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
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
valley composition
Description
The composition corresponding to the valley set of a standard tableau.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a valley if $i-1$ is a descent and $i$ is an ascent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the valley set of $T$.