Identifier
-
Mp00182:
Skew partitions
—outer shape⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001499: Dyck paths ⟶ ℤ
Values
[[1],[]] => [1] => [1,0,1,0] => 1
[[2],[]] => [2] => [1,1,0,0,1,0] => 1
[[1,1],[]] => [1,1] => [1,0,1,1,0,0] => 1
[[2,1],[1]] => [2,1] => [1,0,1,0,1,0] => 2
[[3],[]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[2,1],[]] => [2,1] => [1,0,1,0,1,0] => 2
[[3,1],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => 2
[[2,2],[1]] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[[3,2],[2]] => [3,2] => [1,1,0,0,1,0,1,0] => 2
[[1,1,1],[]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 1
[[2,2,1],[1,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => 2
[[2,1,1],[1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[[3,2,1],[2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[[4],[]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,1],[]] => [3,1] => [1,1,0,1,0,0,1,0] => 2
[[4,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 2
[[2,2],[]] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[[3,2],[1]] => [3,2] => [1,1,0,0,1,0,1,0] => 2
[[4,2],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 2
[[2,1,1],[]] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[[3,2,1],[1,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[[3,1,1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 2
[[4,2,1],[2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 3
[[3,3],[2]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[[4,3],[3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 2
[[2,2,1],[1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => 2
[[3,3,1],[2,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 2
[[3,2,1],[2]] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[[4,3,1],[3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[2,2,2],[1,1]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1
[[3,3,2],[2,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[3,2,2],[2,1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 2
[[4,3,2],[3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[1,1,1,1],[]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1
[[2,2,2,1],[1,1,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 2
[[2,2,1,1],[1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 2
[[3,3,2,1],[2,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[2,1,1,1],[1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 2
[[3,2,2,1],[2,1,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[3,2,1,1],[2,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 3
[[4,3,2,1],[3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[5],[]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[4,1],[]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 2
[[5,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[[3,2],[]] => [3,2] => [1,1,0,0,1,0,1,0] => 2
[[4,2],[1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 2
[[5,2],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[[3,1,1],[]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 2
[[4,2,1],[1,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 3
[[4,1,1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 2
[[5,2,1],[2,1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[[3,3],[1]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[[4,3],[2]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 2
[[5,3],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[2,2,1],[]] => [2,2,1] => [1,0,1,0,1,1,0,0] => 2
[[3,3,1],[1,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 2
[[3,2,1],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[[4,3,1],[2,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[4,2,1],[2]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 3
[[5,3,1],[3,1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[[3,2,2],[1,1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 2
[[4,3,2],[2,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[4,2,2],[2,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[[5,3,2],[3,2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[2,1,1,1],[]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 2
[[3,2,2,1],[1,1,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[3,2,1,1],[1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 3
[[4,3,2,1],[2,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[3,1,1,1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[[4,2,2,1],[2,1,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[[4,2,1,1],[2,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 3
[[5,3,2,1],[3,2,1]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[4,4],[3]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[5,4],[4]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[3,3,1],[2]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 2
[[4,4,1],[3,1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[4,3,1],[3]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[5,4,1],[4,1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[[2,2,2],[1]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1
[[3,3,2],[2,1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[4,4,2],[3,2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[3,2,2],[2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 2
[[4,3,2],[3,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[5,4,2],[4,2]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[2,2,1,1],[1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 2
[[3,3,2,1],[2,1,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[3,3,1,1],[2,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[[4,4,2,1],[3,2,1]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[3,2,1,1],[2]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 3
[[4,3,2,1],[3,1,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[4,3,1,1],[3,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[[5,4,2,1],[4,2,1]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[3,3,3],[2,2]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[4,4,3],[3,3]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[4,3,3],[3,2]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[5,4,3],[4,3]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[2,2,2,1],[1,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 2
[[3,3,3,1],[2,2,1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[3,3,2,1],[2,2]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[4,4,3,1],[3,3,1]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[3,2,2,1],[2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
>>> Load all 1286 entries. <<<[[4,3,3,1],[3,2,1]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[4,3,2,1],[3,2]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[5,4,3,1],[4,3,1]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[2,2,2,2],[1,1,1]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[3,3,3,2],[2,2,2]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[3,3,2,2],[2,2,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,3,2],[3,3,2]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[3,2,2,2],[2,1,1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[4,3,3,2],[3,2,2]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[4,3,2,2],[3,2,1]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[5,4,3,2],[4,3,2]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[1,1,1,1,1],[]] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[2,2,2,2,1],[1,1,1,1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[2,2,2,1,1],[1,1,1]] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,3,2,1],[2,2,2,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[2,2,1,1,1],[1,1]] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[3,3,2,2,1],[2,2,1,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[3,3,2,1,1],[2,2,1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1],[3,3,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[2,1,1,1,1],[1]] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[[3,2,2,2,1],[2,1,1,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[3,2,2,1,1],[2,1,1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,2,1],[3,2,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[3,2,1,1,1],[2,1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[4,3,2,2,1],[3,2,1,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[4,3,2,1,1],[3,2,1]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[4,3,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[6],[]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[5,1],[]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[[6,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[[4,2],[]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 2
[[5,2],[1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[[6,2],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[[4,1,1],[]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 2
[[5,2,1],[1,1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[[5,1,1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[[6,2,1],[2,1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3
[[3,3],[]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[[4,3],[1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 2
[[5,3],[2]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[6,3],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[[3,2,1],[]] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[[4,3,1],[1,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[4,2,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 3
[[5,3,1],[2,1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[[5,2,1],[2]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[[6,3,1],[3,1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[[4,2,2],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[[5,3,2],[2,2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[5,2,2],[2,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[[6,3,2],[3,2]] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[[3,1,1,1],[]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[[4,2,2,1],[1,1,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[[4,2,1,1],[1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 3
[[5,3,2,1],[2,2,1]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[4,1,1,1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[[5,2,2,1],[2,1,1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[[5,2,1,1],[2,1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[[6,3,2,1],[3,2,1]] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[[4,4],[2]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[5,4],[3]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[6,4],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[[3,3,1],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 2
[[4,4,1],[2,1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[4,3,1],[2]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[5,4,1],[3,1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[[5,3,1],[3]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[[6,4,1],[4,1]] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[[2,2,2],[]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1
[[3,3,2],[1,1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[4,4,2],[2,2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[3,2,2],[1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 2
[[4,3,2],[2,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[5,4,2],[3,2]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[4,2,2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[[5,3,2],[3,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[6,4,2],[4,2]] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[[2,2,1,1],[]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 2
[[3,3,2,1],[1,1,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[3,3,1,1],[1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[[4,4,2,1],[2,2,1]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[3,2,1,1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 3
[[4,3,2,1],[2,1,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[4,3,1,1],[2,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[[5,4,2,1],[3,2,1]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[4,2,1,1],[2]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 3
[[5,3,2,1],[3,1,1]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[5,3,1,1],[3,1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[[6,4,2,1],[4,2,1]] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[[4,3,3],[2,2]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[5,4,3],[3,3]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[5,3,3],[3,2]] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[6,4,3],[4,3]] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3
[[3,2,2,1],[1,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[4,3,3,1],[2,2,1]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[4,3,2,1],[2,2]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[5,4,3,1],[3,3,1]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[4,2,2,1],[2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[[5,3,3,1],[3,2,1]] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[[5,3,2,1],[3,2]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[6,4,3,1],[4,3,1]] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[[3,2,2,2],[1,1,1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[4,3,3,2],[2,2,2]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[4,3,2,2],[2,2,1]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[5,4,3,2],[3,3,2]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[4,2,2,2],[2,1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[[5,3,3,2],[3,2,2]] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[[5,3,2,2],[3,2,1]] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[[6,4,3,2],[4,3,2]] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[[2,1,1,1,1],[]] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[[3,2,2,2,1],[1,1,1,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[3,2,2,1,1],[1,1,1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,2,1],[2,2,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[3,2,1,1,1],[1,1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[4,3,2,2,1],[2,2,1,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[4,3,2,1,1],[2,2,1]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[3,3,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[3,1,1,1,1],[1]] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[[4,2,2,2,1],[2,1,1,1]] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[4,2,2,1,1],[2,1,1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[[5,3,3,2,1],[3,2,2,1]] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[[4,2,1,1,1],[2,1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[5,3,2,2,1],[3,2,1,1]] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[[5,3,2,1,1],[3,2,1]] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[6,4,3,2,1],[4,3,2,1]] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[[5,5],[4]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[6,5],[5]] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[[4,4,1],[3]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[5,5,1],[4,1]] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[[5,4,1],[4]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[[6,5,1],[5,1]] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[[3,3,2],[2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[4,4,2],[3,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[5,5,2],[4,2]] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[[4,3,2],[3]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[5,4,2],[4,1]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[6,5,2],[5,2]] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[[3,3,1,1],[2]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[[4,4,2,1],[3,1,1]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[4,4,1,1],[3,1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[[5,5,2,1],[4,2,1]] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[[4,3,1,1],[3]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[[5,4,2,1],[4,1,1]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[5,4,1,1],[4,1]] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[[6,5,2,1],[5,2,1]] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[[3,3,3],[2,1]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[4,4,3],[3,2]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[5,5,3],[4,3]] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[4,3,3],[3,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[5,4,3],[4,2]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[6,5,3],[5,3]] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[[2,2,2,1],[1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 2
[[3,3,3,1],[2,1,1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[3,3,2,1],[2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[4,4,3,1],[3,2,1]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[4,4,2,1],[3,2]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[5,5,3,1],[4,3,1]] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3
[[3,2,2,1],[2]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[4,3,3,1],[3,1,1]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[4,3,2,1],[3,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[5,4,3,1],[4,2,1]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[5,4,2,1],[4,2]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[6,5,3,1],[5,3,1]] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4
[[3,3,2,2],[2,1,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,3,2],[3,2,2]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[4,4,2,2],[3,2,1]] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[5,5,3,2],[4,3,2]] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[[4,3,2,2],[3,1,1]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[5,4,3,2],[4,2,2]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[5,4,2,2],[4,2,1]] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[6,5,3,2],[5,3,2]] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[[2,2,1,1,1],[1]] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[3,3,2,2,1],[2,1,1,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[3,3,2,1,1],[2,1,1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1],[3,2,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[3,3,1,1,1],[2,1]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,2,2,1],[3,2,1,1]] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[[4,4,2,1,1],[3,2,1]] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[[5,5,3,2,1],[4,3,2,1]] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[[3,2,1,1,1],[2]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[4,3,2,2,1],[3,1,1,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[4,3,2,1,1],[3,1,1]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[4,2,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[4,3,1,1,1],[3,1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[5,4,2,2,1],[4,2,1,1]] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[[5,4,2,1,1],[4,2,1]] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[[6,5,3,2,1],[5,3,2,1]] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[[4,4,4],[3,3]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[5,5,4],[4,4]] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[[5,4,4],[4,3]] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[[6,5,4],[5,4]] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[[3,3,3,1],[2,2]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[4,4,4,1],[3,3,1]] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[[4,4,3,1],[3,3]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[5,5,4,1],[4,4,1]] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[[4,3,3,1],[3,2]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[5,4,4,1],[4,3,1]] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[[5,4,3,1],[4,3]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[6,5,4,1],[5,4,1]] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[[2,2,2,2],[1,1]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[3,3,3,2],[2,2,1]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[4,4,4,2],[3,3,2]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[3,3,2,2],[2,2]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,3,2],[3,3,1]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[5,5,4,2],[4,4,2]] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[[3,2,2,2],[2,1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[4,3,3,2],[3,2,1]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[5,4,4,2],[4,3,2]] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[[4,3,2,2],[3,2]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[5,4,3,2],[4,3,1]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[6,5,4,2],[5,4,2]] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[[2,2,2,1,1],[1,1]] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,3,2,1],[2,2,1,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[3,3,3,1,1],[2,2,1]] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[[4,4,4,2,1],[3,3,2,1]] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[[3,3,2,1,1],[2,2]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1],[3,3,1,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[4,4,3,1,1],[3,3,1]] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[[5,5,4,2,1],[4,4,2,1]] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[[3,2,2,1,1],[2,1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,2,1],[3,2,1,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[4,3,3,1,1],[3,2,1]] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[[5,4,4,2,1],[4,3,2,1]] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[[4,3,2,1,1],[3,2]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[4,3,1,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[5,4,3,1,1],[4,3,1]] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[[6,5,4,2,1],[5,4,2,1]] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[[3,3,3,3],[2,2,2]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[4,4,4,3],[3,3,3]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[4,4,3,3],[3,3,2]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[5,5,4,3],[4,4,3]] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[[4,3,3,3],[3,2,2]] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[[5,4,4,3],[4,3,3]] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[[5,4,3,3],[4,3,2]] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[[6,5,4,3],[5,4,3]] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[[2,2,2,2,1],[1,1,1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[3,3,3,3,1],[2,2,2,1]] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[[3,3,3,2,1],[2,2,2]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[4,4,4,3,1],[3,3,3,1]] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[[3,3,2,2,1],[2,2,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[4,4,3,3,1],[3,3,2,1]] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1],[3,3,2]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[5,5,4,3,1],[4,4,3,1]] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[[3,2,2,2,1],[2,1,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[4,3,3,3,1],[3,2,2,1]] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[[4,3,3,2,1],[3,2,2]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[5,4,4,3,1],[4,3,3,1]] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[[4,3,2,2,1],[3,2,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,3,1],[4,3,2,1]] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[4,3,2]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[6,5,4,3,1],[5,4,3,1]] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[[2,2,2,2,2],[1,1,1,1]] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[3,3,3,3,2],[2,2,2,2]] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[[3,3,3,2,2],[2,2,2,1]] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,4,3,2],[3,3,3,2]] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[[3,3,2,2,2],[2,2,1,1]] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[[4,4,3,3,2],[3,3,2,2]] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[[4,4,3,2,2],[3,3,2,1]] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[[5,5,4,3,2],[4,4,3,2]] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[[3,2,2,2,2],[2,1,1,1]] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[[4,3,3,3,2],[3,2,2,2]] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[[4,3,3,2,2],[3,2,2,1]] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[[5,4,4,3,2],[4,3,3,2]] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[[4,3,2,2,2],[3,2,1,1]] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[[5,4,3,3,2],[4,3,2,2]] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,2,2],[4,3,2,1]] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[[6,5,4,3,2],[5,4,3,2]] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[[1,1,1,1,1,1],[]] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[2,2,2,2,2,1],[1,1,1,1,1]] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[2,2,2,2,1,1],[1,1,1,1]] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[3,3,3,3,2,1],[2,2,2,2,1]] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[[2,2,2,1,1,1],[1,1,1]] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[[3,3,3,2,2,1],[2,2,2,1,1]] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[3,3,3,2,1,1],[2,2,2,1]] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[4,4,4,3,2,1],[3,3,3,2,1]] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[[2,2,1,1,1,1],[1,1]] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[[3,3,2,2,2,1],[2,2,1,1,1]] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[3,3,2,2,1,1],[2,2,1,1]] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,4,3,3,2,1],[3,3,2,2,1]] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[[3,3,2,1,1,1],[2,2,1]] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[4,4,3,2,2,1],[3,3,2,1,1]] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[[4,4,3,2,1,1],[3,3,2,1]] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[5,5,4,3,2,1],[4,4,3,2,1]] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[2,1,1,1,1,1],[1]] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[[3,2,2,2,2,1],[2,1,1,1,1]] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[3,2,2,2,1,1],[2,1,1,1]] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[4,3,3,3,2,1],[3,2,2,2,1]] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[[3,2,2,1,1,1],[2,1,1]] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[4,3,3,2,2,1],[3,2,2,1,1]] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4
[[4,3,3,2,1,1],[3,2,2,1]] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[5,4,4,3,2,1],[4,3,3,2,1]] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[3,2,1,1,1,1],[2,1]] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[[4,3,2,2,2,1],[3,2,1,1,1]] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[[4,3,2,2,1,1],[3,2,1,1]] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,4,3,3,2,1],[4,3,2,2,1]] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[[4,3,2,1,1,1],[3,2,1]] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[[5,4,3,2,2,1],[4,3,2,1,1]] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[5,4,3,2,1,1],[4,3,2,1]] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[6,5,4,3,2,1],[5,4,3,2,1]] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[6,1],[]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[[5,2],[]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[[6,2],[1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[[5,1,1],[]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[[6,2,1],[1,1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3
[[6,1,1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[[4,3],[]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 2
[[5,3],[1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[6,3],[2]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[[4,2,1],[]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 3
[[5,3,1],[1,1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[[5,2,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[[6,3,1],[2,1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[[6,2,1],[2]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3
[[5,2,2],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[[6,3,2],[2,2]] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[[6,2,2],[2,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[[4,1,1,1],[]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[[5,2,2,1],[1,1,1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[[5,2,1,1],[1,1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[[6,3,2,1],[2,2,1]] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[[5,1,1,1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[[6,2,2,1],[2,1,1]] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3
[[6,2,1,1],[2,1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[[4,4],[1]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[5,4],[2]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[6,4],[3]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[[3,3,1],[]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 2
[[4,4,1],[1,1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[4,3,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[5,4,1],[2,1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[[5,3,1],[2]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[[6,4,1],[3,1]] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[[6,3,1],[3]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[[3,2,2],[]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 2
[[4,3,2],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[5,4,2],[2,2]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[4,2,2],[1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[[5,3,2],[2,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[6,4,2],[3,2]] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[[5,2,2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[[6,3,2],[3,1]] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[[3,2,1,1],[]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 3
[[4,3,2,1],[1,1,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[4,3,1,1],[1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[[5,4,2,1],[2,2,1]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[4,2,1,1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 3
[[5,3,2,1],[2,1,1]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[5,3,1,1],[2,1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[[6,4,2,1],[3,2,1]] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[[5,2,1,1],[2]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[[6,3,2,1],[3,1,1]] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[[6,3,1,1],[3,1]] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3
[[5,3,3],[2,2]] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[6,4,3],[3,3]] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3
[[6,3,3],[3,2]] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[[4,2,2,1],[1,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[[5,3,3,1],[2,2,1]] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[[5,3,2,1],[2,2]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[6,4,3,1],[3,3,1]] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[[5,2,2,1],[2,1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[[6,3,3,1],[3,2,1]] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 3
[[6,3,2,1],[3,2]] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[[4,2,2,2],[1,1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[[5,3,3,2],[2,2,2]] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[[5,3,2,2],[2,2,1]] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[[6,4,3,2],[3,3,2]] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[[5,2,2,2],[2,1,1]] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[6,3,3,2],[3,2,2]] => [6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 3
[[6,3,2,2],[3,2,1]] => [6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[[3,1,1,1,1],[]] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[[4,2,2,2,1],[1,1,1,1]] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[4,2,2,1,1],[1,1,1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[[5,3,3,2,1],[2,2,2,1]] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[[4,2,1,1,1],[1,1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[5,3,2,2,1],[2,2,1,1]] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[[5,3,2,1,1],[2,2,1]] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[6,4,3,2,1],[3,3,2,1]] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[[4,1,1,1,1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[[5,2,2,2,1],[2,1,1,1]] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[[5,2,2,1,1],[2,1,1]] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[[6,3,3,2,1],[3,2,2,1]] => [6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 4
[[5,2,1,1,1],[2,1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3
[[6,3,2,2,1],[3,2,1,1]] => [6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 4
[[6,3,2,1,1],[3,2,1]] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4
[[5,5],[3]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[6,5],[4]] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[[4,4,1],[2]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[5,5,1],[3,1]] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[[5,4,1],[3]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[[6,5,1],[4,1]] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[[6,4,1],[4]] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[[3,3,2],[1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[4,4,2],[2,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[5,5,2],[3,2]] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[[4,3,2],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[5,4,2],[3,1]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[6,5,2],[4,2]] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[[5,3,2],[3]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[6,4,2],[4,1]] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[[3,3,1,1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[[4,4,2,1],[2,1,1]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[4,4,1,1],[2,1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[[5,5,2,1],[3,2,1]] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[[4,3,1,1],[2]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[[5,4,2,1],[3,1,1]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[5,4,1,1],[3,1]] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[[6,5,2,1],[4,2,1]] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[[5,3,1,1],[3]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[[6,4,2,1],[4,1,1]] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[[6,4,1,1],[4,1]] => [6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3
[[3,3,3],[1,1]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[4,4,3],[2,2]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[5,5,3],[3,3]] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[4,3,3],[2,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[5,4,3],[3,2]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[6,5,3],[4,3]] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[[5,3,3],[3,1]] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[6,4,3],[4,2]] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3
[[2,2,2,1],[]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 2
[[3,3,3,1],[1,1,1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[3,3,2,1],[1,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[4,4,3,1],[2,2,1]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[4,4,2,1],[2,2]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[5,5,3,1],[3,3,1]] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3
[[3,2,2,1],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[4,3,3,1],[2,1,1]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[4,3,2,1],[2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[5,4,3,1],[3,2,1]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[5,4,2,1],[3,2]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[6,5,3,1],[4,3,1]] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4
[[4,2,2,1],[2]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[[5,3,3,1],[3,1,1]] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[[5,3,2,1],[3,1]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[6,4,3,1],[4,2,1]] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[[6,4,2,1],[4,2]] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[[3,3,2,2],[1,1,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,3,2],[2,2,2]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[4,4,2,2],[2,2,1]] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[5,5,3,2],[3,3,2]] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[[4,3,2,2],[2,1,1]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[5,4,3,2],[3,2,2]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[5,4,2,2],[3,2,1]] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[6,5,3,2],[4,3,2]] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[[5,3,2,2],[3,1,1]] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[[6,4,3,2],[4,2,2]] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[[6,4,2,2],[4,2,1]] => [6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[[2,2,1,1,1],[]] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[3,3,2,2,1],[1,1,1,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[3,3,2,1,1],[1,1,1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1],[2,2,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[3,3,1,1,1],[1,1]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,2,2,1],[2,2,1,1]] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[[4,4,2,1,1],[2,2,1]] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[[5,5,3,2,1],[3,3,2,1]] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[[3,2,1,1,1],[1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[4,3,2,2,1],[2,1,1,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[4,3,2,1,1],[2,1,1]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[3,2,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[4,3,1,1,1],[2,1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[5,4,2,2,1],[3,2,1,1]] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[[5,4,2,1,1],[3,2,1]] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[[6,5,3,2,1],[4,3,2,1]] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[[4,2,1,1,1],[2]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[5,3,2,2,1],[3,1,1,1]] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[[5,3,2,1,1],[3,1,1]] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[6,4,3,2,1],[4,2,2,1]] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[[5,3,1,1,1],[3,1]] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[[6,4,2,2,1],[4,2,1,1]] => [6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4
[[6,4,2,1,1],[4,2,1]] => [6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4
[[5,4,4],[3,3]] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[[6,5,4],[4,4]] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[[6,4,4],[4,3]] => [6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[4,3,3,1],[2,2]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[5,4,4,1],[3,3,1]] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[[5,4,3,1],[3,3]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[6,5,4,1],[4,4,1]] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[[5,3,3,1],[3,2]] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[[6,4,4,1],[4,3,1]] => [6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 3
[[6,4,3,1],[4,3]] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[[3,2,2,2],[1,1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[4,3,3,2],[2,2,1]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[5,4,4,2],[3,3,2]] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[[4,3,2,2],[2,2]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[5,4,3,2],[3,3,1]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[6,5,4,2],[4,4,2]] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[[4,2,2,2],[2,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[[5,3,3,2],[3,2,1]] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[[6,4,4,2],[4,3,2]] => [6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[[5,3,2,2],[3,2]] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[[6,4,3,2],[4,3,1]] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[[3,2,2,1,1],[1,1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,2,1],[2,2,1,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[4,3,3,1,1],[2,2,1]] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[[5,4,4,2,1],[3,3,2,1]] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[[4,3,2,1,1],[2,2]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[3,3,1,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[5,4,3,1,1],[3,3,1]] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[[6,5,4,2,1],[4,4,2,1]] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[[4,2,2,1,1],[2,1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[[5,3,3,2,1],[3,2,1,1]] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[[5,3,3,1,1],[3,2,1]] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[[6,4,4,2,1],[4,3,2,1]] => [6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[[5,3,2,1,1],[3,2]] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[6,4,3,2,1],[4,3,1,1]] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[[6,4,3,1,1],[4,3,1]] => [6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4
[[4,3,3,3],[2,2,2]] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[[5,4,4,3],[3,3,3]] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[[5,4,3,3],[3,3,2]] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[[6,5,4,3],[4,4,3]] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[[5,3,3,3],[3,2,2]] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[[6,4,4,3],[4,3,3]] => [6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
[[6,4,3,3],[4,3,2]] => [6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3
[[3,2,2,2,1],[1,1,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[4,3,3,3,1],[2,2,2,1]] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[[4,3,3,2,1],[2,2,2]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[5,4,4,3,1],[3,3,3,1]] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[[4,3,2,2,1],[2,2,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,3,1],[3,3,2,1]] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[3,3,2]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[6,5,4,3,1],[4,4,3,1]] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[[4,2,2,2,1],[2,1,1]] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[5,3,3,3,1],[3,2,2,1]] => [5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 3
[[5,3,3,2,1],[3,2,2]] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[[6,4,4,3,1],[4,3,3,1]] => [6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 4
[[5,3,2,2,1],[3,2,1]] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[[6,4,3,3,1],[4,3,2,1]] => [6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[[6,4,3,2,1],[4,3,2]] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[[3,2,2,2,2],[1,1,1,1]] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[[4,3,3,3,2],[2,2,2,2]] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[[4,3,3,2,2],[2,2,2,1]] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[[5,4,4,3,2],[3,3,3,2]] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[[4,3,2,2,2],[2,2,1,1]] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[[5,4,3,3,2],[3,3,2,2]] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,2,2],[3,3,2,1]] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[[6,5,4,3,2],[4,4,3,2]] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[[4,2,2,2,2],[2,1,1,1]] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[[5,3,3,3,2],[3,2,2,2]] => [5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[[5,3,3,2,2],[3,2,2,1]] => [5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 3
[[6,4,4,3,2],[4,3,3,2]] => [6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
[[5,3,2,2,2],[3,2,1,1]] => [5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[[6,4,3,3,2],[4,3,2,2]] => [6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[[6,4,3,2,2],[4,3,2,1]] => [6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[[2,1,1,1,1,1],[]] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[[3,2,2,2,2,1],[1,1,1,1,1]] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[3,2,2,2,1,1],[1,1,1,1]] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[4,3,3,3,2,1],[2,2,2,2,1]] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[[3,2,2,1,1,1],[1,1,1]] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[4,3,3,2,2,1],[2,2,2,1,1]] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4
[[4,3,3,2,1,1],[2,2,2,1]] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[5,4,4,3,2,1],[3,3,3,2,1]] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[3,2,1,1,1,1],[1,1]] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[[4,3,2,2,2,1],[2,2,1,1,1]] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[[4,3,2,2,1,1],[2,2,1,1]] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,4,3,3,2,1],[3,3,2,2,1]] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[[4,3,2,1,1,1],[2,2,1]] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[[5,4,3,2,2,1],[3,3,2,1,1]] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[5,4,3,2,1,1],[3,3,2,1]] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[6,5,4,3,2,1],[4,4,3,2,1]] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[3,1,1,1,1,1],[1]] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[[4,2,2,2,2,1],[2,1,1,1,1]] => [4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3
[[4,2,2,2,1,1],[2,1,1,1]] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[5,3,3,3,2,1],[3,2,2,2,1]] => [5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[[4,2,2,1,1,1],[2,1,1]] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[[5,3,3,2,2,1],[3,2,2,1,1]] => [5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[[5,3,3,2,1,1],[3,2,2,1]] => [5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4
[[6,4,4,3,2,1],[4,3,3,2,1]] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5
[[4,2,1,1,1,1],[2,1]] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3
[[5,3,2,2,2,1],[3,2,1,1,1]] => [5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 4
[[5,3,2,2,1,1],[3,2,1,1]] => [5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 4
[[6,4,3,3,2,1],[4,3,2,2,1]] => [6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5
[[5,3,2,1,1,1],[3,2,1]] => [5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[6,4,3,2,2,1],[4,3,2,1,1]] => [6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 5
[[6,4,3,2,1,1],[4,3,2,1]] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[[5,5,1],[4]] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[[6,5,1],[5]] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[[4,4,2],[3]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[5,5,2],[4,1]] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[[5,4,2],[4]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[6,5,2],[5,1]] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[[4,4,1,1],[3]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[[5,5,2,1],[4,1,1]] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[[5,5,1,1],[4,1]] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 2
[[5,4,1,1],[4]] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[[6,5,2,1],[5,1,1]] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[[6,5,1,1],[5,1]] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[[3,3,3],[2]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[4,4,3],[3,1]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[5,5,3],[4,2]] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[4,3,3],[3]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[5,4,3],[4,1]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[6,5,3],[5,2]] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[[3,3,2,1],[2]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[4,4,3,1],[3,1,1]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[4,4,2,1],[3,1]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[5,5,3,1],[4,2,1]] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3
[[5,5,2,1],[4,2]] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[[4,3,2,1],[3]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[5,4,3,1],[4,1,1]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[5,4,2,1],[4,1]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[6,5,3,1],[5,2,1]] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4
[[6,5,2,1],[5,2]] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[[4,4,2,2],[3,1,1]] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[5,5,3,2],[4,2,2]] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[[5,5,2,2],[4,2,1]] => [5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[[5,4,2,2],[4,1,1]] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[6,5,3,2],[5,2,2]] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[[6,5,2,2],[5,2,1]] => [6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3
[[3,3,1,1,1],[2]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,2,2,1],[3,1,1,1]] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[[4,4,2,1,1],[3,1,1]] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[[5,5,3,2,1],[4,2,2,1]] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[[4,4,1,1,1],[3,1]] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[[5,5,2,2,1],[4,2,1,1]] => [5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 3
[[5,5,2,1,1],[4,2,1]] => [5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 3
[[4,3,1,1,1],[3]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[5,4,2,2,1],[4,1,1,1]] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[[5,4,2,1,1],[4,1,1]] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[[6,5,3,2,1],[5,2,2,1]] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[[5,4,1,1,1],[4,1]] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[[6,5,2,2,1],[5,2,1,1]] => [6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 4
[[6,5,2,1,1],[5,2,1]] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4
[[4,4,4],[3,2]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[5,5,4],[4,3]] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[[5,4,4],[4,2]] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[[6,5,4],[5,3]] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[[3,3,3,1],[2,1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[4,4,4,1],[3,2,1]] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[[4,4,3,1],[3,2]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[5,5,4,1],[4,3,1]] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[[5,5,3,1],[4,3]] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3
[[4,3,3,1],[3,1]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[5,4,4,1],[4,2,1]] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[[5,4,3,1],[4,2]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[6,5,4,1],[5,3,1]] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[[6,5,3,1],[5,3]] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4
[[2,2,2,2],[1]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[3,3,3,2],[2,1,1]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[4,4,4,2],[3,2,2]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[3,3,2,2],[2,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,3,2],[3,2,1]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[5,5,4,2],[4,3,2]] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[[4,4,2,2],[3,2]] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[5,5,3,2],[4,3,1]] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[[3,2,2,2],[2]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[4,3,3,2],[3,1,1]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[5,4,4,2],[4,2,2]] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[[4,3,2,2],[3,1]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[5,4,3,2],[4,2,1]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[6,5,4,2],[5,3,2]] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[[5,4,2,2],[4,2]] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[6,5,3,2],[5,3,1]] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[[2,2,2,1,1],[1]] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,3,2,1],[2,1,1,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[3,3,3,1,1],[2,1,1]] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[[4,4,4,2,1],[3,2,2,1]] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[[3,3,2,1,1],[2,1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1],[3,2,1,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[4,4,3,1,1],[3,2,1]] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[[5,5,4,2,1],[4,3,2,1]] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[[4,4,2,1,1],[3,2]] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[[5,5,3,2,1],[4,3,1,1]] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[[5,5,3,1,1],[4,3,1]] => [5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 3
[[3,2,2,1,1],[2]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,2,1],[3,1,1,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[4,3,3,1,1],[3,1,1]] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[[5,4,4,2,1],[4,2,2,1]] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[[4,3,2,1,1],[3,1]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[4,2,1,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[5,4,3,1,1],[4,2,1]] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[[6,5,4,2,1],[5,3,2,1]] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[[5,4,2,1,1],[4,2]] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[[6,5,3,2,1],[5,3,1,1]] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[[6,5,3,1,1],[5,3,1]] => [6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[[4,4,3,3],[3,2,2]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[5,5,4,3],[4,3,3]] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[[5,5,3,3],[4,3,2]] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[[5,4,3,3],[4,2,2]] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[[6,5,4,3],[5,3,3]] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[[6,5,3,3],[5,3,2]] => [6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[[3,3,2,2,1],[2,1,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[4,4,3,3,1],[3,2,2,1]] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1],[3,2,2]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[5,5,4,3,1],[4,3,3,1]] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[[4,4,2,2,1],[3,2,1]] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[[5,5,3,3,1],[4,3,2,1]] => [5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 3
[[5,5,3,2,1],[4,3,2]] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[[4,3,2,2,1],[3,1,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,3,1],[4,2,2,1]] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[4,2,2]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[6,5,4,3,1],[5,3,3,1]] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[[5,4,2,2,1],[4,2,1]] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[[6,5,3,3,1],[5,3,2,1]] => [6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[[6,5,3,2,1],[5,3,2]] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[[3,3,2,2,2],[2,1,1,1]] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[[4,4,3,3,2],[3,2,2,2]] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[[4,4,3,2,2],[3,2,2,1]] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[[5,5,4,3,2],[4,3,3,2]] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[[4,4,2,2,2],[3,2,1,1]] => [4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[[5,5,3,3,2],[4,3,2,2]] => [5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[[5,5,3,2,2],[4,3,2,1]] => [5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 3
[[4,3,2,2,2],[3,1,1,1]] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[[5,4,3,3,2],[4,2,2,2]] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,2,2],[4,2,2,1]] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[[6,5,4,3,2],[5,3,3,2]] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[[5,4,2,2,2],[4,2,1,1]] => [5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3
[[6,5,3,3,2],[5,3,2,2]] => [6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4
[[6,5,3,2,2],[5,3,2,1]] => [6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[[2,2,1,1,1,1],[1]] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[[3,3,2,2,2,1],[2,1,1,1,1]] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[3,3,2,2,1,1],[2,1,1,1]] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,4,3,3,2,1],[3,2,2,2,1]] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[[3,3,2,1,1,1],[2,1,1]] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[4,4,3,2,2,1],[3,2,2,1,1]] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[[4,4,3,2,1,1],[3,2,2,1]] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[5,5,4,3,2,1],[4,3,3,2,1]] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[3,3,1,1,1,1],[2,1]] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[[4,4,2,2,2,1],[3,2,1,1,1]] => [4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[[4,4,2,2,1,1],[3,2,1,1]] => [4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3
[[5,5,3,3,2,1],[4,3,2,2,1]] => [5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4
[[4,4,2,1,1,1],[3,2,1]] => [4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[5,5,3,2,2,1],[4,3,2,1,1]] => [5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[[5,5,3,2,1,1],[4,3,2,1]] => [5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[[3,2,1,1,1,1],[2]] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[[4,3,2,2,2,1],[3,1,1,1,1]] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[[4,3,2,2,1,1],[3,1,1,1]] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,4,3,3,2,1],[4,2,2,2,1]] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[[4,3,2,1,1,1],[3,1,1]] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[[5,4,3,2,2,1],[4,2,2,1,1]] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[5,4,3,2,1,1],[4,2,2,1]] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[6,5,4,3,2,1],[5,3,3,2,1]] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[4,3,1,1,1,1],[3,1]] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3
[[5,4,2,2,2,1],[4,2,1,1,1]] => [5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[[5,4,2,2,1,1],[4,2,1,1]] => [5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4
[[6,5,3,3,2,1],[5,3,2,2,1]] => [6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 5
[[5,4,2,1,1,1],[4,2,1]] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[6,5,3,2,2,1],[5,3,2,1,1]] => [6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5
[[6,5,3,2,1,1],[5,3,2,1]] => [6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5
[[4,4,4,1],[3,3]] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[[5,5,4,1],[4,4]] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[[5,4,4,1],[4,3]] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[[6,5,4,1],[5,4]] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[[3,3,3,2],[2,2]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[4,4,4,2],[3,3,1]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[4,4,3,2],[3,3]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[5,5,4,2],[4,4,1]] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[[4,3,3,2],[3,2]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[5,4,4,2],[4,3,1]] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[[5,4,3,2],[4,3]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[6,5,4,2],[5,4,1]] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[[3,3,3,1,1],[2,2]] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[[4,4,4,2,1],[3,3,1,1]] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[[4,4,4,1,1],[3,3,1]] => [4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 2
[[4,4,3,1,1],[3,3]] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[[5,5,4,2,1],[4,4,1,1]] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[[5,5,4,1,1],[4,4,1]] => [5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 3
[[4,3,3,1,1],[3,2]] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[[5,4,4,2,1],[4,3,1,1]] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[[5,4,4,1,1],[4,3,1]] => [5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 3
[[5,4,3,1,1],[4,3]] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[[6,5,4,2,1],[5,4,1,1]] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[[6,5,4,1,1],[5,4,1]] => [6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[[3,3,3,3],[2,2,1]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[4,4,4,3],[3,3,2]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[4,4,3,3],[3,3,1]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[5,5,4,3],[4,4,2]] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[[4,3,3,3],[3,2,1]] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[[5,4,4,3],[4,3,2]] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[[5,4,3,3],[4,3,1]] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[[6,5,4,3],[5,4,2]] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[[2,2,2,2,1],[1,1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[3,3,3,3,1],[2,2,1,1]] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[[3,3,3,2,1],[2,2,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[4,4,4,3,1],[3,3,2,1]] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[[4,4,4,2,1],[3,3,2]] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[[3,3,2,2,1],[2,2]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[4,4,3,3,1],[3,3,1,1]] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1],[3,3,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[5,5,4,3,1],[4,4,2,1]] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[[5,5,4,2,1],[4,4,2]] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[[3,2,2,2,1],[2,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[4,3,3,3,1],[3,2,1,1]] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[[4,3,3,2,1],[3,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[5,4,4,3,1],[4,3,2,1]] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[[5,4,4,2,1],[4,3,2]] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[[4,3,2,2,1],[3,2]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,3,1],[4,3,1,1]] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[4,3,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[6,5,4,3,1],[5,4,2,1]] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[[6,5,4,2,1],[5,4,2]] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[[3,3,3,2,2],[2,2,1,1]] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,4,3,2],[3,3,2,2]] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[[4,4,4,2,2],[3,3,2,1]] => [4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[[4,4,3,2,2],[3,3,1,1]] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[[5,5,4,3,2],[4,4,2,2]] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[[5,5,4,2,2],[4,4,2,1]] => [5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[[4,3,3,2,2],[3,2,1,1]] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[[5,4,4,3,2],[4,3,2,2]] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[[5,4,4,2,2],[4,3,2,1]] => [5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3
[[5,4,3,2,2],[4,3,1,1]] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[[6,5,4,3,2],[5,4,2,2]] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[[6,5,4,2,2],[5,4,2,1]] => [6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[[2,2,2,1,1,1],[1,1]] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[[3,3,3,2,2,1],[2,2,1,1,1]] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[3,3,3,2,1,1],[2,2,1,1]] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[4,4,4,3,2,1],[3,3,2,2,1]] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[[3,3,3,1,1,1],[2,2,1]] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[4,4,4,2,2,1],[3,3,2,1,1]] => [4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[[4,4,4,2,1,1],[3,3,2,1]] => [4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[[3,3,2,1,1,1],[2,2]] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[4,4,3,2,2,1],[3,3,1,1,1]] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[[4,4,3,2,1,1],[3,3,1,1]] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[5,5,4,3,2,1],[4,4,2,2,1]] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[4,4,3,1,1,1],[3,3,1]] => [4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[5,5,4,2,2,1],[4,4,2,1,1]] => [5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4
[[5,5,4,2,1,1],[4,4,2,1]] => [5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[[3,2,2,1,1,1],[2,1]] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[4,3,3,2,2,1],[3,2,1,1,1]] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4
[[4,3,3,2,1,1],[3,2,1,1]] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[5,4,4,3,2,1],[4,3,2,2,1]] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[4,3,3,1,1,1],[3,2,1]] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[5,4,4,2,2,1],[4,3,2,1,1]] => [5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[[5,4,4,2,1,1],[4,3,2,1]] => [5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[[4,3,2,1,1,1],[3,2]] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[[5,4,3,2,2,1],[4,3,1,1,1]] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[5,4,3,2,1,1],[4,3,1,1]] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[6,5,4,3,2,1],[5,4,2,2,1]] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[5,4,3,1,1,1],[4,3,1]] => [5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[6,5,4,2,2,1],[5,4,2,1,1]] => [6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 5
[[6,5,4,2,1,1],[5,4,2,1]] => [6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[[3,3,3,3,1],[2,2,2]] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[[4,4,4,3,1],[3,3,3]] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[[4,4,3,3,1],[3,3,2]] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 3
[[5,5,4,3,1],[4,4,3]] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[[4,3,3,3,1],[3,2,2]] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[[5,4,4,3,1],[4,3,3]] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[[5,4,3,3,1],[4,3,2]] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4
[[6,5,4,3,1],[5,4,3]] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[[2,2,2,2,2],[1,1,1]] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[3,3,3,3,2],[2,2,2,1]] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[[3,3,3,2,2],[2,2,2]] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,4,3,2],[3,3,3,1]] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[[3,3,2,2,2],[2,2,1]] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[[4,4,3,3,2],[3,3,2,1]] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[[4,4,3,2,2],[3,3,2]] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[[5,5,4,3,2],[4,4,3,1]] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[[3,2,2,2,2],[2,1,1]] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[[4,3,3,3,2],[3,2,2,1]] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[[4,3,3,2,2],[3,2,2]] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[[5,4,4,3,2],[4,3,3,1]] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[[4,3,2,2,2],[3,2,1]] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[[5,4,3,3,2],[4,3,2,1]] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,2,2],[4,3,2]] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[[6,5,4,3,2],[5,4,3,1]] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[[2,2,2,2,1,1],[1,1,1]] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[3,3,3,3,2,1],[2,2,2,1,1]] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[[3,3,3,3,1,1],[2,2,2,1]] => [3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[3,3,3,2,1,1],[2,2,2]] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[4,4,4,3,2,1],[3,3,3,1,1]] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[[4,4,4,3,1,1],[3,3,3,1]] => [4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[[3,3,2,2,1,1],[2,2,1]] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,4,3,3,2,1],[3,3,2,1,1]] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[[4,4,3,3,1,1],[3,3,2,1]] => [4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1,1],[3,3,2]] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[5,5,4,3,2,1],[4,4,3,1,1]] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[5,5,4,3,1,1],[4,4,3,1]] => [5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4
[[3,2,2,2,1,1],[2,1,1]] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[4,3,3,3,2,1],[3,2,2,1,1]] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[[4,3,3,3,1,1],[3,2,2,1]] => [4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[[4,3,3,2,1,1],[3,2,2]] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[5,4,4,3,2,1],[4,3,3,1,1]] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[5,4,4,3,1,1],[4,3,3,1]] => [5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[[4,3,2,2,1,1],[3,2,1]] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,4,3,3,2,1],[4,3,2,1,1]] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[[5,4,3,3,1,1],[4,3,2,1]] => [5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1,1],[4,3,2]] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[6,5,4,3,2,1],[5,4,3,1,1]] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[6,5,4,3,1,1],[5,4,3,1]] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5
[[2,2,2,2,2,1],[1,1,1,1]] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[3,3,3,3,2,1],[2,2,2,2]] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[[3,3,3,2,2,1],[2,2,2,1]] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[4,4,4,3,2,1],[3,3,3,2]] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[[3,3,2,2,2,1],[2,2,1,1]] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[4,4,3,3,2,1],[3,3,2,2]] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[[4,4,3,2,2,1],[3,3,2,1]] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[[5,5,4,3,2,1],[4,4,3,2]] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[3,2,2,2,2,1],[2,1,1,1]] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[4,3,3,3,2,1],[3,2,2,2]] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[[4,3,3,2,2,1],[3,2,2,1]] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4
[[5,4,4,3,2,1],[4,3,3,2]] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[4,3,2,2,2,1],[3,2,1,1]] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[[5,4,3,3,2,1],[4,3,2,2]] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[[5,4,3,2,2,1],[4,3,2,1]] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[6,5,4,3,2,1],[5,4,3,2]] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[6,2],[]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[[6,1,1],[]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[[5,3],[]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[5,2,1],[]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[[5,1,1,1],[]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[[4,4],[]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[4,3,1],[]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[4,2,2],[]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[[4,2,1,1],[]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 3
[[4,1,1,1,1],[]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[[3,3,2],[]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[3,3,1,1],[]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[[3,2,2,1],[]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[3,2,1,1,1],[]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[3,1,1,1,1,1],[]] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[[2,2,2,2],[]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[2,2,2,1,1],[]] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[[2,2,1,1,1,1],[]] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[[6,3],[]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[[6,2,1],[]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3
[[6,1,1,1],[]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[[5,4],[]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[5,3,1],[]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[[5,2,2],[]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[[5,2,1,1],[]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[[5,1,1,1,1],[]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[[4,4,1],[]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[4,3,2],[]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[4,3,1,1],[]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[[4,2,2,1],[]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[[4,2,1,1,1],[]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[4,1,1,1,1,1],[]] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[[3,3,3],[]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[3,3,2,1],[]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[3,3,1,1,1],[]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[[3,2,2,2],[]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[3,2,2,1,1],[]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[3,2,1,1,1,1],[]] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[[2,2,2,2,1],[]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[2,2,2,1,1,1],[]] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[[6,4],[]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[[6,3,1],[]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[[6,2,2],[]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[[6,2,1,1],[]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[[6,1,1,1,1],[]] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[[5,5],[]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[5,4,1],[]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[[5,3,2],[]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[5,3,1,1],[]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[[5,2,2,1],[]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[[5,2,1,1,1],[]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3
[[5,1,1,1,1,1],[]] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[4,4,2],[]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[4,4,1,1],[]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[[4,3,3],[]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[4,3,2,1],[]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[4,3,1,1,1],[]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[4,2,2,2],[]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[[4,2,2,1,1],[]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[[4,2,1,1,1,1],[]] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3
[[3,3,3,1],[]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[3,3,2,2],[]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[3,3,2,1,1],[]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[3,3,1,1,1,1],[]] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[[3,2,2,2,1],[]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[3,2,2,1,1,1],[]] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[2,2,2,2,2],[]] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[2,2,2,2,1,1],[]] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[6,5],[]] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[[5,5,1],[]] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[[5,4,2],[]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[5,3,3],[]] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[4,4,3],[]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[4,4,2,1],[]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[4,3,3,1],[]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[4,3,2,2],[]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[3,3,3,2],[]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[3,2,2,2,2],[]] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[[5,5,2],[]] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[[5,4,3],[]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[4,4,4],[]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[4,4,3,1],[]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[4,4,2,2],[]] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[4,3,3,2],[]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[3,3,3,3],[]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[3,3,3,2,1],[]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[3,3,2,2,2],[]] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[[5,5,3],[]] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[5,4,4],[]] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[[4,4,4,1],[]] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[[4,4,3,2],[]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[4,3,3,3],[]] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[[3,3,3,3,1],[]] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[[3,3,3,2,2],[]] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[[5,5,4],[]] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[[4,4,4,2],[]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[4,4,3,3],[]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[3,3,3,3,2],[]] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[[5,5,4,1],[]] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[[4,4,4,3],[]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[4,4,4,3,1],[]] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[[3,2,1,1,1,1],[1]] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[[3,2,2,1,1,1],[1,1]] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[3,3,2,1,1,1],[2,1]] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[4,3,1,1,1],[2]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[3,2,2,2,1,1],[1,1,1]] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[3,3,2,2,1,1],[2,1,1]] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[3,3,3,2,1,1],[2,2,1]] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[4,3,2,1,1],[2,1]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[4,4,2,1,1],[3,1]] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[[4,3,3,1,1],[2,2]] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[[4,4,3,1,1],[3,2]] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[[5,3,1,1],[2]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[[3,2,2,2,2,1],[1,1,1,1]] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[3,3,2,2,2,1],[2,1,1,1]] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[3,3,3,2,2,1],[2,2,1,1]] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[4,3,2,2,1],[2,1,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[4,4,2,2,1],[3,1,1]] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[[3,3,3,3,2,1],[2,2,2,1]] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[[4,3,3,2,1],[2,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[4,4,3,2,1],[3,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[5,3,2,1],[2,1]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[4,4,4,2,1],[3,3,1]] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[[5,4,2,1],[3,1]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[4,3,3,3,1],[2,2,2]] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[[4,4,3,3,1],[3,2,2]] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 3
[[5,3,3,1],[2,2]] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[[4,4,4,3,1],[3,3,2]] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[[5,4,3,1],[3,2]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[5,5,3,1],[4,2]] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3
[[5,4,4,1],[3,3]] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[[5,5,4,1],[4,3]] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[[6,4,1],[3]] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[[4,3,2,2,2],[2,1,1,1]] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[[4,4,2,2,2],[3,1,1,1]] => [4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[[4,3,3,2,2],[2,2,1,1]] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[[4,4,3,2,2],[3,2,1,1]] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[[5,3,2,2],[2,1,1]] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[[4,4,4,2,2],[3,3,1,1]] => [4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[[5,4,2,2],[3,1,1]] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[4,3,3,3,2],[2,2,2,1]] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[[4,4,3,3,2],[3,2,2,1]] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[[5,3,3,2],[2,2,1]] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[[4,4,4,3,2],[3,3,2,1]] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[[5,4,3,2],[3,2,1]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[5,5,3,2],[4,2,1]] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[[5,4,4,2],[3,3,1]] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[[5,5,4,2],[4,3,1]] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[[6,4,2],[3,1]] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[[6,5,2],[4,1]] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[[5,3,3,3],[2,2,2]] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[[5,4,3,3],[3,2,2]] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[[5,5,3,3],[4,2,2]] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[[5,4,4,3],[3,3,2]] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[[5,5,4,3],[4,3,2]] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[[6,4,3],[3,2]] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3
[[6,5,3],[4,2]] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[[6,4,4],[3,3]] => [6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[6,5,4],[4,3]] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[[3,3,3],[1]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[3,3,3,1],[1,1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[4,4,1],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[3,3,2,1],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[2,2,2,2,1],[1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[3,3,3,1],[2]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[3,3,3,1],[1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[3,3,3,2],[1,1,1]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[4,4,2],[1,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[4,4,4],[2,2]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[5,5],[2]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[4,4,3],[2,1]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[3,3,3,3],[2,1,1]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[4,3,3],[1,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[3,3,3,3],[1,1,1]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[4,4,3],[1,1]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[4,4,4],[3,1]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[5,4],[1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[4,4,4],[2,1]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[5,5],[1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[4,4,4],[1,1]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[3,3,2,2],[1,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,2],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[3,3,3,2],[2,1]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[4,3,2],[1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[3,3,3,2],[1,1]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[4,4,2],[1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[2,2,2,2,2],[1,1]] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[3,2,2,2],[1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[3,3,2,2],[2]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[3,3,2,2],[1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[2,2,2,2,2],[1]] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[3,3,3,2],[2]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[3,3,3,2],[1]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[3,3,3,3],[2,2]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[4,3,3],[2]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[4,4,3],[3]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[4,4,3],[2]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[3,3,3,3],[2,1]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[4,3,3],[1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[3,3,3,3],[1,1]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[4,4,3],[1]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[4,4,4],[3]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[4,4,4],[2]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[4,4,4],[1]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[3,3,3,3],[2]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[3,3,3,3],[1]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[4,4,4,1],[1,1]] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[[4,4,3,1],[1]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[4,4,4,1],[2]] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[[4,4,4,1],[1]] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[[3,3,3,3,1],[1]] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[[4,4,4,2],[1,1,1]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[6,5],[3]] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[[6,4],[2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[[5,5,4],[3,2]] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[[5,4,4],[2,2]] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[[5,5,4],[2,2]] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[[6,5],[2]] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[[6,3],[1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[[5,5,3],[3,1]] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[5,4,3],[2,1]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[4,4,4,3],[2,2,1]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[5,5,3],[2,1]] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[5,3,3],[1,1]] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[4,4,3,3],[2,1,1]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[4,3,3,3],[1,1,1]] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[[4,4,3,3],[1,1,1]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[5,4,3],[1,1]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[4,4,4,3],[2,1,1]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[5,5,3],[1,1]] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[4,4,4,3],[1,1,1]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[6,4],[1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[[5,5,4],[3,1]] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[[5,4,4],[2,1]] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[[5,5,4],[2,1]] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[[6,5],[1]] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[[5,4,4],[1,1]] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[[5,5,4],[1,1]] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[[5,5,2],[3]] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[[5,4,2],[2]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[4,4,4,2],[2,2]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[5,5,2],[2]] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[[5,3,2],[1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[4,4,3,2],[2,1]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[4,3,3,2],[1,1]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[3,3,3,3,2],[1,1,1]] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[[4,4,3,2],[1,1]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[5,4,2],[1]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[4,4,4,2],[2,1]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[5,5,2],[1]] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[[4,4,4,2],[1,1]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[4,4,2,2],[2]] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[4,3,2,2],[1]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[3,3,3,2,2],[1,1]] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,2,2],[1]] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[3,3,2,2,2],[1]] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[[3,3,3,2,2],[1]] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,3,2],[2]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[4,3,3,2],[1]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[3,3,3,3,2],[1,1]] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[[4,4,3,2],[1]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[4,4,4,2],[3]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[4,4,4,2],[2]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[4,4,4,2],[1]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[3,3,3,3,2],[2]] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[[3,3,3,3,2],[1]] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[[5,5,3],[3]] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[5,4,3],[2]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[4,4,4,3],[2,2]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[5,5,3],[2]] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[5,3,3],[1]] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[4,4,3,3],[2,1]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[4,3,3,3],[1,1]] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[[4,4,3,3],[1,1]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,4,3],[3,1]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[5,4,3],[1]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[4,4,4,3],[2,1]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[5,5,3],[1]] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[4,4,4,3],[1,1]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[5,5,4],[3]] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[[5,4,4],[2]] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[[5,5,4],[2]] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[[5,4,4],[1]] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[[5,5,4],[1]] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[[4,3,3,3],[2]] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[[4,4,3,3],[3]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,3,3],[2]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[4,3,3,3],[1]] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[[4,4,3,3],[1]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,4,3],[3]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[4,4,4,3],[2]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[4,4,4,3],[1]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,1 3,5,1 5,14,8,1 7,34,34,11,1 11,71,112,63,14,1
$F_{1} = q$
$F_{2} = 2\ q + q^{2}$
$F_{3} = 3\ q + 5\ q^{2} + q^{3}$
$F_{4} = 5\ q + 14\ q^{2} + 8\ q^{3} + q^{4}$
$F_{5} = 7\ q + 34\ q^{2} + 34\ q^{3} + 11\ q^{4} + q^{5}$
$F_{6} = 11\ q + 71\ q^{2} + 112\ q^{3} + 63\ q^{4} + 14\ q^{5} + q^{6}$
Description
The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra.
We use the bijection in the code by Christian Stump to have a bijection to Dyck paths.
We use the bijection in the code by Christian Stump to have a bijection to Dyck paths.
Map
outer shape
Description
The outer shape of the skew partition.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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