Identifier
-
Mp00036:
Gelfand-Tsetlin patterns
—to semistandard tableau⟶
Semistandard tableaux
Mp00077: Semistandard tableaux —shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤ
Values
[[1,0],[0]] => [[2]] => [1] => [1,0,1,0] => 1
[[1,0],[1]] => [[1]] => [1] => [1,0,1,0] => 1
[[2,0],[0]] => [[2,2]] => [2] => [1,1,0,0,1,0] => 1
[[2,0],[1]] => [[1,2]] => [2] => [1,1,0,0,1,0] => 1
[[2,0],[2]] => [[1,1]] => [2] => [1,1,0,0,1,0] => 1
[[1,1],[1]] => [[1],[2]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,0,0],[0,0],[0]] => [[3]] => [1] => [1,0,1,0] => 1
[[1,0,0],[1,0],[0]] => [[2]] => [1] => [1,0,1,0] => 1
[[1,0,0],[1,0],[1]] => [[1]] => [1] => [1,0,1,0] => 1
[[3,0],[0]] => [[2,2,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0],[1]] => [[1,2,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0],[2]] => [[1,1,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0],[3]] => [[1,1,1]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[2,0,0],[0,0],[0]] => [[3,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0],[1,0],[0]] => [[2,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0],[1,0],[1]] => [[1,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0],[2,0],[0]] => [[2,2]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0],[2,0],[1]] => [[1,2]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0],[2,0],[2]] => [[1,1]] => [2] => [1,1,0,0,1,0] => 1
[[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => [1,0,1,0] => 1
[[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1] => [1,0,1,0] => 1
[[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1] => [1,0,1,0] => 1
[[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1] => [1,0,1,0] => 1
[[4,0],[0]] => [[2,2,2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0],[1]] => [[1,2,2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0],[2]] => [[1,1,2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0],[3]] => [[1,1,1,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0],[4]] => [[1,1,1,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2],[2]] => [[1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[3,0,0],[0,0],[0]] => [[3,3,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0],[1,0],[0]] => [[2,3,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0],[1,0],[1]] => [[1,3,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0],[2,0],[0]] => [[2,2,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0],[2,0],[1]] => [[1,2,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0],[2,0],[2]] => [[1,1,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0],[3,0],[0]] => [[2,2,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0],[3,0],[1]] => [[1,2,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0],[3,0],[2]] => [[1,1,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0],[3,0],[3]] => [[1,1,1]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [2] => [1,1,0,0,1,0] => 1
[[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1] => [1,0,1,0] => 1
[[5,0],[0]] => [[2,2,2,2,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0],[1]] => [[1,2,2,2,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0],[2]] => [[1,1,2,2,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0],[3]] => [[1,1,1,2,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0],[4]] => [[1,1,1,1,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0],[5]] => [[1,1,1,1,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
>>> Load all 764 entries. <<<[[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [2] => [1,1,0,0,1,0] => 1
[[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1] => [1,0,1,0] => 1
[[6,0],[0]] => [[2,2,2,2,2,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0],[1]] => [[1,2,2,2,2,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0],[2]] => [[1,1,2,2,2,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0],[3]] => [[1,1,1,2,2,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0],[4]] => [[1,1,1,1,2,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0],[5]] => [[1,1,1,1,1,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[3,3],[3]] => [[1,1,1],[2,2,2]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[5]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[5]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[5]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[5]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[5]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[5]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,6]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [2] => [1,1,0,0,1,0] => 1
[[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[6]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[6]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[6]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[6]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[6]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1] => [1,0,1,0] => 1
[[6,0,0],[0,0],[0]] => [[3,3,3,3,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[1,0],[0]] => [[2,3,3,3,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[1,0],[1]] => [[1,3,3,3,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[2,0],[0]] => [[2,2,3,3,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[2,0],[1]] => [[1,2,3,3,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[2,0],[2]] => [[1,1,3,3,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[3,0],[0]] => [[2,2,2,3,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[3,0],[1]] => [[1,2,2,3,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[3,0],[2]] => [[1,1,2,3,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[3,0],[3]] => [[1,1,1,3,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[4,0],[0]] => [[2,2,2,2,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[4,0],[1]] => [[1,2,2,2,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[4,0],[2]] => [[1,1,2,2,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[4,0],[3]] => [[1,1,1,2,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[4,0],[4]] => [[1,1,1,1,3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[5,0],[0]] => [[2,2,2,2,2,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[5,0],[1]] => [[1,2,2,2,2,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[5,0],[2]] => [[1,1,2,2,2,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[5,0],[3]] => [[1,1,1,2,2,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[5,0],[4]] => [[1,1,1,1,2,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[5,0],[5]] => [[1,1,1,1,1,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[6,0],[0]] => [[2,2,2,2,2,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[6,0],[1]] => [[1,2,2,2,2,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[6,0],[2]] => [[1,1,2,2,2,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[6,0],[3]] => [[1,1,1,2,2,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[6,0],[4]] => [[1,1,1,1,2,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[6,0,0],[6,0],[5]] => [[1,1,1,1,1,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[4,1,1],[1,1],[1]] => [[1,3,3,3],[2],[3]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1],[2,1],[1]] => [[1,2,3,3],[2],[3]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1],[2,1],[2]] => [[1,1,3,3],[2],[3]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1],[3,1],[1]] => [[1,2,2,3],[2],[3]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1],[3,1],[2]] => [[1,1,2,3],[2],[3]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1],[3,1],[3]] => [[1,1,1,3],[2],[3]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1],[4,1],[1]] => [[1,2,2,2],[2],[3]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1],[4,1],[2]] => [[1,1,2,2],[2],[3]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1],[4,1],[3]] => [[1,1,1,2],[2],[3]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1],[4,1],[4]] => [[1,1,1,1],[2],[3]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[3,3,0],[3,0],[0]] => [[2,2,2],[3,3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,3,0],[3,0],[1]] => [[1,2,2],[3,3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,3,0],[3,0],[2]] => [[1,1,2],[3,3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,3,0],[3,0],[3]] => [[1,1,1],[3,3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,3,0],[3,1],[1]] => [[1,2,2],[2,3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,3,0],[3,1],[2]] => [[1,1,2],[2,3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,3,0],[3,1],[3]] => [[1,1,1],[2,3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,3,0],[3,2],[2]] => [[1,1,2],[2,2,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,3,0],[3,2],[3]] => [[1,1,1],[2,2,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,3,0],[3,3],[3]] => [[1,1,1],[2,2,2]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[2,2,2],[2,2],[2]] => [[1,1],[2,2],[3,3]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[5,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1,4]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[5,0,0,0],[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[3,1,1,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,4],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[2,1,1],[1,1],[1]] => [[1,3,4],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[2,1,1],[2,1],[1]] => [[1,2,4],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[2,1,1],[2,1],[2]] => [[1,1,4],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0],[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,5]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,5]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4],[5]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4],[5]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4],[5]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,1,1,1,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3],[5]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[[1,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[[3,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,6,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,6]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5],[6]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5],[6]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5],[6]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5],[6]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[6]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[6]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[6]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[6]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[6]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[6]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[5]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[5]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[5]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[5]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[5]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[5]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[[2,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[7,7]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,7]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,7]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,7]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,7]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,7]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,7]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,6]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [2] => [1,1,0,0,1,0] => 1
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [2] => [1,1,0,0,1,0] => 1
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6],[7]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[7]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[7]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[7]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[7]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[7]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[6]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[6]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[6]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[6]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[6]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => [1,0,1,1,0,0] => 2
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1] => [1,0,1,0] => 1
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1] => [1,0,1,0] => 1
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4],[5]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[5]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[5]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4],[5]] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1]] => [[1]] => [1] => [1,0,1,0] => 1
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5,6]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5,6],[2],[3]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5,6],[2],[4]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5,6],[3],[4]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,6],[2],[5]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,6],[3],[5]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,6],[4],[5]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5],[2],[6]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5],[3],[6]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5],[4],[6]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[5],[6]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,4,6]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,4,6]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,5,6]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,5,6]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,5,6]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5,6],[2],[3],[4]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,6],[2],[3],[5]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,6],[2],[4],[5]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,6],[3],[4],[5]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2],[3],[6]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2],[4],[6]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3],[4],[6]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[5],[6]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[5],[6]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,5],[3,6]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5],[4,6]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5],[4,6]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[5,6]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[5,6]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[[2]] => [[1,1]] => [2] => [1,1,0,0,1,0] => 1
[[3]] => [[1,1,1]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[4]] => [[1,1,1,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[5]] => [[1,1,1,1,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
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Generating function
$F_{(2, 1)} = 2\ q$
$F_{(2, 2)} = 3\ q + q^{2}$
$F_{(3, 1)} = 3\ q$
$F_{(3, 2)} = 6\ q + 3\ q^{2}$
$F_{(4, 1)} = 4\ q$
$F_{(4, 2)} = 10\ q + 6\ q^{2}$
$F_{(5, 1)} = 5\ q$
$F_{(5, 2)} = 15\ q + 10\ q^{2}$
$F_{(6, 1)} = 6\ q$
$F_{(6, 2)} = 21\ q + 15\ q^{2}$
$F_{(7, 2)} = 28\ q + 21\ q^{2}$
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Map
to semistandard tableau
Description
Return the Gelfand-Tsetlin pattern as a semistandard Young tableau.
Let $G$ be a Gelfand-Tsetlin pattern and let $\lambda^{(k)}$ be its $(n-k+1)$-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
$$ \lambda^{(0)} \subseteq \lambda^{(1)} \subseteq \cdots \subseteq \lambda^{(n)}, $$
where $\lambda^{(0)}$ is the empty partition.
Each skew shape $\lambda^{(k)} / \lambda^{(k-1)}$ is moreover a horizontal strip.
We now define a semistandard tableau $T(G)$ by inserting $k$ into the cells of the skew shape $\lambda^{(k)} / \lambda^{(k-1)}$, for $k=1,\dots,n$.
Let $G$ be a Gelfand-Tsetlin pattern and let $\lambda^{(k)}$ be its $(n-k+1)$-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
$$ \lambda^{(0)} \subseteq \lambda^{(1)} \subseteq \cdots \subseteq \lambda^{(n)}, $$
where $\lambda^{(0)}$ is the empty partition.
Each skew shape $\lambda^{(k)} / \lambda^{(k-1)}$ is moreover a horizontal strip.
We now define a semistandard tableau $T(G)$ by inserting $k$ into the cells of the skew shape $\lambda^{(k)} / \lambda^{(k-1)}$, for $k=1,\dots,n$.
Map
shape
Description
Return the shape of a tableau.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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