Identifier
-
Mp00183:
Skew partitions
—inner shape⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St000015: Dyck paths ⟶ ℤ (values match St000053The number of valleys of the Dyck path., St001068Number of torsionless simple modules in the corresponding Nakayama algebra., St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra.)
Values
[[1],[]] => [] => [] => [1,0] => 1
[[2],[]] => [] => [] => [1,0] => 1
[[1,1],[]] => [] => [] => [1,0] => 1
[[2,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3],[]] => [] => [] => [1,0] => 1
[[2,1],[]] => [] => [] => [1,0] => 1
[[3,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[2,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[1,1,1],[]] => [] => [] => [1,0] => 1
[[2,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[2,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4],[]] => [] => [] => [1,0] => 1
[[3,1],[]] => [] => [] => [1,0] => 1
[[4,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[2,2],[]] => [] => [] => [1,0] => 1
[[3,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[2,1,1],[]] => [] => [] => [1,0] => 1
[[3,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[3,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[2,2,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[3,2,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,3,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[2,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[3,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[1,1,1,1],[]] => [] => [] => [1,0] => 1
[[2,2,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[2,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[2,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[3,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5],[]] => [] => [] => [1,0] => 1
[[4,1],[]] => [] => [] => [1,0] => 1
[[5,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,2],[]] => [] => [] => [1,0] => 1
[[4,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[3,1,1],[]] => [] => [] => [1,0] => 1
[[4,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[3,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[2,2,1],[]] => [] => [] => [1,0] => 1
[[3,3,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,2,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,3,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,2,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,3,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[3,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,3,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,3,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[2,1,1,1],[]] => [] => [] => [1,0] => 1
[[3,2,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[3,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,3,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[3,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[4,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,4],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[3,3,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[4,3,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,4,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[2,2,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[3,2,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,3,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4,2],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[2,2,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[3,3,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[3,2,1,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,3,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[4,3,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4,2,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[3,3,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,3],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[4,3,3],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,4,3],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[2,2,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,3,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[3,3,2,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,3,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[3,2,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
>>> Load all 1259 entries. <<<[[4,3,3,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[4,3,2,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,4,3,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[2,2,2,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,3,2],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[3,3,2,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[3,2,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[4,3,2,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[2,2,2,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[2,2,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[3,3,2,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[2,1,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[3,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[3,2,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[4,3,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[6],[]] => [] => [] => [1,0] => 1
[[5,1],[]] => [] => [] => [1,0] => 1
[[6,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,2],[]] => [] => [] => [1,0] => 1
[[5,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[6,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,1,1],[]] => [] => [] => [1,0] => 1
[[5,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[5,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[6,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[3,3],[]] => [] => [] => [1,0] => 1
[[4,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[6,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[3,2,1],[]] => [] => [] => [1,0] => 1
[[4,3,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,2,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,3,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,2,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[6,3,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[4,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[5,3,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[5,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[6,3,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[3,1,1,1],[]] => [] => [] => [1,0] => 1
[[4,2,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[5,3,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[5,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[6,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[4,4],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[6,4],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[3,3,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,4,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,3,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[6,4,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[2,2,2],[]] => [] => [] => [1,0] => 1
[[3,3,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[3,2,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,3,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,4,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[4,2,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,3,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[6,4,2],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[2,2,1,1],[]] => [] => [] => [1,0] => 1
[[3,3,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[3,2,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,3,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,4,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[4,2,1,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,3,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[5,3,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[6,4,2,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[4,3,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[5,4,3],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[5,3,3],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[6,4,3],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[3,2,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,3,3,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,3,2,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[5,4,3,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[4,2,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,3,3,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,3,2,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[6,4,3,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[3,2,2,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,3,3,2],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[4,3,2,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[5,4,3,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[4,2,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[5,3,3,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[5,3,2,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[6,4,3,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[2,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[3,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[3,2,2,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[3,2,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,3,2,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[5,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[3,1,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[4,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[5,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[4,2,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,3,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[6,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[5,5],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[4,4,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,5,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[5,4,1],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[3,3,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,5,2],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[4,3,2],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,4,2],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[3,3,1,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[4,4,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,5,2,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[4,3,1,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,4,2,1],[4,1,1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[5,4,1,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[3,3,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,3],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,5,3],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[4,3,3],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4,3],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[2,2,2,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[3,3,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,3,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[4,4,2,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,5,3,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[3,2,2,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,3,3,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[4,3,2,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4,3,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[5,4,2,1],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[3,3,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,4,3,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[4,4,2,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,5,3,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[4,3,2,2],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[5,4,3,2],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[[5,4,2,2],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[2,2,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[3,3,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,4,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[3,3,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[4,4,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,5,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[3,2,1,1,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,3,2,2,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[4,3,2,1,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[5,4,3,2,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 4
[[4,3,1,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4,2,2,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 4
[[5,4,2,1,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[4,4,4],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[5,4,4],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[3,3,3,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,4,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[4,4,3,1],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[4,3,3,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,4,4,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[5,4,3,1],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[2,2,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,3,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,4,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[3,3,2,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,3,2],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[3,2,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,3,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,4,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[4,3,2,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,4,3,2],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[2,2,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,3,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[3,3,3,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,4,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[3,3,2,1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,3,2,1],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[[4,4,3,1,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[3,2,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,3,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[4,3,3,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,4,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[4,3,2,1,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,4,3,2,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 4
[[5,4,3,1,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[3,3,3,3],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[4,4,3,3],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[4,3,3,3],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[5,4,3,3],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[2,2,2,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,3,3,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[3,3,3,2,1],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[3,3,2,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,3,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[4,4,3,2,1],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[3,2,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,3,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[4,3,3,2,1],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[4,3,2,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,3,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[5,4,3,2,1],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[3,3,3,2,2],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[3,3,2,2,2],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,4,3,2,2],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[3,2,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[4,3,3,2,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[4,3,2,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,4,3,2,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[1,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[2,2,2,1,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,3,2,1,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[2,2,1,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,2,2,1,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[3,3,2,1,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[2,1,1,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[3,2,2,1,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[3,2,1,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[4,3,2,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[7],[]] => [] => [] => [1,0] => 1
[[6,1],[]] => [] => [] => [1,0] => 1
[[7,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,2],[]] => [] => [] => [1,0] => 1
[[6,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[7,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,1,1],[]] => [] => [] => [1,0] => 1
[[6,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[6,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[7,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3],[]] => [] => [] => [1,0] => 1
[[5,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[6,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[7,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[4,2,1],[]] => [] => [] => [1,0] => 1
[[5,3,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[5,2,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[6,3,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[6,2,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[7,3,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[6,3,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[6,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[7,3,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[4,1,1,1],[]] => [] => [] => [1,0] => 1
[[5,2,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[5,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[6,3,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[5,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[6,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[6,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[7,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[4,4],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,4],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[6,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[7,4],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[3,3,1],[]] => [] => [] => [1,0] => 1
[[4,4,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,3,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,4,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,3,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[6,4,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[6,3,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[7,4,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[3,2,2],[]] => [] => [] => [1,0] => 1
[[4,3,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[5,4,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,2,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,3,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[6,4,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,2,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[6,3,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[7,4,2],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[3,2,1,1],[]] => [] => [] => [1,0] => 1
[[4,3,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,3,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[5,4,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,2,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,3,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[5,3,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[6,4,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,2,1,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[6,3,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[6,3,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[7,4,2,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[5,3,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[6,4,3],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[6,3,3],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[7,4,3],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[4,2,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[5,3,3,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[5,3,2,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[6,4,3,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[5,2,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[6,3,3,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[6,3,2,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[7,4,3,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[4,2,2,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[5,3,3,2],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[5,3,2,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[6,4,3,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[5,2,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[6,3,3,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[6,3,2,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[7,4,3,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[3,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[4,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[4,2,2,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[5,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[4,2,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[5,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[5,3,2,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[6,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[4,1,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[5,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[6,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[5,2,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[6,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[6,3,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[7,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[5,5],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[6,5],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[4,4,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,5,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[6,5,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[6,4,1],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[3,3,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,5,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[4,3,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,4,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[6,5,2],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[5,3,2],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[6,4,2],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[3,3,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,4,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,5,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[4,3,1,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,4,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[5,4,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[6,5,2,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[5,3,1,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[6,4,2,1],[4,1,1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[6,4,1,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[3,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[5,5,3],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[4,3,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,4,3],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[6,5,3],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[5,3,3],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[6,4,3],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[2,2,2,1],[]] => [] => [] => [1,0] => 1
[[3,3,3,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,3,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,2,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[5,5,3,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[3,2,2,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,3,3,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,4,3,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,2,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[6,5,3,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[4,2,2,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,3,3,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[5,3,2,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[6,4,3,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[6,4,2,1],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[3,3,2,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,3,2],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[4,4,2,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[5,5,3,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[4,3,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[5,4,3,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[5,4,2,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[6,5,3,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[5,3,2,2],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[6,4,3,2],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[[6,4,2,2],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[2,2,1,1,1],[]] => [] => [] => [1,0] => 1
[[3,3,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[3,3,2,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[3,3,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,4,2,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[5,5,3,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[3,2,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,3,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[4,3,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[5,4,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[4,3,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,4,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,4,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[6,5,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[4,2,1,1,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,3,2,2,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[5,3,2,1,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[6,4,3,2,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 4
[[5,3,1,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[6,4,2,2,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 4
[[6,4,2,1,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[5,4,4],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[6,4,4],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[4,3,3,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[5,4,4,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[5,4,3,1],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[5,3,3,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[6,4,4,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[6,4,3,1],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[3,2,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,3,3,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[5,4,4,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[4,3,2,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[5,4,3,2],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[4,2,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,3,3,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[6,4,4,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[5,3,2,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[6,4,3,2],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[3,2,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,3,3,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,3,3,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[5,4,4,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[4,3,2,1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[5,4,3,2,1],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[[5,4,3,1,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[4,2,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,3,3,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,3,3,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[6,4,4,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[5,3,2,1,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[6,4,3,2,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 4
[[6,4,3,1,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[4,3,3,3],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[5,4,3,3],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[5,3,3,3],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[6,4,3,3],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[3,2,2,2,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,3,3,3,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[4,3,3,2,1],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[4,3,2,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[5,4,3,3,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[5,4,3,2,1],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[4,2,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[5,3,3,3,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[5,3,3,2,1],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[5,3,2,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[6,4,3,3,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[6,4,3,2,1],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[4,3,3,2,2],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[4,3,2,2,2],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[5,4,3,2,2],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[4,2,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[5,3,3,2,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[5,3,2,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[6,4,3,2,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[2,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[3,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[3,2,2,1,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,3,3,2,1,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[3,2,1,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,3,2,2,1,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,3,2,1,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[5,4,3,2,1,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[3,1,1,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[4,2,2,1,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[5,3,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[4,2,1,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,3,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,3,2,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[6,4,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[5,5,1],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[4,4,2],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,5,2],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[5,4,2],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[4,4,1,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,5,2,1],[4,1,1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[5,5,1,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[5,4,1,1],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[3,3,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,3],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,5,3],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[4,3,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,4,3],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[3,3,2,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,3,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[4,4,2,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,5,3,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[5,5,2,1],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[4,3,2,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,4,3,1],[4,1,1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[5,4,2,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[4,4,2,2],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[5,5,3,2],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[[5,5,2,2],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[5,4,2,2],[4,1,1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[3,3,1,1,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,2,2,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[4,4,2,1,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[5,5,3,2,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 4
[[4,4,1,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,5,2,2,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 4
[[5,5,2,1,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[4,3,1,1,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,4,2,2,1],[4,1,1,1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 3
[[5,4,2,1,1],[4,1,1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[5,4,1,1,1],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[4,4,4],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,5,4],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[5,4,4],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[3,3,3,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,4,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[4,4,3,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,5,4,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[5,5,3,1],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[4,3,3,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4,4,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[5,4,3,1],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[2,2,2,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,4,4,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[3,3,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,3,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,5,4,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[4,4,2,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,5,3,2],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[3,2,2,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,3,3,2],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[5,4,4,2],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[[4,3,2,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4,3,2],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[5,4,2,2],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[2,2,2,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[3,3,3,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,4,4,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[3,3,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,3,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[4,4,3,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,5,4,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[4,4,2,1,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,5,3,2,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 4
[[5,5,3,1,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[3,2,2,1,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,3,3,2,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[4,3,3,1,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[5,4,4,2,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 4
[[4,3,2,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4,3,2,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 4
[[5,4,3,1,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[5,4,2,1,1],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[4,4,3,3],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[5,5,3,3],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[5,4,3,3],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[[3,3,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,4,3,3,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[4,4,3,2,1],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[4,4,2,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,5,3,3,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[5,5,3,2,1],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[4,3,2,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[5,4,3,3,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 4
[[5,4,3,2,1],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[[5,4,2,2,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[4,4,3,2,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[4,4,2,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,5,3,2,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[4,3,2,2,2],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[5,4,3,2,2],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 4
[[5,4,2,2,2],[4,2,1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 4
[[2,2,1,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[3,3,2,1,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,4,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[3,3,1,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[4,4,2,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,5,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[3,2,1,1,1,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,3,2,2,1,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[4,3,2,1,1,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[5,4,3,2,1,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 4
[[4,3,1,1,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4,2,2,1,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 4
[[5,4,2,1,1,1],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[4,4,4,1],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[5,4,4,1],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[3,3,3,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,4,2],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[4,4,3,2],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[4,3,3,2],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,4,4,2],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[5,4,3,2],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[3,3,3,1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,4,2,1],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[[4,4,4,1,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[4,4,3,1,1],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[4,3,3,1,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,4,4,2,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 4
[[5,4,4,1,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[5,4,3,1,1],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[3,3,3,3],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,4,3],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[4,4,3,3],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[4,3,3,3],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,4,3],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[5,4,3,3],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[2,2,2,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,3,3,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[3,3,3,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,4,3,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[4,4,4,2,1],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[3,3,2,2,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,3,3,1],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[[4,4,3,2,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[3,2,2,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,3,3,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[4,3,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,4,3,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[5,4,4,2,1],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[4,3,2,2,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,4,3,3,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,4,4,2,2],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[4,4,3,2,2],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[[4,3,3,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,4,4,2,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[5,4,3,2,2],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 4
[[2,2,2,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,3,2,1,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[3,3,3,1,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,4,2,1,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[3,3,2,1,1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,3,2,1,1],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[[4,4,3,1,1,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[3,2,2,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,3,2,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[4,3,3,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,4,2,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[4,3,2,1,1,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,4,3,2,1,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 4
[[5,4,3,1,1,1],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[3,3,3,3,1],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[4,4,3,3,1],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[4,3,3,3,1],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[5,4,3,3,1],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[2,2,2,2,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[3,3,3,2,2],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[3,3,2,2,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,3,2],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[4,4,3,2,2],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[3,2,2,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,3,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[4,3,3,2,2],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[4,3,2,2,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,3,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[5,4,3,2,2],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,3,3,1,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[3,3,3,2,1,1],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[3,3,2,2,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,3,1,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[4,4,3,2,1,1],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[3,2,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,3,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[4,3,3,2,1,1],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[4,3,2,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,3,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[5,4,3,2,1,1],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[3,3,3,2,2,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[3,3,2,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,4,3,2,2,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[3,2,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[4,3,3,2,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[4,3,2,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,4,3,2,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[1,1,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[2,2,2,2,1,1,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[2,2,2,1,1,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,3,2,1,1,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[2,2,1,1,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,2,2,1,1,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[3,3,2,1,1,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1,1,1],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[2,1,1,1,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,2,2,2,1,1,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[3,2,2,1,1,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,2,1,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[3,2,1,1,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,2,2,1,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[4,3,2,1,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[8],[]] => [] => [] => [1,0] => 1
[[7,1],[]] => [] => [] => [1,0] => 1
[[6,2],[]] => [] => [] => [1,0] => 1
[[6,1,1],[]] => [] => [] => [1,0] => 1
[[5,3],[]] => [] => [] => [1,0] => 1
[[5,2,1],[]] => [] => [] => [1,0] => 1
[[5,1,1,1],[]] => [] => [] => [1,0] => 1
[[4,4],[]] => [] => [] => [1,0] => 1
[[4,3,1],[]] => [] => [] => [1,0] => 1
[[4,2,2],[]] => [] => [] => [1,0] => 1
[[4,2,1,1],[]] => [] => [] => [1,0] => 1
[[4,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[3,3,2],[]] => [] => [] => [1,0] => 1
[[3,3,1,1],[]] => [] => [] => [1,0] => 1
[[3,2,2,1],[]] => [] => [] => [1,0] => 1
[[3,2,1,1,1],[]] => [] => [] => [1,0] => 1
[[3,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[2,2,2,2],[]] => [] => [] => [1,0] => 1
[[2,2,2,1,1],[]] => [] => [] => [1,0] => 1
[[2,2,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[2,1,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[1,1,1,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[9],[]] => [] => [] => [1,0] => 1
[[8,1],[]] => [] => [] => [1,0] => 1
[[7,2],[]] => [] => [] => [1,0] => 1
[[7,1,1],[]] => [] => [] => [1,0] => 1
[[6,3],[]] => [] => [] => [1,0] => 1
[[6,2,1],[]] => [] => [] => [1,0] => 1
[[6,1,1,1],[]] => [] => [] => [1,0] => 1
[[5,4],[]] => [] => [] => [1,0] => 1
[[5,3,1],[]] => [] => [] => [1,0] => 1
[[5,2,2],[]] => [] => [] => [1,0] => 1
[[5,2,1,1],[]] => [] => [] => [1,0] => 1
[[5,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[4,4,1],[]] => [] => [] => [1,0] => 1
[[4,3,2],[]] => [] => [] => [1,0] => 1
[[4,3,1,1],[]] => [] => [] => [1,0] => 1
[[4,2,2,1],[]] => [] => [] => [1,0] => 1
[[4,2,1,1,1],[]] => [] => [] => [1,0] => 1
[[4,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[3,3,3],[]] => [] => [] => [1,0] => 1
[[3,3,2,1],[]] => [] => [] => [1,0] => 1
[[3,3,1,1,1],[]] => [] => [] => [1,0] => 1
[[3,2,2,2],[]] => [] => [] => [1,0] => 1
[[3,2,2,1,1],[]] => [] => [] => [1,0] => 1
[[3,2,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[3,1,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[2,2,2,2,1],[]] => [] => [] => [1,0] => 1
[[2,2,2,1,1,1],[]] => [] => [] => [1,0] => 1
[[2,2,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[2,1,1,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[1,1,1,1,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[10],[]] => [] => [] => [1,0] => 1
[[9,1],[]] => [] => [] => [1,0] => 1
[[8,2],[]] => [] => [] => [1,0] => 1
[[8,1,1],[]] => [] => [] => [1,0] => 1
[[7,3],[]] => [] => [] => [1,0] => 1
[[7,2,1],[]] => [] => [] => [1,0] => 1
[[7,1,1,1],[]] => [] => [] => [1,0] => 1
[[6,4],[]] => [] => [] => [1,0] => 1
[[6,3,1],[]] => [] => [] => [1,0] => 1
[[6,2,2],[]] => [] => [] => [1,0] => 1
[[6,2,1,1],[]] => [] => [] => [1,0] => 1
[[6,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[5,5],[]] => [] => [] => [1,0] => 1
[[5,4,1],[]] => [] => [] => [1,0] => 1
[[5,3,2],[]] => [] => [] => [1,0] => 1
[[5,3,1,1],[]] => [] => [] => [1,0] => 1
[[5,2,2,1],[]] => [] => [] => [1,0] => 1
[[5,2,1,1,1],[]] => [] => [] => [1,0] => 1
[[5,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[4,4,2],[]] => [] => [] => [1,0] => 1
[[4,4,1,1],[]] => [] => [] => [1,0] => 1
[[4,3,3],[]] => [] => [] => [1,0] => 1
[[4,3,2,1],[]] => [] => [] => [1,0] => 1
[[4,3,1,1,1],[]] => [] => [] => [1,0] => 1
[[4,2,2,2],[]] => [] => [] => [1,0] => 1
[[4,2,2,1,1],[]] => [] => [] => [1,0] => 1
[[4,2,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[4,1,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[3,3,3,1],[]] => [] => [] => [1,0] => 1
[[3,3,2,2],[]] => [] => [] => [1,0] => 1
[[3,3,2,1,1],[]] => [] => [] => [1,0] => 1
[[3,3,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[3,2,2,2,1],[]] => [] => [] => [1,0] => 1
[[3,2,2,1,1,1],[]] => [] => [] => [1,0] => 1
[[3,2,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[3,1,1,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[2,2,2,2,2],[]] => [] => [] => [1,0] => 1
[[2,2,2,2,1,1],[]] => [] => [] => [1,0] => 1
[[2,2,2,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[2,2,1,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[2,1,1,1,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[1,1,1,1,1,1,1,1,1,1],[]] => [] => [] => [1,0] => 1
[[6,5],[]] => [] => [] => [1,0] => 1
[[5,5,1],[]] => [] => [] => [1,0] => 1
[[5,4,2],[]] => [] => [] => [1,0] => 1
[[5,3,3],[]] => [] => [] => [1,0] => 1
[[4,4,3],[]] => [] => [] => [1,0] => 1
[[4,4,2,1],[]] => [] => [] => [1,0] => 1
[[4,3,3,1],[]] => [] => [] => [1,0] => 1
[[4,3,2,2],[]] => [] => [] => [1,0] => 1
[[3,3,3,2],[]] => [] => [] => [1,0] => 1
[[3,2,2,2,2],[]] => [] => [] => [1,0] => 1
[[6,6],[]] => [] => [] => [1,0] => 1
[[5,5,2],[]] => [] => [] => [1,0] => 1
[[5,4,3],[]] => [] => [] => [1,0] => 1
[[4,4,4],[]] => [] => [] => [1,0] => 1
[[4,4,3,1],[]] => [] => [] => [1,0] => 1
[[4,4,2,2],[]] => [] => [] => [1,0] => 1
[[4,3,3,2],[]] => [] => [] => [1,0] => 1
[[3,3,3,3],[]] => [] => [] => [1,0] => 1
[[3,3,3,2,1],[]] => [] => [] => [1,0] => 1
[[3,3,2,2,2],[]] => [] => [] => [1,0] => 1
[[2,2,2,2,2,2],[]] => [] => [] => [1,0] => 1
[[5,5,3],[]] => [] => [] => [1,0] => 1
[[5,4,4],[]] => [] => [] => [1,0] => 1
[[4,4,4,1],[]] => [] => [] => [1,0] => 1
[[4,4,3,2],[]] => [] => [] => [1,0] => 1
[[4,3,3,3],[]] => [] => [] => [1,0] => 1
[[3,3,3,3,1],[]] => [] => [] => [1,0] => 1
[[3,3,3,2,2],[]] => [] => [] => [1,0] => 1
[[5,5,4],[]] => [] => [] => [1,0] => 1
[[4,4,4,2],[]] => [] => [] => [1,0] => 1
[[4,4,3,3],[]] => [] => [] => [1,0] => 1
[[3,3,3,3,2],[]] => [] => [] => [1,0] => 1
[[5,5,5],[]] => [] => [] => [1,0] => 1
[[5,5,4,1],[]] => [] => [] => [1,0] => 1
[[4,4,4,3],[]] => [] => [] => [1,0] => 1
[[3,3,3,3,3],[]] => [] => [] => [1,0] => 1
[[5,5,5,1],[]] => [] => [] => [1,0] => 1
[[4,4,4,4],[]] => [] => [] => [1,0] => 1
[[4,4,4,3,1],[]] => [] => [] => [1,0] => 1
[[3,3,3,3,3,1],[]] => [] => [] => [1,0] => 1
[[4,4,4,4,1],[]] => [] => [] => [1,0] => 1
[[2,2,1,1,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[2,2,2,1,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,2,1,1,1,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[3,2,2,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,2,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,1,1,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,3,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,2,1,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[4,3,3,1,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,3,1,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,3,1,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,3,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,4,2,2,1],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[4,3,3,2,1],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,3,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,4,2,1],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[5,4,2,1],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[4,3,3,3,1],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[4,4,3,3,1],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[5,3,3,1],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,4,3,1],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[5,4,3,1],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,5,3,1],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[5,4,4,1],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[5,5,4,1],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[6,4,1],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,3,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[[5,4,2,2],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[5,3,3,2],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[5,4,3,2],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,5,3,2],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[5,4,4,2],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[5,5,4,2],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[6,4,2],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[6,5,2],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[5,3,3,3],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[5,4,3,3],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[5,5,3,3],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[[5,4,4,3],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[5,5,4,3],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[6,4,3],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[6,5,3],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[6,4,4],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[6,5,4],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[7,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[3,3,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,2,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[2,2,2,2,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[3,3,3,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,4],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[5,5],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[3,3,3,3],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,3,3],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,4],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,5],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[3,3,3,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[2,2,2,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,2,2,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,2,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[3,3,2,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[2,2,2,2,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[3,3,3,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,3,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[4,4,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[3,3,3,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[4,4,4],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,4],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[3,3,3,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,3,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4,1],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,4,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,3,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[6,6],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[5,5,5],[4,3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[6,5],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,5,5],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[6,6],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[4,4,4,4],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[6,4],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,5,4],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[4,4,4,4],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[5,4,4],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,4,4],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[5,5,4],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[5,5,5],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[6,5],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,5,5],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[6,6],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,5,5],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[3,3,3,3,3],[2,2,2,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[6,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,5,3],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,4,3],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[5,5,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[5,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,3,3],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[4,3,3,3],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,3,3,3],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[4,4,3,3],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[5,4,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,4,3],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[5,5,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,4,3],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,4,4],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[6,4],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,5,4],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[4,4,4,4],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,4],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,4,4],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[5,5,4],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,5,5],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[6,5],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,5,5],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[6,6],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,5,5],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,4,4,4],[3,1,1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[[5,4,4],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,4,4],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[5,5,4],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,4,4],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[5,5,5],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[5,5,2],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,4,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,4,2],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[5,5,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,3,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,3,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,3,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,3,3,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,3,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[5,4,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,5,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[2,2,2,2,2,2],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,2,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,3,2,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,2,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[2,2,2,2,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,2,2,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,2,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,3,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,3,3,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,3,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,3,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4,2],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[4,4,4,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,4,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,3,2],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[3,3,3,3,2],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,3,3],[2,2,2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[5,5,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,4,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,4,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[5,5,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[3,3,3,3,3],[2,2,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[[5,3,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,3,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[3,3,3,3,3],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[3,3,3,3,3],[1,1,1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,4,3],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,5,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,4,4],[3,3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[5,5,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[4,4,4,4],[3,2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5,4,4],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,4,4],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[5,5,4],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[5,5,5],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[5,5,5],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,5,5],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,4,4],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,4,4],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4,4],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[5,5,4],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4,4],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[5,5,5],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,3,3],[2,2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[[4,3,3,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,3,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[4,4,3,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[3,3,3,3,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[[4,3,3,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,3,3],[1,1]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[4,4,3,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[4,4,4,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,4,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[3,3,3,3,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[3,3,3,3,3],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[4,4,4,4],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,4,4],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[5,5,5,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[4,4,4,4,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[7,7],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[5,5,5,5],[4,3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[5,5,5,5],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[6,6,6],[4,2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[5,5,5,5],[4,2,2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[[5,5,5,5],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[5,5,5,5],[4,3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[5,5,5,5],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[5,5,5,5],[4,2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[5,5,5,5],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[4,4,4,4,4],[3,3,1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[2,2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[3,3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,4,4,4,4],[3,3,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[4,4,4,4,4],[3,2,2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[4,4,4,4,4],[3,3,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[4,4,4,4,4],[3,2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[[5,5,5,5],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[3,3,3,3,3,3],[2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[4,4,4,4,3],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,5,5,4],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[4,4,4,4,4],[3,1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[5,5,5,5],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[4,4,4,4,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[5,5,5,5,5],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[5,5,5,5,1],[]] => [] => [] => [1,0] => 1
[[5,5,5,5,5,5],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[4,4,4,4,4,4],[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[4,4,4,4,4,1],[]] => [] => [] => [1,0] => 1
[[5,5,5,5,5,1],[]] => [] => [] => [1,0] => 1
[[5,5,5,5,4],[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[5,5,5,5,5],[4,1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[5,5,5,4,1],[]] => [] => [] => [1,0] => 1
[[5,5,5,5,1],[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
[[6,6,6,6,1],[]] => [] => [] => [1,0] => 1
[[6,6,6,6,6,1],[]] => [] => [] => [1,0] => 1
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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
$F_{1} = q$
$F_{2} = 2\ q + q^{2}$
$F_{3} = 3\ q + 5\ q^{2} + q^{3}$
$F_{4} = 5\ q + 14\ q^{2} + 8\ q^{3} + q^{4}$
$F_{5} = 7\ q + 34\ q^{2} + 34\ q^{3} + 11\ q^{4} + q^{5}$
Description
The number of peaks of a Dyck path.
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to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
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inner shape
Description
The inner shape of a skew partition.
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