Identifier
-
Mp00077:
Semistandard tableaux
—shape⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
St000668: Integer partitions ⟶ ℤ
Values
[[1],[2],[3]] => [1,1,1] => [1,1] => [2] => 2
[[1,1],[2,2]] => [2,2] => [2] => [1,1] => 1
[[1],[2],[4]] => [1,1,1] => [1,1] => [2] => 2
[[1],[3],[4]] => [1,1,1] => [1,1] => [2] => 2
[[2],[3],[4]] => [1,1,1] => [1,1] => [2] => 2
[[1,1],[2,3]] => [2,2] => [2] => [1,1] => 1
[[1,1],[3,3]] => [2,2] => [2] => [1,1] => 1
[[1,2],[2,3]] => [2,2] => [2] => [1,1] => 1
[[1,2],[3,3]] => [2,2] => [2] => [1,1] => 1
[[2,2],[3,3]] => [2,2] => [2] => [1,1] => 1
[[1,1],[2],[3]] => [2,1,1] => [1,1] => [2] => 2
[[1,2],[2],[3]] => [2,1,1] => [1,1] => [2] => 2
[[1,3],[2],[3]] => [2,1,1] => [1,1] => [2] => 2
[[1,1,1],[2,2]] => [3,2] => [2] => [1,1] => 1
[[1,1,2],[2,2]] => [3,2] => [2] => [1,1] => 1
[[1],[2],[5]] => [1,1,1] => [1,1] => [2] => 2
[[1],[3],[5]] => [1,1,1] => [1,1] => [2] => 2
[[1],[4],[5]] => [1,1,1] => [1,1] => [2] => 2
[[2],[3],[5]] => [1,1,1] => [1,1] => [2] => 2
[[2],[4],[5]] => [1,1,1] => [1,1] => [2] => 2
[[3],[4],[5]] => [1,1,1] => [1,1] => [2] => 2
[[1,1],[2,4]] => [2,2] => [2] => [1,1] => 1
[[1,1],[3,4]] => [2,2] => [2] => [1,1] => 1
[[1,1],[4,4]] => [2,2] => [2] => [1,1] => 1
[[1,2],[2,4]] => [2,2] => [2] => [1,1] => 1
[[1,2],[3,4]] => [2,2] => [2] => [1,1] => 1
[[1,3],[2,4]] => [2,2] => [2] => [1,1] => 1
[[1,2],[4,4]] => [2,2] => [2] => [1,1] => 1
[[1,3],[3,4]] => [2,2] => [2] => [1,1] => 1
[[1,3],[4,4]] => [2,2] => [2] => [1,1] => 1
[[2,2],[3,4]] => [2,2] => [2] => [1,1] => 1
[[2,2],[4,4]] => [2,2] => [2] => [1,1] => 1
[[2,3],[3,4]] => [2,2] => [2] => [1,1] => 1
[[2,3],[4,4]] => [2,2] => [2] => [1,1] => 1
[[3,3],[4,4]] => [2,2] => [2] => [1,1] => 1
[[1,1],[2],[4]] => [2,1,1] => [1,1] => [2] => 2
[[1,1],[3],[4]] => [2,1,1] => [1,1] => [2] => 2
[[1,2],[2],[4]] => [2,1,1] => [1,1] => [2] => 2
[[1,2],[3],[4]] => [2,1,1] => [1,1] => [2] => 2
[[1,3],[2],[4]] => [2,1,1] => [1,1] => [2] => 2
[[1,4],[2],[3]] => [2,1,1] => [1,1] => [2] => 2
[[1,4],[2],[4]] => [2,1,1] => [1,1] => [2] => 2
[[1,3],[3],[4]] => [2,1,1] => [1,1] => [2] => 2
[[1,4],[3],[4]] => [2,1,1] => [1,1] => [2] => 2
[[2,2],[3],[4]] => [2,1,1] => [1,1] => [2] => 2
[[2,3],[3],[4]] => [2,1,1] => [1,1] => [2] => 2
[[2,4],[3],[4]] => [2,1,1] => [1,1] => [2] => 2
[[1],[2],[3],[4]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[1,1,1],[2,3]] => [3,2] => [2] => [1,1] => 1
[[1,1,1],[3,3]] => [3,2] => [2] => [1,1] => 1
[[1,1,2],[2,3]] => [3,2] => [2] => [1,1] => 1
[[1,1,3],[2,2]] => [3,2] => [2] => [1,1] => 1
[[1,1,2],[3,3]] => [3,2] => [2] => [1,1] => 1
[[1,1,3],[2,3]] => [3,2] => [2] => [1,1] => 1
[[1,1,3],[3,3]] => [3,2] => [2] => [1,1] => 1
[[1,2,2],[2,3]] => [3,2] => [2] => [1,1] => 1
[[1,2,2],[3,3]] => [3,2] => [2] => [1,1] => 1
[[1,2,3],[2,3]] => [3,2] => [2] => [1,1] => 1
[[1,2,3],[3,3]] => [3,2] => [2] => [1,1] => 1
[[2,2,2],[3,3]] => [3,2] => [2] => [1,1] => 1
[[2,2,3],[3,3]] => [3,2] => [2] => [1,1] => 1
[[1,1,1],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,2],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,3],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,2],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,3],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,3],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,1],[2,2],[3]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[2,3],[3]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[2,3],[3]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,1],[2,2]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,2],[2,2]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,2],[2,2]] => [4,2] => [2] => [1,1] => 1
[[1,1,1],[2,2,2]] => [3,3] => [3] => [3] => 3
[[1],[2],[6]] => [1,1,1] => [1,1] => [2] => 2
[[1],[3],[6]] => [1,1,1] => [1,1] => [2] => 2
[[1],[4],[6]] => [1,1,1] => [1,1] => [2] => 2
[[1],[5],[6]] => [1,1,1] => [1,1] => [2] => 2
[[2],[3],[6]] => [1,1,1] => [1,1] => [2] => 2
[[2],[4],[6]] => [1,1,1] => [1,1] => [2] => 2
[[2],[5],[6]] => [1,1,1] => [1,1] => [2] => 2
[[3],[4],[6]] => [1,1,1] => [1,1] => [2] => 2
[[3],[5],[6]] => [1,1,1] => [1,1] => [2] => 2
[[4],[5],[6]] => [1,1,1] => [1,1] => [2] => 2
[[1,1],[2,5]] => [2,2] => [2] => [1,1] => 1
[[1,1],[3,5]] => [2,2] => [2] => [1,1] => 1
[[1,1],[4,5]] => [2,2] => [2] => [1,1] => 1
[[1,1],[5,5]] => [2,2] => [2] => [1,1] => 1
[[1,2],[2,5]] => [2,2] => [2] => [1,1] => 1
[[1,2],[3,5]] => [2,2] => [2] => [1,1] => 1
[[1,3],[2,5]] => [2,2] => [2] => [1,1] => 1
[[1,2],[4,5]] => [2,2] => [2] => [1,1] => 1
[[1,4],[2,5]] => [2,2] => [2] => [1,1] => 1
[[1,2],[5,5]] => [2,2] => [2] => [1,1] => 1
[[1,3],[3,5]] => [2,2] => [2] => [1,1] => 1
[[1,3],[4,5]] => [2,2] => [2] => [1,1] => 1
[[1,4],[3,5]] => [2,2] => [2] => [1,1] => 1
[[1,3],[5,5]] => [2,2] => [2] => [1,1] => 1
[[1,4],[4,5]] => [2,2] => [2] => [1,1] => 1
[[1,4],[5,5]] => [2,2] => [2] => [1,1] => 1
[[2,2],[3,5]] => [2,2] => [2] => [1,1] => 1
>>> Load all 1265 entries. <<<[[2,2],[4,5]] => [2,2] => [2] => [1,1] => 1
[[2,2],[5,5]] => [2,2] => [2] => [1,1] => 1
[[2,3],[3,5]] => [2,2] => [2] => [1,1] => 1
[[2,3],[4,5]] => [2,2] => [2] => [1,1] => 1
[[2,4],[3,5]] => [2,2] => [2] => [1,1] => 1
[[2,3],[5,5]] => [2,2] => [2] => [1,1] => 1
[[2,4],[4,5]] => [2,2] => [2] => [1,1] => 1
[[2,4],[5,5]] => [2,2] => [2] => [1,1] => 1
[[3,3],[4,5]] => [2,2] => [2] => [1,1] => 1
[[3,3],[5,5]] => [2,2] => [2] => [1,1] => 1
[[3,4],[4,5]] => [2,2] => [2] => [1,1] => 1
[[3,4],[5,5]] => [2,2] => [2] => [1,1] => 1
[[4,4],[5,5]] => [2,2] => [2] => [1,1] => 1
[[1,1],[2],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,1],[3],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,1],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,2],[2],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,2],[3],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,3],[2],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,5],[2],[3]] => [2,1,1] => [1,1] => [2] => 2
[[1,2],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,4],[2],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,5],[2],[4]] => [2,1,1] => [1,1] => [2] => 2
[[1,5],[2],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,3],[3],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,3],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,4],[3],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,5],[3],[4]] => [2,1,1] => [1,1] => [2] => 2
[[1,5],[3],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,4],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,5],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[2,2],[3],[5]] => [2,1,1] => [1,1] => [2] => 2
[[2,2],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[2,3],[3],[5]] => [2,1,1] => [1,1] => [2] => 2
[[2,3],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[2,4],[3],[5]] => [2,1,1] => [1,1] => [2] => 2
[[2,5],[3],[4]] => [2,1,1] => [1,1] => [2] => 2
[[2,5],[3],[5]] => [2,1,1] => [1,1] => [2] => 2
[[2,4],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[2,5],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[3,3],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[3,4],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[3,5],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1],[2],[3],[5]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[1],[2],[4],[5]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[1],[3],[4],[5]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[2],[3],[4],[5]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[1,1,1],[2,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,1],[3,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,1],[4,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,2],[2,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,4],[2,2]] => [3,2] => [2] => [1,1] => 1
[[1,1,2],[3,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,3],[2,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,4],[2,3]] => [3,2] => [2] => [1,1] => 1
[[1,1,2],[4,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,4],[2,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,3],[3,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,4],[3,3]] => [3,2] => [2] => [1,1] => 1
[[1,1,3],[4,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,4],[3,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,4],[4,4]] => [3,2] => [2] => [1,1] => 1
[[1,2,2],[2,4]] => [3,2] => [2] => [1,1] => 1
[[1,2,2],[3,4]] => [3,2] => [2] => [1,1] => 1
[[1,2,3],[2,4]] => [3,2] => [2] => [1,1] => 1
[[1,2,4],[2,3]] => [3,2] => [2] => [1,1] => 1
[[1,2,2],[4,4]] => [3,2] => [2] => [1,1] => 1
[[1,2,4],[2,4]] => [3,2] => [2] => [1,1] => 1
[[1,2,3],[3,4]] => [3,2] => [2] => [1,1] => 1
[[1,2,4],[3,3]] => [3,2] => [2] => [1,1] => 1
[[1,3,3],[2,4]] => [3,2] => [2] => [1,1] => 1
[[1,2,3],[4,4]] => [3,2] => [2] => [1,1] => 1
[[1,2,4],[3,4]] => [3,2] => [2] => [1,1] => 1
[[1,3,4],[2,4]] => [3,2] => [2] => [1,1] => 1
[[1,2,4],[4,4]] => [3,2] => [2] => [1,1] => 1
[[1,3,3],[3,4]] => [3,2] => [2] => [1,1] => 1
[[1,3,3],[4,4]] => [3,2] => [2] => [1,1] => 1
[[1,3,4],[3,4]] => [3,2] => [2] => [1,1] => 1
[[1,3,4],[4,4]] => [3,2] => [2] => [1,1] => 1
[[2,2,2],[3,4]] => [3,2] => [2] => [1,1] => 1
[[2,2,2],[4,4]] => [3,2] => [2] => [1,1] => 1
[[2,2,3],[3,4]] => [3,2] => [2] => [1,1] => 1
[[2,2,4],[3,3]] => [3,2] => [2] => [1,1] => 1
[[2,2,3],[4,4]] => [3,2] => [2] => [1,1] => 1
[[2,2,4],[3,4]] => [3,2] => [2] => [1,1] => 1
[[2,2,4],[4,4]] => [3,2] => [2] => [1,1] => 1
[[2,3,3],[3,4]] => [3,2] => [2] => [1,1] => 1
[[2,3,3],[4,4]] => [3,2] => [2] => [1,1] => 1
[[2,3,4],[3,4]] => [3,2] => [2] => [1,1] => 1
[[2,3,4],[4,4]] => [3,2] => [2] => [1,1] => 1
[[3,3,3],[4,4]] => [3,2] => [2] => [1,1] => 1
[[3,3,4],[4,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,1],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,1],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,2],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,2],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,3],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,4],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,4],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,3],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,4],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,2],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,2],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,3],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,4],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,4],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,3],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,3],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,4],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,4],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,4],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,4,4],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,4,4],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,3],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,4],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,4,4],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[2,2,2],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[2,2,3],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[2,2,4],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[2,3,3],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[2,3,4],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[2,4,4],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,1],[2,2],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[2,3],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[2,4],[3]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[2,4],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[3,3],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[3,4],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[2,3],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[2,4],[3]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[2,4],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[3,3],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[2,4],[3]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[3,4],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[2,4],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[3,4],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,2],[3,3],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,2],[3,4],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,3],[3,4],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,2],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,3],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,4],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,1,1,1],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,1],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,2],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,3],[2,2]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,2],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,3],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,3],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,2],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,3],[2,2]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,2],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,3],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,3,3],[2,2]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,3],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,3,3],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,3,3],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,2],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,2],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,3],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,3],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,2,3,3],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,2,3,3],[3,3]] => [4,2] => [2] => [1,1] => 1
[[2,2,2,2],[3,3]] => [4,2] => [2] => [1,1] => 1
[[2,2,2,3],[3,3]] => [4,2] => [2] => [1,1] => 1
[[2,2,3,3],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,1],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,1,2],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,1,3],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,2,2],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,2,3],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,3,3],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,2,2],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,2,3],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,3,3],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,3,3,3],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,1],[2,2,3]] => [3,3] => [3] => [3] => 3
[[1,1,1],[2,3,3]] => [3,3] => [3] => [3] => 3
[[1,1,1],[3,3,3]] => [3,3] => [3] => [3] => 3
[[1,1,2],[2,2,3]] => [3,3] => [3] => [3] => 3
[[1,1,2],[2,3,3]] => [3,3] => [3] => [3] => 3
[[1,1,2],[3,3,3]] => [3,3] => [3] => [3] => 3
[[1,2,2],[2,3,3]] => [3,3] => [3] => [3] => 3
[[1,2,2],[3,3,3]] => [3,3] => [3] => [3] => 3
[[2,2,2],[3,3,3]] => [3,3] => [3] => [3] => 3
[[1,1,1],[2,2],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1],[2,3],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2],[2,2],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2],[2,3],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,3],[2,2],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,3],[2,3],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2],[2,3],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,3],[2,3],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[2,2],[3,3]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,1,1,1,1],[2,2]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,1,2],[2,2]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,2,2],[2,2]] => [5,2] => [2] => [1,1] => 1
[[1,1,2,2,2],[2,2]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,1],[2,2,2]] => [4,3] => [3] => [3] => 3
[[1,1,1,2],[2,2,2]] => [4,3] => [3] => [3] => 3
[[1],[2],[7]] => [1,1,1] => [1,1] => [2] => 2
[[1],[3],[7]] => [1,1,1] => [1,1] => [2] => 2
[[1],[4],[7]] => [1,1,1] => [1,1] => [2] => 2
[[1],[5],[7]] => [1,1,1] => [1,1] => [2] => 2
[[1],[6],[7]] => [1,1,1] => [1,1] => [2] => 2
[[2],[3],[7]] => [1,1,1] => [1,1] => [2] => 2
[[2],[4],[7]] => [1,1,1] => [1,1] => [2] => 2
[[2],[5],[7]] => [1,1,1] => [1,1] => [2] => 2
[[2],[6],[7]] => [1,1,1] => [1,1] => [2] => 2
[[3],[4],[7]] => [1,1,1] => [1,1] => [2] => 2
[[3],[5],[7]] => [1,1,1] => [1,1] => [2] => 2
[[3],[6],[7]] => [1,1,1] => [1,1] => [2] => 2
[[4],[5],[7]] => [1,1,1] => [1,1] => [2] => 2
[[4],[6],[7]] => [1,1,1] => [1,1] => [2] => 2
[[5],[6],[7]] => [1,1,1] => [1,1] => [2] => 2
[[1,1],[2,6]] => [2,2] => [2] => [1,1] => 1
[[1,1],[3,6]] => [2,2] => [2] => [1,1] => 1
[[1,1],[4,6]] => [2,2] => [2] => [1,1] => 1
[[1,1],[5,6]] => [2,2] => [2] => [1,1] => 1
[[1,1],[6,6]] => [2,2] => [2] => [1,1] => 1
[[1,2],[2,6]] => [2,2] => [2] => [1,1] => 1
[[1,2],[3,6]] => [2,2] => [2] => [1,1] => 1
[[1,3],[2,6]] => [2,2] => [2] => [1,1] => 1
[[1,2],[4,6]] => [2,2] => [2] => [1,1] => 1
[[1,4],[2,6]] => [2,2] => [2] => [1,1] => 1
[[1,2],[5,6]] => [2,2] => [2] => [1,1] => 1
[[1,5],[2,6]] => [2,2] => [2] => [1,1] => 1
[[1,2],[6,6]] => [2,2] => [2] => [1,1] => 1
[[1,3],[3,6]] => [2,2] => [2] => [1,1] => 1
[[1,3],[4,6]] => [2,2] => [2] => [1,1] => 1
[[1,4],[3,6]] => [2,2] => [2] => [1,1] => 1
[[1,3],[5,6]] => [2,2] => [2] => [1,1] => 1
[[1,5],[3,6]] => [2,2] => [2] => [1,1] => 1
[[1,3],[6,6]] => [2,2] => [2] => [1,1] => 1
[[1,4],[4,6]] => [2,2] => [2] => [1,1] => 1
[[1,4],[5,6]] => [2,2] => [2] => [1,1] => 1
[[1,5],[4,6]] => [2,2] => [2] => [1,1] => 1
[[1,4],[6,6]] => [2,2] => [2] => [1,1] => 1
[[1,5],[5,6]] => [2,2] => [2] => [1,1] => 1
[[1,5],[6,6]] => [2,2] => [2] => [1,1] => 1
[[2,2],[3,6]] => [2,2] => [2] => [1,1] => 1
[[2,2],[4,6]] => [2,2] => [2] => [1,1] => 1
[[2,2],[5,6]] => [2,2] => [2] => [1,1] => 1
[[2,2],[6,6]] => [2,2] => [2] => [1,1] => 1
[[2,3],[3,6]] => [2,2] => [2] => [1,1] => 1
[[2,3],[4,6]] => [2,2] => [2] => [1,1] => 1
[[2,4],[3,6]] => [2,2] => [2] => [1,1] => 1
[[2,3],[5,6]] => [2,2] => [2] => [1,1] => 1
[[2,5],[3,6]] => [2,2] => [2] => [1,1] => 1
[[2,3],[6,6]] => [2,2] => [2] => [1,1] => 1
[[2,4],[4,6]] => [2,2] => [2] => [1,1] => 1
[[2,4],[5,6]] => [2,2] => [2] => [1,1] => 1
[[2,5],[4,6]] => [2,2] => [2] => [1,1] => 1
[[2,4],[6,6]] => [2,2] => [2] => [1,1] => 1
[[2,5],[5,6]] => [2,2] => [2] => [1,1] => 1
[[2,5],[6,6]] => [2,2] => [2] => [1,1] => 1
[[3,3],[4,6]] => [2,2] => [2] => [1,1] => 1
[[3,3],[5,6]] => [2,2] => [2] => [1,1] => 1
[[3,3],[6,6]] => [2,2] => [2] => [1,1] => 1
[[3,4],[4,6]] => [2,2] => [2] => [1,1] => 1
[[3,4],[5,6]] => [2,2] => [2] => [1,1] => 1
[[3,5],[4,6]] => [2,2] => [2] => [1,1] => 1
[[3,4],[6,6]] => [2,2] => [2] => [1,1] => 1
[[3,5],[5,6]] => [2,2] => [2] => [1,1] => 1
[[3,5],[6,6]] => [2,2] => [2] => [1,1] => 1
[[4,4],[5,6]] => [2,2] => [2] => [1,1] => 1
[[4,4],[6,6]] => [2,2] => [2] => [1,1] => 1
[[4,5],[5,6]] => [2,2] => [2] => [1,1] => 1
[[4,5],[6,6]] => [2,2] => [2] => [1,1] => 1
[[5,5],[6,6]] => [2,2] => [2] => [1,1] => 1
[[1,1],[2],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,1],[3],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,1],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,1],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,2],[2],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,2],[3],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,3],[2],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,6],[2],[3]] => [2,1,1] => [1,1] => [2] => 2
[[1,2],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,4],[2],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,6],[2],[4]] => [2,1,1] => [1,1] => [2] => 2
[[1,2],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,5],[2],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,6],[2],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,6],[2],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,3],[3],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,3],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,4],[3],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,6],[3],[4]] => [2,1,1] => [1,1] => [2] => 2
[[1,3],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,5],[3],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,6],[3],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,6],[3],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,4],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,4],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,5],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,6],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[1,6],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,5],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1,6],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,2],[3],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,2],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,2],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,3],[3],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,3],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,4],[3],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,6],[3],[4]] => [2,1,1] => [1,1] => [2] => 2
[[2,3],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,5],[3],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,6],[3],[5]] => [2,1,1] => [1,1] => [2] => 2
[[2,6],[3],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,4],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,4],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,5],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,6],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[2,6],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,5],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[2,6],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[3,3],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[3,3],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[3,4],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[3,4],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[3,5],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[3,6],[4],[5]] => [2,1,1] => [1,1] => [2] => 2
[[3,6],[4],[6]] => [2,1,1] => [1,1] => [2] => 2
[[3,5],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[3,6],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[4,4],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[4,5],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[4,6],[5],[6]] => [2,1,1] => [1,1] => [2] => 2
[[1],[2],[3],[6]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[1],[2],[4],[6]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[1],[2],[5],[6]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[1],[3],[4],[6]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[1],[3],[5],[6]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[1],[4],[5],[6]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[2],[3],[4],[6]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[2],[3],[5],[6]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[2],[4],[5],[6]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[3],[4],[5],[6]] => [1,1,1,1] => [1,1,1] => [2,1] => 2
[[1,1,1],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,1],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,1],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,1],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,2],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,5],[2,2]] => [3,2] => [2] => [1,1] => 1
[[1,1,2],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,3],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,5],[2,3]] => [3,2] => [2] => [1,1] => 1
[[1,1,2],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,4],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,5],[2,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,2],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,5],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,3],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,5],[3,3]] => [3,2] => [2] => [1,1] => 1
[[1,1,3],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,4],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,5],[3,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,3],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,5],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,4],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,5],[4,4]] => [3,2] => [2] => [1,1] => 1
[[1,1,4],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,5],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,5],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,2],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,2],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,3],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,5],[2,3]] => [3,2] => [2] => [1,1] => 1
[[1,2,2],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,4],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,5],[2,4]] => [3,2] => [2] => [1,1] => 1
[[1,2,2],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,5],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,3],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,5],[3,3]] => [3,2] => [2] => [1,1] => 1
[[1,3,3],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,3],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,4],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,5],[3,4]] => [3,2] => [2] => [1,1] => 1
[[1,3,4],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,3,5],[2,4]] => [3,2] => [2] => [1,1] => 1
[[1,2,3],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,5],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,3,5],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,4],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,5],[4,4]] => [3,2] => [2] => [1,1] => 1
[[1,4,4],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,4],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,5],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,4,5],[2,5]] => [3,2] => [2] => [1,1] => 1
[[1,2,5],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,3,3],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,3,3],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,3,4],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,3,5],[3,4]] => [3,2] => [2] => [1,1] => 1
[[1,3,3],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,3,5],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,3,4],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,3,5],[4,4]] => [3,2] => [2] => [1,1] => 1
[[1,4,4],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,3,4],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,3,5],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,4,5],[3,5]] => [3,2] => [2] => [1,1] => 1
[[1,3,5],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,4,4],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,4,4],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,4,5],[4,5]] => [3,2] => [2] => [1,1] => 1
[[1,4,5],[5,5]] => [3,2] => [2] => [1,1] => 1
[[2,2,2],[3,5]] => [3,2] => [2] => [1,1] => 1
[[2,2,2],[4,5]] => [3,2] => [2] => [1,1] => 1
[[2,2,2],[5,5]] => [3,2] => [2] => [1,1] => 1
[[2,2,3],[3,5]] => [3,2] => [2] => [1,1] => 1
[[2,2,5],[3,3]] => [3,2] => [2] => [1,1] => 1
[[2,2,3],[4,5]] => [3,2] => [2] => [1,1] => 1
[[2,2,4],[3,5]] => [3,2] => [2] => [1,1] => 1
[[2,2,5],[3,4]] => [3,2] => [2] => [1,1] => 1
[[2,2,3],[5,5]] => [3,2] => [2] => [1,1] => 1
[[2,2,5],[3,5]] => [3,2] => [2] => [1,1] => 1
[[2,2,4],[4,5]] => [3,2] => [2] => [1,1] => 1
[[2,2,5],[4,4]] => [3,2] => [2] => [1,1] => 1
[[2,2,4],[5,5]] => [3,2] => [2] => [1,1] => 1
[[2,2,5],[4,5]] => [3,2] => [2] => [1,1] => 1
[[2,2,5],[5,5]] => [3,2] => [2] => [1,1] => 1
[[2,3,3],[3,5]] => [3,2] => [2] => [1,1] => 1
[[2,3,3],[4,5]] => [3,2] => [2] => [1,1] => 1
[[2,3,4],[3,5]] => [3,2] => [2] => [1,1] => 1
[[2,3,5],[3,4]] => [3,2] => [2] => [1,1] => 1
[[2,3,3],[5,5]] => [3,2] => [2] => [1,1] => 1
[[2,3,5],[3,5]] => [3,2] => [2] => [1,1] => 1
[[2,3,4],[4,5]] => [3,2] => [2] => [1,1] => 1
[[2,3,5],[4,4]] => [3,2] => [2] => [1,1] => 1
[[2,4,4],[3,5]] => [3,2] => [2] => [1,1] => 1
[[2,3,4],[5,5]] => [3,2] => [2] => [1,1] => 1
[[2,3,5],[4,5]] => [3,2] => [2] => [1,1] => 1
[[2,4,5],[3,5]] => [3,2] => [2] => [1,1] => 1
[[2,3,5],[5,5]] => [3,2] => [2] => [1,1] => 1
[[2,4,4],[4,5]] => [3,2] => [2] => [1,1] => 1
[[2,4,4],[5,5]] => [3,2] => [2] => [1,1] => 1
[[2,4,5],[4,5]] => [3,2] => [2] => [1,1] => 1
[[2,4,5],[5,5]] => [3,2] => [2] => [1,1] => 1
[[3,3,3],[4,5]] => [3,2] => [2] => [1,1] => 1
[[3,3,3],[5,5]] => [3,2] => [2] => [1,1] => 1
[[3,3,4],[4,5]] => [3,2] => [2] => [1,1] => 1
[[3,3,5],[4,4]] => [3,2] => [2] => [1,1] => 1
[[3,3,4],[5,5]] => [3,2] => [2] => [1,1] => 1
[[3,3,5],[4,5]] => [3,2] => [2] => [1,1] => 1
[[3,3,5],[5,5]] => [3,2] => [2] => [1,1] => 1
[[3,4,4],[4,5]] => [3,2] => [2] => [1,1] => 1
[[3,4,4],[5,5]] => [3,2] => [2] => [1,1] => 1
[[3,4,5],[4,5]] => [3,2] => [2] => [1,1] => 1
[[3,4,5],[5,5]] => [3,2] => [2] => [1,1] => 1
[[4,4,4],[5,5]] => [3,2] => [2] => [1,1] => 1
[[4,4,5],[5,5]] => [3,2] => [2] => [1,1] => 1
[[1,1,1],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,1],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,1],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,2],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,2],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,3],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,5],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,2],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,4],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,5],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,5],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,3],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,3],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,4],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,5],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,5],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,4],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1,5],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,2],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,2],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,3],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,5],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,2],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,4],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,5],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,5],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,3],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,3],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,5],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,3],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,4],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,5],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,4],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,5],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,4,5],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,5],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,5],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,5,5],[2],[3]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,4],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,4,4],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,4,5],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,2,5],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,4,5],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,5,5],[2],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,5,5],[2],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,3],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,3],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,4],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,5],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,5],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,4],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,4,4],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,4,5],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,3,5],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,4,5],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,5,5],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[1,5,5],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,4,4],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,4,5],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,5,5],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,2,2],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,2,2],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,2,3],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,2,3],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,2,4],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,2,5],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[2,2,5],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,2,4],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,2,5],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,3,3],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,3,3],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,3,4],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,3,5],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[2,3,5],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,3,4],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,4,4],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,4,5],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[2,3,5],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,4,5],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,5,5],[3],[4]] => [3,1,1] => [1,1] => [2] => 2
[[2,5,5],[3],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,4,4],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,4,5],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[2,5,5],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[3,3,3],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[3,3,4],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[3,3,5],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[3,4,4],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[3,4,5],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[3,5,5],[4],[5]] => [3,1,1] => [1,1] => [2] => 2
[[1,1],[2,2],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[2,3],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[2,5],[3]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[2,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[2,5],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[2,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[3,3],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[3,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[3,5],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[3,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[4,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[4,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[2,3],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[2,5],[3]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[2,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[2,5],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[2,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[3,3],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[2,5],[3]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[3,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[3,5],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[2,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[2,5],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,4],[2,5],[3]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[3,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[2,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[4,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,4],[2,5],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[4,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,4],[2,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[3,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[3,5],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[3,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[4,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,4],[3,5],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[4,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,4],[3,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,4],[4,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,2],[3,3],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,2],[3,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,2],[3,5],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,2],[3,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,2],[4,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,2],[4,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,3],[3,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,3],[3,5],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,3],[3,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,3],[4,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,4],[3,5],[4]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,3],[4,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,4],[3,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[2,4],[4,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[3,3],[4,4],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[3,3],[4,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[3,4],[4,5],[5]] => [2,2,1] => [2,1] => [1,1,1] => 1
[[1,1],[2],[3],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,1],[2],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,1],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,2],[2],[3],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,2],[2],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,3],[2],[3],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,2],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,3],[2],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,4],[2],[3],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,5],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,5],[2],[3],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,4],[2],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,5],[2],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,3],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,4],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1,5],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[2,2],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[2,3],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[2,4],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[2,5],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => [2,1] => 2
[[1],[2],[3],[4],[5]] => [1,1,1,1,1] => [1,1,1,1] => [4] => 4
[[1,1,1,1],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,1],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,1],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,2],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,4],[2,2]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,2],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,3],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,4],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,2],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,4],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,3],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,4],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,3],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,2],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,4],[2,2]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,2],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,3],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,4],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,3,4],[2,2]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,2],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,4],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,4,4],[2,2]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,3],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,4],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,3,3],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,3,4],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,3],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,3,4],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,4,4],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,2,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,4,4],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,3,3],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,3,4],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,3,3],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,3,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,4,4],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,1,3,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,4,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,4,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,2],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,2],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,3],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,4],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,2],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,4],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,3],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,4],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,2,3,3],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,3,4],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,3],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,3,4],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,4,4],[2,3]] => [4,2] => [2] => [1,1] => 1
[[1,2,2,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,4,4],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,3,3],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,3,4],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,3,3,3],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,3,3],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,3,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,4,4],[3,3]] => [4,2] => [2] => [1,1] => 1
[[1,3,3,4],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,3,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,4,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,3,4,4],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,4,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,3,3,3],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,3,3,3],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,3,3,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,3,3,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,3,4,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,3,4,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[2,2,2,2],[3,4]] => [4,2] => [2] => [1,1] => 1
[[2,2,2,2],[4,4]] => [4,2] => [2] => [1,1] => 1
[[2,2,2,3],[3,4]] => [4,2] => [2] => [1,1] => 1
[[2,2,2,4],[3,3]] => [4,2] => [2] => [1,1] => 1
[[2,2,2,3],[4,4]] => [4,2] => [2] => [1,1] => 1
[[2,2,2,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[2,2,2,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[2,2,3,3],[3,4]] => [4,2] => [2] => [1,1] => 1
[[2,2,3,4],[3,3]] => [4,2] => [2] => [1,1] => 1
[[2,2,3,3],[4,4]] => [4,2] => [2] => [1,1] => 1
[[2,2,3,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[2,2,4,4],[3,3]] => [4,2] => [2] => [1,1] => 1
[[2,2,3,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[2,2,4,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[2,2,4,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[2,3,3,3],[3,4]] => [4,2] => [2] => [1,1] => 1
[[2,3,3,3],[4,4]] => [4,2] => [2] => [1,1] => 1
[[2,3,3,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[2,3,3,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[2,3,4,4],[3,4]] => [4,2] => [2] => [1,1] => 1
[[2,3,4,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[3,3,3,3],[4,4]] => [4,2] => [2] => [1,1] => 1
[[3,3,3,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[3,3,4,4],[4,4]] => [4,2] => [2] => [1,1] => 1
[[1,1,1,1],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,1,1],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,1,2],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,1,2],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,1,3],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,1,4],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,1,4],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,1,3],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,1,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,2,2],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,2,2],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,2,3],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,2,4],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,2,4],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,2,3],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,3,3],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,3,4],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,2,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,3,4],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,4,4],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,4,4],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,3,3],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,3,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,4,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,2,2],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,2,2],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,2,3],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,2,4],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,2,4],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,2,3],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,3,3],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,3,4],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,2,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,3,4],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,4,4],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,4,4],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,3,3],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,3,3,3],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,3,3,4],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,3,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,3,3,4],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,3,4,4],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,4,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,3,4,4],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,4,4,4],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,4,4,4],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,3,3,3],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,3,3,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,3,4,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,4,4,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[2,2,2,2],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[2,2,2,3],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[2,2,2,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[2,2,3,3],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[2,2,3,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[2,2,4,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[2,3,3,3],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[2,3,3,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[2,3,4,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[2,4,4,4],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,1,1],[2,2,4]] => [3,3] => [3] => [3] => 3
[[1,1,1],[2,3,4]] => [3,3] => [3] => [3] => 3
[[1,1,1],[2,4,4]] => [3,3] => [3] => [3] => 3
[[1,1,1],[3,3,4]] => [3,3] => [3] => [3] => 3
[[1,1,1],[3,4,4]] => [3,3] => [3] => [3] => 3
[[1,1,1],[4,4,4]] => [3,3] => [3] => [3] => 3
[[1,1,2],[2,2,4]] => [3,3] => [3] => [3] => 3
[[1,1,2],[2,3,4]] => [3,3] => [3] => [3] => 3
[[1,1,3],[2,2,4]] => [3,3] => [3] => [3] => 3
[[1,1,2],[2,4,4]] => [3,3] => [3] => [3] => 3
[[1,1,2],[3,3,4]] => [3,3] => [3] => [3] => 3
[[1,1,3],[2,3,4]] => [3,3] => [3] => [3] => 3
[[1,1,2],[3,4,4]] => [3,3] => [3] => [3] => 3
[[1,1,3],[2,4,4]] => [3,3] => [3] => [3] => 3
[[1,1,2],[4,4,4]] => [3,3] => [3] => [3] => 3
[[1,1,3],[3,3,4]] => [3,3] => [3] => [3] => 3
[[1,1,3],[3,4,4]] => [3,3] => [3] => [3] => 3
[[1,1,3],[4,4,4]] => [3,3] => [3] => [3] => 3
[[1,2,2],[2,3,4]] => [3,3] => [3] => [3] => 3
[[1,2,2],[2,4,4]] => [3,3] => [3] => [3] => 3
[[1,2,2],[3,3,4]] => [3,3] => [3] => [3] => 3
[[1,2,3],[2,3,4]] => [3,3] => [3] => [3] => 3
[[1,2,2],[3,4,4]] => [3,3] => [3] => [3] => 3
[[1,2,3],[2,4,4]] => [3,3] => [3] => [3] => 3
[[1,2,2],[4,4,4]] => [3,3] => [3] => [3] => 3
[[1,2,3],[3,3,4]] => [3,3] => [3] => [3] => 3
[[1,2,3],[3,4,4]] => [3,3] => [3] => [3] => 3
[[1,3,3],[2,4,4]] => [3,3] => [3] => [3] => 3
[[1,2,3],[4,4,4]] => [3,3] => [3] => [3] => 3
[[1,3,3],[3,4,4]] => [3,3] => [3] => [3] => 3
[[1,3,3],[4,4,4]] => [3,3] => [3] => [3] => 3
[[2,2,2],[3,3,4]] => [3,3] => [3] => [3] => 3
[[2,2,2],[3,4,4]] => [3,3] => [3] => [3] => 3
[[2,2,2],[4,4,4]] => [3,3] => [3] => [3] => 3
[[2,2,3],[3,3,4]] => [3,3] => [3] => [3] => 3
[[2,2,3],[3,4,4]] => [3,3] => [3] => [3] => 3
[[2,2,3],[4,4,4]] => [3,3] => [3] => [3] => 3
[[2,3,3],[3,4,4]] => [3,3] => [3] => [3] => 3
[[2,3,3],[4,4,4]] => [3,3] => [3] => [3] => 3
[[3,3,3],[4,4,4]] => [3,3] => [3] => [3] => 3
[[1,1,1],[2,2],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1],[2,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1],[2,4],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1],[2,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1],[3,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2],[2,2],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2],[2,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2],[2,4],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,3],[2,2],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,4],[2,2],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2],[2,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,4],[2,2],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2],[3,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,3],[2,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,3],[2,4],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,4],[2,3],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,3],[2,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,4],[2,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,4],[2,4],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,4],[2,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,3],[3,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,3],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,4],[3,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,4],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2],[2,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2],[2,4],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2],[2,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2],[3,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,3],[2,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,3],[2,4],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,4],[2,3],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,3],[2,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,4],[2,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,4],[2,4],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,4],[2,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,3],[3,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,3,3],[2,4],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,3],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,4],[3,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,3,3],[2,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,3,4],[2,4],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,4],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,3,4],[2,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,3,3],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,3,4],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[2,2,2],[3,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[2,2,2],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[2,2,3],[3,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[2,2,3],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[2,2,4],[3,3],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[2,2,4],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[2,3,3],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[2,3,4],[3,4],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,1,2],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,1,3],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,1,4],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,2,2],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,2,3],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,2,4],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,3,3],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,3,4],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,4,4],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,1],[2,2],[3,4]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,1],[2,2],[4,4]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,1],[2,3],[3,4]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,1],[2,3],[4,4]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,1],[3,3],[4,4]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,2],[2,3],[3,4]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,2],[2,3],[4,4]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,2],[3,3],[4,4]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[2,2],[3,3],[4,4]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,1],[2,2],[3],[4]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,1],[2,3],[3],[4]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,1],[2,4],[3],[4]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,2],[2,3],[3],[4]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,2],[2,4],[3],[4]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,3],[2,4],[3],[4]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,1,1,1,1],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,1,1],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,1,2],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,1,3],[2,2]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,1,2],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,1,3],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,1,3],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,2,2],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,2,3],[2,2]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,2,2],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,2,3],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,3,3],[2,2]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,2,3],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,3,3],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,3,3],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,2,2,2],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,2,2,3],[2,2]] => [5,2] => [2] => [1,1] => 1
[[1,1,2,2,2],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,2,2,3],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,2,3,3],[2,2]] => [5,2] => [2] => [1,1] => 1
[[1,1,2,2,3],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,2,3,3],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,3,3,3],[2,2]] => [5,2] => [2] => [1,1] => 1
[[1,1,2,3,3],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,3,3,3],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,3,3,3],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,2,2,2,2],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,2,2,2,2],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,2,2,2,3],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,2,2,2,3],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,2,2,3,3],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,2,2,3,3],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,2,3,3,3],[2,3]] => [5,2] => [2] => [1,1] => 1
[[1,2,3,3,3],[3,3]] => [5,2] => [2] => [1,1] => 1
[[2,2,2,2,2],[3,3]] => [5,2] => [2] => [1,1] => 1
[[2,2,2,2,3],[3,3]] => [5,2] => [2] => [1,1] => 1
[[2,2,2,3,3],[3,3]] => [5,2] => [2] => [1,1] => 1
[[2,2,3,3,3],[3,3]] => [5,2] => [2] => [1,1] => 1
[[1,1,1,1,1],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,1,1,1,2],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,1,1,1,3],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,1,1,2,2],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,1,1,2,3],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,1,1,3,3],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,1,2,2,2],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,1,2,2,3],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,1,2,3,3],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,1,3,3,3],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,2,2,2,2],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,2,2,2,3],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,2,2,3,3],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,2,3,3,3],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,3,3,3,3],[2],[3]] => [5,1,1] => [1,1] => [2] => 2
[[1,1,1,1],[2,2,3]] => [4,3] => [3] => [3] => 3
[[1,1,1,1],[2,3,3]] => [4,3] => [3] => [3] => 3
[[1,1,1,1],[3,3,3]] => [4,3] => [3] => [3] => 3
[[1,1,1,2],[2,2,3]] => [4,3] => [3] => [3] => 3
[[1,1,1,3],[2,2,2]] => [4,3] => [3] => [3] => 3
[[1,1,1,2],[2,3,3]] => [4,3] => [3] => [3] => 3
[[1,1,1,3],[2,2,3]] => [4,3] => [3] => [3] => 3
[[1,1,1,2],[3,3,3]] => [4,3] => [3] => [3] => 3
[[1,1,1,3],[2,3,3]] => [4,3] => [3] => [3] => 3
[[1,1,1,3],[3,3,3]] => [4,3] => [3] => [3] => 3
[[1,1,2,2],[2,2,3]] => [4,3] => [3] => [3] => 3
[[1,1,2,2],[2,3,3]] => [4,3] => [3] => [3] => 3
[[1,1,2,3],[2,2,3]] => [4,3] => [3] => [3] => 3
[[1,1,2,2],[3,3,3]] => [4,3] => [3] => [3] => 3
[[1,1,2,3],[2,3,3]] => [4,3] => [3] => [3] => 3
[[1,1,2,3],[3,3,3]] => [4,3] => [3] => [3] => 3
[[1,2,2,2],[2,3,3]] => [4,3] => [3] => [3] => 3
[[1,2,2,2],[3,3,3]] => [4,3] => [3] => [3] => 3
[[1,2,2,3],[2,3,3]] => [4,3] => [3] => [3] => 3
[[1,2,2,3],[3,3,3]] => [4,3] => [3] => [3] => 3
[[2,2,2,2],[3,3,3]] => [4,3] => [3] => [3] => 3
[[2,2,2,3],[3,3,3]] => [4,3] => [3] => [3] => 3
[[1,1,1,1],[2,2],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,1],[2,3],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2],[2,2],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2],[2,3],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,3],[2,2],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,3],[2,3],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,2],[2,2],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,2],[2,3],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,3],[2,2],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,3],[2,3],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,1,3,3],[2,2],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,1,3,3],[2,3],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2,2],[2,3],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2,3],[2,3],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,2,3,3],[2,3],[3]] => [4,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1],[2,2,2],[3]] => [3,3,1] => [3,1] => [3,1] => 3
[[1,1,1],[2,2,3],[3]] => [3,3,1] => [3,1] => [3,1] => 3
[[1,1,1],[2,3,3],[3]] => [3,3,1] => [3,1] => [3,1] => 3
[[1,1,2],[2,2,3],[3]] => [3,3,1] => [3,1] => [3,1] => 3
[[1,1,2],[2,3,3],[3]] => [3,3,1] => [3,1] => [3,1] => 3
[[1,2,2],[2,3,3],[3]] => [3,3,1] => [3,1] => [3,1] => 3
[[1,1,1],[2,2],[3,3]] => [3,2,2] => [2,2] => [1,1,1,1] => 1
[[1,1,2],[2,2],[3,3]] => [3,2,2] => [2,2] => [1,1,1,1] => 1
[[1,1,3],[2,2],[3,3]] => [3,2,2] => [2,2] => [1,1,1,1] => 1
[[1,1,1,1,1,1],[2,2]] => [6,2] => [2] => [1,1] => 1
[[1,1,1,1,1,2],[2,2]] => [6,2] => [2] => [1,1] => 1
[[1,1,1,1,2,2],[2,2]] => [6,2] => [2] => [1,1] => 1
[[1,1,1,2,2,2],[2,2]] => [6,2] => [2] => [1,1] => 1
[[1,1,2,2,2,2],[2,2]] => [6,2] => [2] => [1,1] => 1
[[1,1,1,1,1],[2,2,2]] => [5,3] => [3] => [3] => 3
[[1,1,1,1,2],[2,2,2]] => [5,3] => [3] => [3] => 3
[[1,1,1,2,2],[2,2,2]] => [5,3] => [3] => [3] => 3
[[1,1,1,1],[2,2,2,2]] => [4,4] => [4] => [2,2] => 2
[[1,1,1,1],[2,2,2],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,2],[2,2,2],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,1],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,2],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,3],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,2,2],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,2,3],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,1],[2,2,2],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,2],[2,2,2],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,1],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,2],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,3],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,2,2],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,2,3],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,1],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,2],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,3],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,4],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,2,2],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,2,3],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,2,4],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,1],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,2],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,3],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,2,2],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,2,3],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,1],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,2],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,1,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,2,2],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,2,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,2,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,3,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,1,3,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,2,2,2],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,2,2,3],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,2,2,2],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,2,2,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,2,2,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,2,3,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,2,3,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => [3,1,1,1] => 3
[[1,2,3,4],[5],[6]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,3,5],[4,6]] => [4,2] => [2] => [1,1] => 1
[[1,2,3,5],[4],[6]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,3,4],[5,6]] => [4,2] => [2] => [1,1] => 1
[[1,2,3,6],[4],[5]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,3],[4],[5],[6]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,2,4,5],[3,6]] => [4,2] => [2] => [1,1] => 1
[[1,2,4,6],[3,5]] => [4,2] => [2] => [1,1] => 1
[[1,2,4],[3,5],[6]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,4,5],[3],[6]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,4,6],[3],[5]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,4],[3],[5],[6]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,2,3,6],[4,5]] => [4,2] => [2] => [1,1] => 1
[[1,2,3],[4,5],[6]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,5,6],[3],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,2,5],[3,6],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,5],[3],[4],[6]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,2,3],[4,6],[5]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,4],[3,6],[5]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,6],[3],[4],[5]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => [1,1,1,1] => [4] => 4
[[1,3,4,5],[2,6]] => [4,2] => [2] => [1,1] => 1
[[1,3,4,6],[2,5]] => [4,2] => [2] => [1,1] => 1
[[1,3,4],[2,5],[6]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,3,5,6],[2,4]] => [4,2] => [2] => [1,1] => 1
[[1,3,5],[2,4,6]] => [3,3] => [3] => [3] => 3
[[1,3,5],[2,4],[6]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,3,4],[2,5,6]] => [3,3] => [3] => [3] => 3
[[1,3,6],[2,4],[5]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[2,4],[5],[6]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,3,4,5],[2],[6]] => [4,1,1] => [1,1] => [2] => 2
[[1,3,4,6],[2],[5]] => [4,1,1] => [1,1] => [2] => 2
[[1,3,4],[2],[5],[6]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,3,5,6],[2],[4]] => [4,1,1] => [1,1] => [2] => 2
[[1,3,5],[2,6],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,3,5],[2],[4],[6]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,3,4],[2,6],[5]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,3,6],[2],[4],[5]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,3],[2],[4],[5],[6]] => [2,1,1,1,1] => [1,1,1,1] => [4] => 4
[[1,2,5,6],[3,4]] => [4,2] => [2] => [1,1] => 1
[[1,2,5],[3,4,6]] => [3,3] => [3] => [3] => 3
[[1,2,5],[3,4],[6]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2,4],[3,5,6]] => [3,3] => [3] => [3] => 3
[[1,2,6],[3,4],[5]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[3,4],[5],[6]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,4,5,6],[2],[3]] => [4,1,1] => [1,1] => [2] => 2
[[1,4,5],[2,6],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,4,6],[2,5],[3]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,4],[2,5],[3,6]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,4],[2,5],[3],[6]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,4,5],[2],[3],[6]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,4,6],[2],[3],[5]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,4],[2],[3],[5],[6]] => [2,1,1,1,1] => [1,1,1,1] => [4] => 4
[[1,2,3],[4,5,6]] => [3,3] => [3] => [3] => 3
[[1,2,6],[3,5],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,2],[3,5],[4],[6]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,3,6],[2,5],[4]] => [3,2,1] => [2,1] => [1,1,1] => 1
[[1,3],[2,5],[4,6]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,3],[2,5],[4],[6]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,2],[3,5],[4,6]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,5,6],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => [2,1] => 2
[[1,5],[2,6],[3],[4]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,5],[2],[3],[4],[6]] => [2,1,1,1,1] => [1,1,1,1] => [4] => 4
[[1,2],[3,6],[4],[5]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,3],[2,4],[5,6]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,3],[2,6],[4],[5]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,2],[3,4],[5,6]] => [2,2,2] => [2,2] => [1,1,1,1] => 1
[[1,4],[2,6],[3],[5]] => [2,2,1,1] => [2,1,1] => [2,1,1] => 2
[[1,6],[2],[3],[4],[5]] => [2,1,1,1,1] => [1,1,1,1] => [4] => 4
[[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => [1,1,1,1,1] => [4,1] => 4
[[1,1,1,1,2,2,2],[3,3],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,2,2,2],[3,3],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,1,2,2,3],[3,3],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,2,2,3],[3,3],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,2,3,3],[3,3],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,2,2,2,3],[3,3],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,2,2,3,3],[3,3],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,1,2,2,2],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,2,2,2],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,1,2,2,3],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,2,2,3],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,2,3],[3,3,4],[4]] => [6,3,1] => [3,1] => [3,1] => 3
[[1,1,2,2,2,2,3],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,2,2,3],[3,3,4],[4]] => [6,3,1] => [3,1] => [3,1] => 3
[[1,1,1,1,2,2,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,2,2,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,2,4,4],[3,3],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,2,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,2,2,2,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,2,2,4,4],[3,3],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,2,2,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,1,2,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,2,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,3,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,2,2,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,2,3,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,1,2,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,2,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,3,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,1,2,3,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,2,2,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,2,3,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,2,3,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,3,3,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,1,2,3,3,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2,2,2,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2,2,3,3,3],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2,2,2,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2,2,3,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2,2,3,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2,3,3,3,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
[[1,2,2,3,3,4,4],[3,4],[4]] => [7,2,1] => [2,1] => [1,1,1] => 1
search for individual values
searching the database for the individual values of this statistic
Description
The least common multiple of the parts of the partition.
Map
shape
Description
Return the shape of a tableau.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
Glaisher-Franklin
Description
The Glaisher-Franklin bijection on integer partitions.
This map sends the set of even part sizes, each divided by two, to the set of repeated part sizes, see [1, 3.3.1].
This map sends the set of even part sizes, each divided by two, to the set of repeated part sizes, see [1, 3.3.1].
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