Identifier
Values
[[1],[2],[3]] => [1,1,1] => [1,1] => [1] => 1
[[1],[2],[4]] => [1,1,1] => [1,1] => [1] => 1
[[1],[3],[4]] => [1,1,1] => [1,1] => [1] => 1
[[2],[3],[4]] => [1,1,1] => [1,1] => [1] => 1
[[1,1],[2],[3]] => [2,1,1] => [1,1] => [1] => 1
[[1,2],[2],[3]] => [2,1,1] => [1,1] => [1] => 1
[[1,3],[2],[3]] => [2,1,1] => [1,1] => [1] => 1
[[1],[2],[5]] => [1,1,1] => [1,1] => [1] => 1
[[1],[3],[5]] => [1,1,1] => [1,1] => [1] => 1
[[1],[4],[5]] => [1,1,1] => [1,1] => [1] => 1
[[2],[3],[5]] => [1,1,1] => [1,1] => [1] => 1
[[2],[4],[5]] => [1,1,1] => [1,1] => [1] => 1
[[3],[4],[5]] => [1,1,1] => [1,1] => [1] => 1
[[1,1],[2],[4]] => [2,1,1] => [1,1] => [1] => 1
[[1,1],[3],[4]] => [2,1,1] => [1,1] => [1] => 1
[[1,2],[2],[4]] => [2,1,1] => [1,1] => [1] => 1
[[1,2],[3],[4]] => [2,1,1] => [1,1] => [1] => 1
[[1,3],[2],[4]] => [2,1,1] => [1,1] => [1] => 1
[[1,4],[2],[3]] => [2,1,1] => [1,1] => [1] => 1
[[1,4],[2],[4]] => [2,1,1] => [1,1] => [1] => 1
[[1,3],[3],[4]] => [2,1,1] => [1,1] => [1] => 1
[[1,4],[3],[4]] => [2,1,1] => [1,1] => [1] => 1
[[2,2],[3],[4]] => [2,1,1] => [1,1] => [1] => 1
[[2,3],[3],[4]] => [2,1,1] => [1,1] => [1] => 1
[[2,4],[3],[4]] => [2,1,1] => [1,1] => [1] => 1
[[1],[2],[3],[4]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1,1],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,2],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,3],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,2],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,3],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,3],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,1],[2,2],[3]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[2,3],[3]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[2,3],[3]] => [2,2,1] => [2,1] => [1] => 1
[[1],[2],[6]] => [1,1,1] => [1,1] => [1] => 1
[[1],[3],[6]] => [1,1,1] => [1,1] => [1] => 1
[[1],[4],[6]] => [1,1,1] => [1,1] => [1] => 1
[[1],[5],[6]] => [1,1,1] => [1,1] => [1] => 1
[[2],[3],[6]] => [1,1,1] => [1,1] => [1] => 1
[[2],[4],[6]] => [1,1,1] => [1,1] => [1] => 1
[[2],[5],[6]] => [1,1,1] => [1,1] => [1] => 1
[[3],[4],[6]] => [1,1,1] => [1,1] => [1] => 1
[[3],[5],[6]] => [1,1,1] => [1,1] => [1] => 1
[[4],[5],[6]] => [1,1,1] => [1,1] => [1] => 1
[[1,1],[2],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,1],[3],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,1],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,2],[2],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,2],[3],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,3],[2],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,5],[2],[3]] => [2,1,1] => [1,1] => [1] => 1
[[1,2],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,4],[2],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,5],[2],[4]] => [2,1,1] => [1,1] => [1] => 1
[[1,5],[2],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,3],[3],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,3],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,4],[3],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,5],[3],[4]] => [2,1,1] => [1,1] => [1] => 1
[[1,5],[3],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,4],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,5],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[2,2],[3],[5]] => [2,1,1] => [1,1] => [1] => 1
[[2,2],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[2,3],[3],[5]] => [2,1,1] => [1,1] => [1] => 1
[[2,3],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[2,4],[3],[5]] => [2,1,1] => [1,1] => [1] => 1
[[2,5],[3],[4]] => [2,1,1] => [1,1] => [1] => 1
[[2,5],[3],[5]] => [2,1,1] => [1,1] => [1] => 1
[[2,4],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[2,5],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[3,3],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[3,4],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[3,5],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1],[2],[3],[5]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[1],[2],[4],[5]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[1],[3],[4],[5]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[2],[3],[4],[5]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1,1],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,1],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,2],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,2],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,3],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,4],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,4],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,3],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,4],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,2],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,2],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,3],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,4],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,4],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,3],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,3],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,4],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,4],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,4],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,4,4],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,4,4],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,3],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
>>> Load all 720 entries. <<<
[[1,3,4],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,4,4],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[2,2,2],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[2,2,3],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[2,2,4],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[2,3,3],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[2,3,4],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[2,4,4],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,1],[2,2],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[2,3],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[2,4],[3]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[2,4],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[3,3],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[3,4],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[2,3],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[2,4],[3]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[2,4],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[3,3],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,3],[2,4],[3]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[3,4],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,3],[2,4],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,3],[3,4],[4]] => [2,2,1] => [2,1] => [1] => 1
[[2,2],[3,3],[4]] => [2,2,1] => [2,1] => [1] => 1
[[2,2],[3,4],[4]] => [2,2,1] => [2,1] => [1] => 1
[[2,3],[3,4],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,2],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,3],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,4],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1,1,1],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,1,2],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,1,3],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,2,2],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,2,3],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,3,3],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,2,2],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,2,3],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,3,3],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,3,3,3],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,1],[2,2],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,1],[2,3],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,2],[2,2],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,2],[2,3],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,3],[2,2],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,3],[2,3],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,2],[2,3],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,3],[2,3],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,1],[2,2],[3,3]] => [2,2,2] => [2,2] => [2] => 2
[[1],[2],[7]] => [1,1,1] => [1,1] => [1] => 1
[[1],[3],[7]] => [1,1,1] => [1,1] => [1] => 1
[[1],[4],[7]] => [1,1,1] => [1,1] => [1] => 1
[[1],[5],[7]] => [1,1,1] => [1,1] => [1] => 1
[[1],[6],[7]] => [1,1,1] => [1,1] => [1] => 1
[[2],[3],[7]] => [1,1,1] => [1,1] => [1] => 1
[[2],[4],[7]] => [1,1,1] => [1,1] => [1] => 1
[[2],[5],[7]] => [1,1,1] => [1,1] => [1] => 1
[[2],[6],[7]] => [1,1,1] => [1,1] => [1] => 1
[[3],[4],[7]] => [1,1,1] => [1,1] => [1] => 1
[[3],[5],[7]] => [1,1,1] => [1,1] => [1] => 1
[[3],[6],[7]] => [1,1,1] => [1,1] => [1] => 1
[[4],[5],[7]] => [1,1,1] => [1,1] => [1] => 1
[[4],[6],[7]] => [1,1,1] => [1,1] => [1] => 1
[[5],[6],[7]] => [1,1,1] => [1,1] => [1] => 1
[[1,1],[2],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,1],[3],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,1],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,1],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,2],[2],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,2],[3],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,3],[2],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,6],[2],[3]] => [2,1,1] => [1,1] => [1] => 1
[[1,2],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,4],[2],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,6],[2],[4]] => [2,1,1] => [1,1] => [1] => 1
[[1,2],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,5],[2],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,6],[2],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,6],[2],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,3],[3],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,3],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,4],[3],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,6],[3],[4]] => [2,1,1] => [1,1] => [1] => 1
[[1,3],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,5],[3],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,6],[3],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,6],[3],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,4],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,4],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,5],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,6],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[1,6],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,5],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1,6],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,2],[3],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,2],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,2],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,3],[3],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,3],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,4],[3],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,6],[3],[4]] => [2,1,1] => [1,1] => [1] => 1
[[2,3],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,5],[3],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,6],[3],[5]] => [2,1,1] => [1,1] => [1] => 1
[[2,6],[3],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,4],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,4],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,5],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,6],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[2,6],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,5],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[2,6],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[3,3],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[3,3],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[3,4],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[3,4],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[3,5],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[3,6],[4],[5]] => [2,1,1] => [1,1] => [1] => 1
[[3,6],[4],[6]] => [2,1,1] => [1,1] => [1] => 1
[[3,5],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[3,6],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[4,4],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[4,5],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[4,6],[5],[6]] => [2,1,1] => [1,1] => [1] => 1
[[1],[2],[3],[6]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[1],[2],[4],[6]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[1],[2],[5],[6]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[1],[3],[4],[6]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[1],[3],[5],[6]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[1],[4],[5],[6]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[2],[3],[4],[6]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[2],[3],[5],[6]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[2],[4],[5],[6]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[3],[4],[5],[6]] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1,1],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,1],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,1],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,2],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,2],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,3],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,5],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,2],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,4],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,5],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,5],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,3],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,3],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,4],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,5],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,5],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,4],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1,5],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,2],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,2],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,3],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,5],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,2],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,4],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,5],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,5],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,3],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,3],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,5],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,3],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,4],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,5],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,4],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,5],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,4,5],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,5],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,5],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,5,5],[2],[3]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,4],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,4,4],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,4,5],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,2,5],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,4,5],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,5,5],[2],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,5,5],[2],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,3],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,3],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,4],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,5],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,5],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,4],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,4,4],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,4,5],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,3,5],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,4,5],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,5,5],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[1,5,5],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,4,4],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,4,5],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,5,5],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,2,2],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,2,2],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,2,3],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,2,3],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,2,4],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,2,5],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[2,2,5],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,2,4],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,2,5],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,3,3],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,3,3],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,3,4],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,3,5],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[2,3,5],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,3,4],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,4,4],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,4,5],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[2,3,5],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,4,5],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,5,5],[3],[4]] => [3,1,1] => [1,1] => [1] => 1
[[2,5,5],[3],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,4,4],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,4,5],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[2,5,5],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[3,3,3],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[3,3,4],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[3,3,5],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[3,4,4],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[3,4,5],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[3,5,5],[4],[5]] => [3,1,1] => [1,1] => [1] => 1
[[1,1],[2,2],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[2,3],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[2,5],[3]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[2,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[2,5],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[2,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[3,3],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[3,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[3,5],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[3,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[4,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[4,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[2,3],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[2,5],[3]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[2,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[2,5],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[2,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[3,3],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,3],[2,5],[3]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[3,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[3,5],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,3],[2,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,3],[2,5],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,4],[2,5],[3]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[3,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,3],[2,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[4,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,4],[2,5],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,2],[4,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,4],[2,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,3],[3,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,3],[3,5],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,3],[3,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,3],[4,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,4],[3,5],[4]] => [2,2,1] => [2,1] => [1] => 1
[[1,3],[4,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,4],[3,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,4],[4,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[2,2],[3,3],[5]] => [2,2,1] => [2,1] => [1] => 1
[[2,2],[3,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[2,2],[3,5],[4]] => [2,2,1] => [2,1] => [1] => 1
[[2,2],[3,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[2,2],[4,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[2,2],[4,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[2,3],[3,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[2,3],[3,5],[4]] => [2,2,1] => [2,1] => [1] => 1
[[2,3],[3,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[2,3],[4,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[2,4],[3,5],[4]] => [2,2,1] => [2,1] => [1] => 1
[[2,3],[4,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[2,4],[3,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[2,4],[4,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[3,3],[4,4],[5]] => [2,2,1] => [2,1] => [1] => 1
[[3,3],[4,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[3,4],[4,5],[5]] => [2,2,1] => [2,1] => [1] => 1
[[1,1],[2],[3],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1],[2],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,2],[2],[3],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,2],[2],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,3],[2],[3],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,2],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,3],[2],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,4],[2],[3],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,5],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,5],[2],[3],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,4],[2],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,5],[2],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,3],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,4],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1,5],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[2,2],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[2,3],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[2,4],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[2,5],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[[1],[2],[3],[4],[5]] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[1,1,1,1],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,1,1],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,1,2],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,1,2],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,1,3],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,1,4],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,1,4],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,1,3],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,1,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,2,2],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,2,2],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,2,3],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,2,4],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,2,4],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,2,3],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,3,3],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,3,4],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,2,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,3,4],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,4,4],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,4,4],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,3,3],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,3,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,4,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,2,2],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,2,2],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,2,3],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,2,4],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,2,4],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,2,3],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,3,3],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,3,4],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,2,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,3,4],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,4,4],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,4,4],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,3,3],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,3,3,3],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,3,3,4],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,3,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,3,3,4],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,3,4,4],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,4,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,3,4,4],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,4,4,4],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,4,4,4],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,3,3,3],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,3,3,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,3,4,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,4,4,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[2,2,2,2],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[2,2,2,3],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[2,2,2,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[2,2,3,3],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[2,2,3,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[2,2,4,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[2,3,3,3],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[2,3,3,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[2,3,4,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[2,4,4,4],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,1,1],[2,2],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,1],[2,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,1],[2,4],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,1],[2,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,1],[3,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,1],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,2],[2,2],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,2],[2,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,2],[2,4],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,3],[2,2],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,4],[2,2],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,2],[2,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,4],[2,2],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,2],[3,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,3],[2,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,3],[2,4],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,4],[2,3],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,2],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,3],[2,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,4],[2,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,4],[2,4],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,4],[2,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,3],[3,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,3],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,4],[3,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,4],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,2],[2,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,2],[2,4],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,2],[2,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,2],[3,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,3],[2,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,3],[2,4],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,4],[2,3],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,2],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,3],[2,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,4],[2,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,4],[2,4],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,4],[2,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,3],[3,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,3,3],[2,4],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,3],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,4],[3,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,3,3],[2,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,3,4],[2,4],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,4],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,3,4],[2,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,3,3],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,3,4],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[2,2,2],[3,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[2,2,2],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[2,2,3],[3,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[2,2,3],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[2,2,4],[3,3],[4]] => [3,2,1] => [2,1] => [1] => 1
[[2,2,4],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[2,3,3],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[2,3,4],[3,4],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,1,1],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1,2],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1,3],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1,4],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,2,2],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,2,3],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,2,4],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,3,3],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,3,4],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,4,4],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,1],[2,2],[3,4]] => [2,2,2] => [2,2] => [2] => 2
[[1,1],[2,2],[4,4]] => [2,2,2] => [2,2] => [2] => 2
[[1,1],[2,3],[3,4]] => [2,2,2] => [2,2] => [2] => 2
[[1,1],[2,3],[4,4]] => [2,2,2] => [2,2] => [2] => 2
[[1,1],[3,3],[4,4]] => [2,2,2] => [2,2] => [2] => 2
[[1,2],[2,3],[3,4]] => [2,2,2] => [2,2] => [2] => 2
[[1,2],[2,3],[4,4]] => [2,2,2] => [2,2] => [2] => 2
[[1,2],[3,3],[4,4]] => [2,2,2] => [2,2] => [2] => 2
[[2,2],[3,3],[4,4]] => [2,2,2] => [2,2] => [2] => 2
[[1,1],[2,2],[3],[4]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,1],[2,3],[3],[4]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,1],[2,4],[3],[4]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,2],[2,3],[3],[4]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,2],[2,4],[3],[4]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,3],[2,4],[3],[4]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,1,1,1,1],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,1,1,1,2],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,1,1,1,3],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,1,1,2,2],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,1,1,2,3],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,1,1,3,3],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,1,2,2,2],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,1,2,2,3],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,1,2,3,3],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,1,3,3,3],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,2,2,2,2],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,2,2,2,3],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,2,2,3,3],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,2,3,3,3],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,3,3,3,3],[2],[3]] => [5,1,1] => [1,1] => [1] => 1
[[1,1,1,1],[2,2],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,1,1,1],[2,3],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,1,1,2],[2,2],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,1,1,2],[2,3],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,1,1,3],[2,2],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,1,1,3],[2,3],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,1,2,2],[2,2],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,1,2,2],[2,3],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,1,2,3],[2,2],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,1,2,3],[2,3],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,1,3,3],[2,2],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,1,3,3],[2,3],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,2,2,2],[2,3],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,2,2,3],[2,3],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,2,3,3],[2,3],[3]] => [4,2,1] => [2,1] => [1] => 1
[[1,1,1],[2,2,2],[3]] => [3,3,1] => [3,1] => [1] => 1
[[1,1,1],[2,2,3],[3]] => [3,3,1] => [3,1] => [1] => 1
[[1,1,1],[2,3,3],[3]] => [3,3,1] => [3,1] => [1] => 1
[[1,1,2],[2,2,3],[3]] => [3,3,1] => [3,1] => [1] => 1
[[1,1,2],[2,3,3],[3]] => [3,3,1] => [3,1] => [1] => 1
[[1,2,2],[2,3,3],[3]] => [3,3,1] => [3,1] => [1] => 1
[[1,1,1],[2,2],[3,3]] => [3,2,2] => [2,2] => [2] => 2
[[1,1,2],[2,2],[3,3]] => [3,2,2] => [2,2] => [2] => 2
[[1,1,3],[2,2],[3,3]] => [3,2,2] => [2,2] => [2] => 2
[[1,1,1,1],[2,2,2],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,2],[2,2,2],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,1],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,2],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,3],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,2,2],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,2,3],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,1],[2,2,2],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,2],[2,2,2],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,1],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,2],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,3],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,2,2],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,2,3],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,1],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,2],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,3],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,4],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,2,2],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,2,3],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,2,4],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,1],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,2],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,3],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,2,2],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,2,3],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,1],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,2],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,1,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,2,2],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,2,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,2,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,3,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,1,3,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,2,2,2],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,2,2,3],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,2,2,2],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,2,2,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,2,2,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,2,3,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,2,3,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[[1,2,3,4],[5],[6]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,3,5],[4],[6]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,3,6],[4],[5]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,3],[4],[5],[6]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,2,4],[3,5],[6]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,4,5],[3],[6]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,4,6],[3],[5]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,4],[3],[5],[6]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,2,3],[4,5],[6]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,5,6],[3],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,2,5],[3,6],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,5],[3],[4],[6]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,2,3],[4,6],[5]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,4],[3,6],[5]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,6],[3],[4],[5]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[1,3,4],[2,5],[6]] => [3,2,1] => [2,1] => [1] => 1
[[1,3,5],[2,4],[6]] => [3,2,1] => [2,1] => [1] => 1
[[1,3,6],[2,4],[5]] => [3,2,1] => [2,1] => [1] => 1
[[1,3],[2,4],[5],[6]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,3,4,5],[2],[6]] => [4,1,1] => [1,1] => [1] => 1
[[1,3,4,6],[2],[5]] => [4,1,1] => [1,1] => [1] => 1
[[1,3,4],[2],[5],[6]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,3,5,6],[2],[4]] => [4,1,1] => [1,1] => [1] => 1
[[1,3,5],[2,6],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,3,5],[2],[4],[6]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,3,4],[2,6],[5]] => [3,2,1] => [2,1] => [1] => 1
[[1,3,6],[2],[4],[5]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,3],[2],[4],[5],[6]] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[1,2,5],[3,4],[6]] => [3,2,1] => [2,1] => [1] => 1
[[1,2,6],[3,4],[5]] => [3,2,1] => [2,1] => [1] => 1
[[1,2],[3,4],[5],[6]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,4,5,6],[2],[3]] => [4,1,1] => [1,1] => [1] => 1
[[1,4,5],[2,6],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,4,6],[2,5],[3]] => [3,2,1] => [2,1] => [1] => 1
[[1,4],[2,5],[3,6]] => [2,2,2] => [2,2] => [2] => 2
[[1,4],[2,5],[3],[6]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,4,5],[2],[3],[6]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,4,6],[2],[3],[5]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,4],[2],[3],[5],[6]] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[1,2,6],[3,5],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,2],[3,5],[4],[6]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,3,6],[2,5],[4]] => [3,2,1] => [2,1] => [1] => 1
[[1,3],[2,5],[4,6]] => [2,2,2] => [2,2] => [2] => 2
[[1,3],[2,5],[4],[6]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,2],[3,5],[4,6]] => [2,2,2] => [2,2] => [2] => 2
[[1,5,6],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[[1,5],[2,6],[3],[4]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,5],[2],[3],[4],[6]] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[[1,2],[3,6],[4],[5]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,3],[2,4],[5,6]] => [2,2,2] => [2,2] => [2] => 2
[[1,3],[2,6],[4],[5]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,2],[3,4],[5,6]] => [2,2,2] => [2,2] => [2] => 2
[[1,4],[2,6],[3],[5]] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[[1,6],[2],[3],[4],[5]] => [2,1,1,1,1] => [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] => [1,1,1,1] => 1
[[1,1,1,1,2,2,2],[3,3],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,2,2,2],[3,3],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,1,2,2,3],[3,3],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,2,2,3],[3,3],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,2,3,3],[3,3],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,2,2,2,2,3],[3,3],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,2,2,2,3,3],[3,3],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,1,2,2,2],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,2,2,2],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,1,2,2,3],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,2,2,3],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,2,3],[3,3,4],[4]] => [6,3,1] => [3,1] => [1] => 1
[[1,1,2,2,2,2,3],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,2,2,2,3],[3,3,4],[4]] => [6,3,1] => [3,1] => [1] => 1
[[1,1,1,1,2,2,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,2,2,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,2,4,4],[3,3],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,2,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,2,2,2,2,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,2,2,2,4,4],[3,3],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,2,2,2,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,1,2,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,2,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,3,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,2,2,2,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,2,2,3,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,1,2,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,2,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,3,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,1,2,3,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,2,2,2,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,2,2,3,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,2,2,3,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,2,3,3,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,1,2,3,3,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,2,2,2,2,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,2,2,2,3,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,2,2,2,2,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,2,2,2,3,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,2,2,2,3,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,2,2,3,3,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
[[1,2,2,3,3,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1] => 1
search for individual values
searching the database for the individual values of this statistic
Description
Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight.
Given $\lambda$ count how many integer partitions $w$ (weight) there are, such that
$P_{\lambda,w}$ is integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has only integer lattice points as vertices.
See also St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight., St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. and St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight..
Map
shape
Description
Return the shape of a tableau.
Map
first row removal
Description
Removes the first entry of an integer partition