Identifier
-
Mp00189:
Skew partitions
—rotate⟶
Skew partitions
Mp00182: Skew partitions —outer shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St000053: Dyck paths ⟶ ℤ (values match St000015The number of peaks of a 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],[]] => [1] => [1,0,1,0] => 1
[[2],[]] => [[2],[]] => [2] => [1,1,0,0,1,0] => 1
[[1,1],[]] => [[1,1],[]] => [1,1] => [1,0,1,1,0,0] => 1
[[2,1],[1]] => [[2,1],[1]] => [2,1] => [1,0,1,0,1,0] => 2
[[3],[]] => [[3],[]] => [3] => [1,1,1,0,0,0,1,0] => 1
[[2,1],[]] => [[2,2],[1]] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[[3,1],[1]] => [[3,2],[2]] => [3,2] => [1,1,0,0,1,0,1,0] => 2
[[2,2],[1]] => [[2,1],[]] => [2,1] => [1,0,1,0,1,0] => 2
[[3,2],[2]] => [[3,1],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => 2
[[1,1,1],[]] => [[1,1,1],[]] => [1,1,1] => [1,0,1,1,1,0,0,0] => 1
[[2,2,1],[1,1]] => [[2,1,1],[1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[[2,1,1],[1]] => [[2,2,1],[1,1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => 2
[[3,2,1],[2,1]] => [[3,2,1],[2,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[[4],[]] => [[4],[]] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,1],[]] => [[3,3],[2]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[[4,1],[1]] => [[4,3],[3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 2
[[2,2],[]] => [[2,2],[]] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[[3,2],[1]] => [[3,2],[1]] => [3,2] => [1,1,0,0,1,0,1,0] => 2
[[4,2],[2]] => [[4,2],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 2
[[2,1,1],[]] => [[2,2,2],[1,1]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1
[[3,2,1],[1,1]] => [[3,2,2],[2,1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 2
[[3,1,1],[1]] => [[3,3,2],[2,2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[4,2,1],[2,1]] => [[4,3,2],[3,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[3,3],[2]] => [[3,1],[]] => [3,1] => [1,1,0,1,0,0,1,0] => 2
[[4,3],[3]] => [[4,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 2
[[2,2,1],[1]] => [[2,2,1],[1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => 2
[[3,3,1],[2,1]] => [[3,2,1],[2]] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[[3,2,1],[2]] => [[3,3,1],[2,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 2
[[4,3,1],[3,1]] => [[4,3,1],[3,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[2,2,2],[1,1]] => [[2,1,1],[]] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[[3,3,2],[2,2]] => [[3,1,1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 2
[[3,2,2],[2,1]] => [[3,2,1],[1,1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[[4,3,2],[3,2]] => [[4,2,1],[2,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 3
[[1,1,1,1],[]] => [[1,1,1,1],[]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1
[[2,2,2,1],[1,1,1]] => [[2,1,1,1],[1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 2
[[2,2,1,1],[1,1]] => [[2,2,1,1],[1,1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 2
[[3,3,2,1],[2,2,1]] => [[3,2,1,1],[2,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 3
[[2,1,1,1],[1]] => [[2,2,2,1],[1,1,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 2
[[3,2,2,1],[2,1,1]] => [[3,2,2,1],[2,1,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[3,2,1,1],[2,1]] => [[3,3,2,1],[2,2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[4,3,2,1],[3,2,1]] => [[4,3,2,1],[3,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[5],[]] => [[5],[]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[4,1],[]] => [[4,4],[3]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[5,1],[1]] => [[5,4],[4]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[3,2],[]] => [[3,3],[1]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[[4,2],[1]] => [[4,3],[2]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 2
[[5,2],[2]] => [[5,3],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[3,1,1],[]] => [[3,3,3],[2,2]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[4,2,1],[1,1]] => [[4,3,3],[3,2]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[4,1,1],[1]] => [[4,4,3],[3,3]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[5,2,1],[2,1]] => [[5,4,3],[4,3]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[3,3],[1]] => [[3,2],[]] => [3,2] => [1,1,0,0,1,0,1,0] => 2
[[4,3],[2]] => [[4,2],[1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 2
[[5,3],[3]] => [[5,2],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[[2,2,1],[]] => [[2,2,2],[1]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1
[[3,3,1],[1,1]] => [[3,2,2],[2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 2
[[3,2,1],[1]] => [[3,3,2],[2,1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[4,3,1],[2,1]] => [[4,3,2],[3,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[4,2,1],[2]] => [[4,4,2],[3,2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[5,3,1],[3,1]] => [[5,4,2],[4,2]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[3,2,2],[1,1]] => [[3,2,2],[1,1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 2
[[4,3,2],[2,2]] => [[4,2,2],[2,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[[4,2,2],[2,1]] => [[4,3,2],[2,2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[5,3,2],[3,2]] => [[5,3,2],[3,2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[3,2,2,1],[1,1,1]] => [[3,2,2,2],[2,1,1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[3,2,1,1],[1,1]] => [[3,3,2,2],[2,2,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,3,2,1],[2,2,1]] => [[4,3,2,2],[3,2,1]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[3,1,1,1],[1]] => [[3,3,3,2],[2,2,2]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[4,2,2,1],[2,1,1]] => [[4,3,3,2],[3,2,2]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[4,2,1,1],[2,1]] => [[4,4,3,2],[3,3,2]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[5,3,2,1],[3,2,1]] => [[5,4,3,2],[4,3,2]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[4,4],[3]] => [[4,1],[]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 2
[[5,4],[4]] => [[5,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[[3,3,1],[2]] => [[3,3,1],[2]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 2
[[4,4,1],[3,1]] => [[4,3,1],[3]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[4,3,1],[3]] => [[4,4,1],[3,1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[5,4,1],[4,1]] => [[5,4,1],[4,1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[[2,2,2],[1]] => [[2,2,1],[]] => [2,2,1] => [1,0,1,0,1,1,0,0] => 2
[[3,3,2],[2,1]] => [[3,2,1],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[[4,4,2],[3,2]] => [[4,2,1],[2]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 3
[[3,2,2],[2]] => [[3,3,1],[1,1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 2
[[4,3,2],[3,1]] => [[4,3,1],[2,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[5,4,2],[4,2]] => [[5,3,1],[3,1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[[2,2,1,1],[1]] => [[2,2,2,1],[1,1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 2
[[3,3,2,1],[2,1,1]] => [[3,2,2,1],[2,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[3,3,1,1],[2,1]] => [[3,3,2,1],[2,2]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[4,4,2,1],[3,2,1]] => [[4,3,2,1],[3,2]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[3,2,1,1],[2]] => [[3,3,3,1],[2,2,1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[4,3,2,1],[3,1,1]] => [[4,3,3,1],[3,2,1]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[4,3,1,1],[3,1]] => [[4,4,3,1],[3,3,1]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[5,4,2,1],[4,2,1]] => [[5,4,3,1],[4,3,1]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[3,3,3],[2,2]] => [[3,1,1],[]] => [3,1,1] => [1,0,1,1,0,0,1,0] => 2
[[4,4,3],[3,3]] => [[4,1,1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 2
[[4,3,3],[3,2]] => [[4,2,1],[1,1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 3
[[5,4,3],[4,3]] => [[5,2,1],[2,1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[[2,2,2,1],[1,1]] => [[2,2,1,1],[1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 2
[[3,3,3,1],[2,2,1]] => [[3,2,1,1],[2]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 3
[[3,3,2,1],[2,2]] => [[3,3,1,1],[2,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[[4,4,3,1],[3,3,1]] => [[4,3,1,1],[3,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[[3,2,2,1],[2,1]] => [[3,3,2,1],[2,1,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
>>> Load all 1067 entries. <<<[[4,3,3,1],[3,2,1]] => [[4,3,2,1],[3,1,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[4,3,2,1],[3,2]] => [[4,4,2,1],[3,2,1]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[5,4,3,1],[4,3,1]] => [[5,4,2,1],[4,2,1]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[2,2,2,2],[1,1,1]] => [[2,1,1,1],[]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 2
[[3,3,3,2],[2,2,2]] => [[3,1,1,1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[[3,3,2,2],[2,2,1]] => [[3,2,1,1],[1,1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 3
[[4,4,3,2],[3,3,2]] => [[4,2,1,1],[2,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 3
[[3,2,2,2],[2,1,1]] => [[3,2,2,1],[1,1,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[4,3,3,2],[3,2,2]] => [[4,2,2,1],[2,1,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[[4,3,2,2],[3,2,1]] => [[4,3,2,1],[2,2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[5,4,3,2],[4,3,2]] => [[5,3,2,1],[3,2,1]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[1,1,1,1,1],[]] => [[1,1,1,1,1],[]] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[2,2,2,2,1],[1,1,1,1]] => [[2,1,1,1,1],[1]] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[[2,2,2,1,1],[1,1,1]] => [[2,2,1,1,1],[1,1]] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[3,3,3,2,1],[2,2,2,1]] => [[3,2,1,1,1],[2,1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[2,2,1,1,1],[1,1]] => [[2,2,2,1,1],[1,1,1]] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,2,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1,1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[3,3,2,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2,1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2,1]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[2,1,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1,1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[3,2,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[3,2,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[4,3,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[3,2,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[4,3,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[4,3,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[5,4,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[6],[]] => [[6],[]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[5,1],[]] => [[5,5],[4]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[6,1],[1]] => [[6,5],[5]] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[[4,2],[]] => [[4,4],[2]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[5,2],[1]] => [[5,4],[3]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[6,2],[2]] => [[6,4],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[[4,1,1],[]] => [[4,4,4],[3,3]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[5,2,1],[1,1]] => [[5,4,4],[4,3]] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[[5,1,1],[1]] => [[5,5,4],[4,4]] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[[6,2,1],[2,1]] => [[6,5,4],[5,4]] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[[3,3],[]] => [[3,3],[]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[[4,3],[1]] => [[4,3],[1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 2
[[5,3],[2]] => [[5,3],[2]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[6,3],[3]] => [[6,3],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[[3,2,1],[]] => [[3,3,3],[2,1]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[4,3,1],[1,1]] => [[4,3,3],[3,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[4,2,1],[1]] => [[4,4,3],[3,2]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[5,3,1],[2,1]] => [[5,4,3],[4,2]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[5,2,1],[2]] => [[5,5,3],[4,3]] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[6,3,1],[3,1]] => [[6,5,3],[5,3]] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[[4,2,2],[1,1]] => [[4,3,3],[2,2]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[5,3,2],[2,2]] => [[5,3,3],[3,2]] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[5,2,2],[2,1]] => [[5,4,3],[3,3]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[6,3,2],[3,2]] => [[6,4,3],[4,3]] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3
[[3,1,1,1],[]] => [[3,3,3,3],[2,2,2]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[4,2,2,1],[1,1,1]] => [[4,3,3,3],[3,2,2]] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[[4,2,1,1],[1,1]] => [[4,4,3,3],[3,3,2]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[5,3,2,1],[2,2,1]] => [[5,4,3,3],[4,3,2]] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[[4,1,1,1],[1]] => [[4,4,4,3],[3,3,3]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[5,2,2,1],[2,1,1]] => [[5,4,4,3],[4,3,3]] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[[5,2,1,1],[2,1]] => [[5,5,4,3],[4,4,3]] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[[6,3,2,1],[3,2,1]] => [[6,5,4,3],[5,4,3]] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[[4,4],[2]] => [[4,2],[]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 2
[[5,4],[3]] => [[5,2],[1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[[6,4],[4]] => [[6,2],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[[3,3,1],[1]] => [[3,3,2],[2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[4,4,1],[2,1]] => [[4,3,2],[3]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[4,3,1],[2]] => [[4,4,2],[3,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[5,4,1],[3,1]] => [[5,4,2],[4,1]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[5,3,1],[3]] => [[5,5,2],[4,2]] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[[6,4,1],[4,1]] => [[6,5,2],[5,2]] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[[2,2,2],[]] => [[2,2,2],[]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1
[[3,3,2],[1,1]] => [[3,2,2],[1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 2
[[4,4,2],[2,2]] => [[4,2,2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[[3,2,2],[1]] => [[3,3,2],[1,1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[4,3,2],[2,1]] => [[4,3,2],[2,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[5,4,2],[3,2]] => [[5,3,2],[3,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[4,2,2],[2]] => [[4,4,2],[2,2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[5,3,2],[3,1]] => [[5,4,2],[3,2]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[6,4,2],[4,2]] => [[6,4,2],[4,2]] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[[2,2,1,1],[]] => [[2,2,2,2],[1,1]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[3,3,2,1],[1,1,1]] => [[3,2,2,2],[2,1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[3,3,1,1],[1,1]] => [[3,3,2,2],[2,2]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,2,1],[2,2,1]] => [[4,3,2,2],[3,2]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[3,2,1,1],[1]] => [[3,3,3,2],[2,2,1]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[4,3,2,1],[2,1,1]] => [[4,3,3,2],[3,2,1]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[4,3,1,1],[2,1]] => [[4,4,3,2],[3,3,1]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[5,4,2,1],[3,2,1]] => [[5,4,3,2],[4,3,1]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[4,2,1,1],[2]] => [[4,4,4,2],[3,3,2]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[5,3,2,1],[3,1,1]] => [[5,4,4,2],[4,3,2]] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[[5,3,1,1],[3,1]] => [[5,5,4,2],[4,4,2]] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[[6,4,2,1],[4,2,1]] => [[6,5,4,2],[5,4,2]] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[[4,3,3],[2,2]] => [[4,2,2],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[[5,4,3],[3,3]] => [[5,2,2],[2,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[[5,3,3],[3,2]] => [[5,3,2],[2,2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[6,4,3],[4,3]] => [[6,3,2],[3,2]] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[[3,2,2,1],[1,1]] => [[3,3,2,2],[2,1,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,3,3,1],[2,2,1]] => [[4,3,2,2],[3,1,1]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[4,3,2,1],[2,2]] => [[4,4,2,2],[3,2,1]] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[5,4,3,1],[3,3,1]] => [[5,4,2,2],[4,2,1]] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[4,2,2,1],[2,1]] => [[4,4,3,2],[3,2,2]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[5,3,3,1],[3,2,1]] => [[5,4,3,2],[4,2,2]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[5,3,2,1],[3,2]] => [[5,5,3,2],[4,3,2]] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[[6,4,3,1],[4,3,1]] => [[6,5,3,2],[5,3,2]] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[[3,2,2,2],[1,1,1]] => [[3,2,2,2],[1,1,1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[4,3,3,2],[2,2,2]] => [[4,2,2,2],[2,1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[[4,3,2,2],[2,2,1]] => [[4,3,2,2],[2,2,1]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[5,4,3,2],[3,3,2]] => [[5,3,2,2],[3,2,1]] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[[4,2,2,2],[2,1,1]] => [[4,3,3,2],[2,2,2]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[5,3,3,2],[3,2,2]] => [[5,3,3,2],[3,2,2]] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[[5,3,2,2],[3,2,1]] => [[5,4,3,2],[3,3,2]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[6,4,3,2],[4,3,2]] => [[6,4,3,2],[4,3,2]] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[[2,1,1,1,1],[]] => [[2,2,2,2,2],[1,1,1,1]] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[3,2,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1,1]] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[[3,2,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1,1]] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[[4,3,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1,1]] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[[3,2,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2,1]] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[[4,3,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2,1]] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2,1]] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[[5,4,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2,1]] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[[3,1,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,2]] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[[4,2,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,2]] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[[4,2,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,2]] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[[5,3,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,2]] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[[4,2,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,2]] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[[5,3,2,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,3,2]] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[[5,3,2,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,3,2]] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[[6,4,3,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,3,2]] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[[5,5],[4]] => [[5,1],[]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[[6,5],[5]] => [[6,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[[4,4,1],[3]] => [[4,4,1],[3]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[5,5,1],[4,1]] => [[5,4,1],[4]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[[5,4,1],[4]] => [[5,5,1],[4,1]] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[[6,5,1],[5,1]] => [[6,5,1],[5,1]] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[[3,3,2],[2]] => [[3,3,1],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 2
[[4,4,2],[3,1]] => [[4,3,1],[2]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[5,5,2],[4,2]] => [[5,3,1],[3]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[[4,3,2],[3]] => [[4,4,1],[2,1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[5,4,2],[4,1]] => [[5,4,1],[3,1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[[6,5,2],[5,2]] => [[6,4,1],[4,1]] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[[3,3,1,1],[2]] => [[3,3,3,1],[2,2]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[4,4,2,1],[3,1,1]] => [[4,3,3,1],[3,2]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[4,4,1,1],[3,1]] => [[4,4,3,1],[3,3]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[5,5,2,1],[4,2,1]] => [[5,4,3,1],[4,3]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[4,3,1,1],[3]] => [[4,4,4,1],[3,3,1]] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[[5,4,2,1],[4,1,1]] => [[5,4,4,1],[4,3,1]] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[[5,4,1,1],[4,1]] => [[5,5,4,1],[4,4,1]] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[[6,5,2,1],[5,2,1]] => [[6,5,4,1],[5,4,1]] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[[3,3,3],[2,1]] => [[3,2,1],[]] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[[4,4,3],[3,2]] => [[4,2,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 3
[[5,5,3],[4,3]] => [[5,2,1],[2]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[[4,3,3],[3,1]] => [[4,3,1],[1,1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[5,4,3],[4,2]] => [[5,3,1],[2,1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[[6,5,3],[5,3]] => [[6,3,1],[3,1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[[2,2,2,1],[1]] => [[2,2,2,1],[1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 2
[[3,3,3,1],[2,1,1]] => [[3,2,2,1],[2]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[3,3,2,1],[2,1]] => [[3,3,2,1],[2,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[4,4,3,1],[3,2,1]] => [[4,3,2,1],[3,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[4,4,2,1],[3,2]] => [[4,4,2,1],[3,2]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[5,5,3,1],[4,3,1]] => [[5,4,2,1],[4,2]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[3,2,2,1],[2]] => [[3,3,3,1],[2,1,1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[4,3,3,1],[3,1,1]] => [[4,3,3,1],[3,1,1]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[4,3,2,1],[3,1]] => [[4,4,3,1],[3,2,1]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[5,4,3,1],[4,2,1]] => [[5,4,3,1],[4,2,1]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[5,4,2,1],[4,2]] => [[5,5,3,1],[4,3,1]] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3
[[6,5,3,1],[5,3,1]] => [[6,5,3,1],[5,3,1]] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4
[[3,3,2,2],[2,1,1]] => [[3,2,2,1],[1,1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[4,4,3,2],[3,2,2]] => [[4,2,2,1],[2,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[[4,4,2,2],[3,2,1]] => [[4,3,2,1],[2,2]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[5,5,3,2],[4,3,2]] => [[5,3,2,1],[3,2]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[4,3,2,2],[3,1,1]] => [[4,3,3,1],[2,2,1]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[5,4,3,2],[4,2,2]] => [[5,3,3,1],[3,2,1]] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[[5,4,2,2],[4,2,1]] => [[5,4,3,1],[3,3,1]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[6,5,3,2],[5,3,2]] => [[6,4,3,1],[4,3,1]] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[[2,2,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[3,3,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[3,3,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[4,4,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[3,3,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[4,4,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[4,4,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[5,5,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[3,2,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2,1]] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[[4,3,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2,1]] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[[4,3,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2,1]] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 3
[[5,4,3,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,2,1]] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4
[[4,3,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3,1]] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[[5,4,2,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,3,1]] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[[5,4,2,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,3,1]] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[[6,5,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3,1]] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[[4,4,4],[3,3]] => [[4,1,1],[]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 2
[[5,5,4],[4,4]] => [[5,1,1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[[5,4,4],[4,3]] => [[5,2,1],[1,1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[[6,5,4],[5,4]] => [[6,2,1],[2,1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3
[[3,3,3,1],[2,2]] => [[3,3,1,1],[2]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[[4,4,4,1],[3,3,1]] => [[4,3,1,1],[3]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[[4,4,3,1],[3,3]] => [[4,4,1,1],[3,1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[[5,5,4,1],[4,4,1]] => [[5,4,1,1],[4,1]] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[[4,3,3,1],[3,2]] => [[4,4,2,1],[3,1,1]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[5,4,4,1],[4,3,1]] => [[5,4,2,1],[4,1,1]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[5,4,3,1],[4,3]] => [[5,5,2,1],[4,2,1]] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[[6,5,4,1],[5,4,1]] => [[6,5,2,1],[5,2,1]] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[[2,2,2,2],[1,1]] => [[2,2,1,1],[]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 2
[[3,3,3,2],[2,2,1]] => [[3,2,1,1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 3
[[4,4,4,2],[3,3,2]] => [[4,2,1,1],[2]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 3
[[3,3,2,2],[2,2]] => [[3,3,1,1],[1,1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[[4,4,3,2],[3,3,1]] => [[4,3,1,1],[2,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[[5,5,4,2],[4,4,2]] => [[5,3,1,1],[3,1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[[3,2,2,2],[2,1]] => [[3,3,2,1],[1,1,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[4,3,3,2],[3,2,1]] => [[4,3,2,1],[2,1,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[5,4,4,2],[4,3,2]] => [[5,3,2,1],[3,1,1]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[4,3,2,2],[3,2]] => [[4,4,2,1],[2,2,1]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[5,4,3,2],[4,3,1]] => [[5,4,2,1],[3,2,1]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[6,5,4,2],[5,4,2]] => [[6,4,2,1],[4,2,1]] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[[2,2,2,1,1],[1,1]] => [[2,2,2,1,1],[1,1]] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,3,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[3,3,3,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,4,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[3,3,2,1,1],[2,2]] => [[3,3,3,1,1],[2,2,1]] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[[4,4,3,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2,1]] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[[4,4,3,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3,1]] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[[5,5,4,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3,1]] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[[3,2,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[4,3,3,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,1,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[4,3,3,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,1,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[5,4,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[4,3,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2,1]] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[[5,4,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2,1]] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[[5,4,3,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,2,1]] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[[6,5,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2,1]] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[[3,3,3,3],[2,2,2]] => [[3,1,1,1],[]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[[4,4,4,3],[3,3,3]] => [[4,1,1,1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[[4,4,3,3],[3,3,2]] => [[4,2,1,1],[1,1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 3
[[5,5,4,3],[4,4,3]] => [[5,2,1,1],[2,1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[[4,3,3,3],[3,2,2]] => [[4,2,2,1],[1,1,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[[5,4,4,3],[4,3,3]] => [[5,2,2,1],[2,1,1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[[5,4,3,3],[4,3,2]] => [[5,3,2,1],[2,2,1]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[6,5,4,3],[5,4,3]] => [[6,3,2,1],[3,2,1]] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[[2,2,2,2,1],[1,1,1]] => [[2,2,1,1,1],[1]] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[3,3,3,3,1],[2,2,2,1]] => [[3,2,1,1,1],[2]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[3,3,3,2,1],[2,2,2]] => [[3,3,1,1,1],[2,1]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,4,3,1],[3,3,3,1]] => [[4,3,1,1,1],[3,1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[3,3,2,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1,1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,3,1],[3,3,2,1]] => [[4,3,2,1,1],[3,1,1]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[4,4,3,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2,1]] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[[5,5,4,3,1],[4,4,3,1]] => [[5,4,2,1,1],[4,2,1]] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[[3,2,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[4,3,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[4,3,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1,1]] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[[5,4,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1,1]] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[[4,3,2,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[5,4,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[5,4,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2,1]] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[[6,5,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2,1]] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[[2,2,2,2,2],[1,1,1,1]] => [[2,1,1,1,1],[]] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[[3,3,3,3,2],[2,2,2,2]] => [[3,1,1,1,1],[1]] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[[3,3,3,2,2],[2,2,2,1]] => [[3,2,1,1,1],[1,1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[4,4,4,3,2],[3,3,3,2]] => [[4,2,1,1,1],[2,1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[3,3,2,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1,1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[4,4,3,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1,1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[[4,4,3,2,2],[3,3,2,1]] => [[4,3,2,1,1],[2,2,1]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[5,5,4,3,2],[4,4,3,2]] => [[5,3,2,1,1],[3,2,1]] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[3,2,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[4,3,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1,1]] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[4,3,3,2,2],[3,2,2,1]] => [[4,3,2,2,1],[2,2,1,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[5,4,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1,1]] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[[4,3,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[5,4,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2,1]] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[[5,4,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[6,5,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2,1]] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[[1,1,1,1,1,1],[]] => [[1,1,1,1,1,1],[]] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[2,2,2,2,2,1],[1,1,1,1,1]] => [[2,1,1,1,1,1],[1]] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[[2,2,2,2,1,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1,1]] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[[3,3,3,3,2,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2,1]] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[[2,2,2,1,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1,1]] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[[3,3,3,2,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1,1]] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[3,3,3,2,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2,1]] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[4,4,4,3,2,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,2,1]] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[[2,2,1,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1,1]] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[3,3,2,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1,1]] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[3,3,2,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1,1]] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,4,3,3,2,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,2,1,1]] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[3,3,2,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2,1]] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[4,4,3,2,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,2,1]] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[4,4,3,2,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,2,1]] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[5,5,4,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2,1]] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[2,1,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1,1]] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[3,2,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1,1]] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[3,2,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1,1]] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[4,3,3,3,2,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,2,1,1,1]] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[[3,2,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1,1]] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[4,3,3,2,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,2,1,1]] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4
[[4,3,3,2,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,2,1,1]] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[[5,4,4,3,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1,1]] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[3,2,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2,1]] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[[4,3,2,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,2,1]] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[[4,3,2,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,2,1]] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[[5,4,3,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,2,1]] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[[4,3,2,1,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,3,2,1]] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[[5,4,3,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,2,1]] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[5,4,3,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,2,1]] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[6,5,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2,1]] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[5,2],[]] => [[5,5],[3]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[6,2],[1]] => [[6,5],[4]] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[[4,3],[]] => [[4,4],[1]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[5,3],[1]] => [[5,4],[2]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[6,3],[2]] => [[6,4],[3]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[[4,2,1],[]] => [[4,4,4],[3,2]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[5,3,1],[1,1]] => [[5,4,4],[4,2]] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[[5,2,1],[1]] => [[5,5,4],[4,3]] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[[6,3,1],[2,1]] => [[6,5,4],[5,3]] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[[5,2,2],[1,1]] => [[5,4,4],[3,3]] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[[6,3,2],[2,2]] => [[6,4,4],[4,3]] => [6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[6,2,2],[2,1]] => [[6,5,4],[4,4]] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[[4,4],[1]] => [[4,3],[]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 2
[[5,4],[2]] => [[5,3],[1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[6,4],[3]] => [[6,3],[2]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[[3,3,1],[]] => [[3,3,3],[2]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[4,4,1],[1,1]] => [[4,3,3],[3]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[4,3,1],[1]] => [[4,4,3],[3,1]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[5,4,1],[2,1]] => [[5,4,3],[4,1]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[5,3,1],[2]] => [[5,5,3],[4,2]] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[6,4,1],[3,1]] => [[6,5,3],[5,2]] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[[3,2,2],[]] => [[3,3,3],[1,1]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[4,3,2],[1,1]] => [[4,3,3],[2,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[5,4,2],[2,2]] => [[5,3,3],[3,1]] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[4,2,2],[1]] => [[4,4,3],[2,2]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[5,3,2],[2,1]] => [[5,4,3],[3,2]] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[6,4,2],[3,2]] => [[6,4,3],[4,2]] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3
[[5,2,2],[2]] => [[5,5,3],[3,3]] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[6,3,2],[3,1]] => [[6,5,3],[4,3]] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[4,3,2,1],[1,1,1]] => [[4,3,3,3],[3,2,1]] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[[4,3,1,1],[1,1]] => [[4,4,3,3],[3,3,1]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[5,4,2,1],[2,2,1]] => [[5,4,3,3],[4,3,1]] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[[4,2,1,1],[1]] => [[4,4,4,3],[3,3,2]] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[5,3,2,1],[2,1,1]] => [[5,4,4,3],[4,3,2]] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[[5,3,1,1],[2,1]] => [[5,5,4,3],[4,4,2]] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[[6,4,2,1],[3,2,1]] => [[6,5,4,3],[5,4,2]] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[[5,3,3],[2,2]] => [[5,3,3],[2,2]] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[6,4,3],[3,3]] => [[6,3,3],[3,2]] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[[6,3,3],[3,2]] => [[6,4,3],[3,3]] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3
[[4,2,2,1],[1,1]] => [[4,4,3,3],[3,2,2]] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[5,3,3,1],[2,2,1]] => [[5,4,3,3],[4,2,2]] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[[5,3,2,1],[2,2]] => [[5,5,3,3],[4,3,2]] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[[6,4,3,1],[3,3,1]] => [[6,5,3,3],[5,3,2]] => [6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[[5,2,2,1],[2,1]] => [[5,5,4,3],[4,3,3]] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[[6,3,3,1],[3,2,1]] => [[6,5,4,3],[5,3,3]] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[[4,2,2,2],[1,1,1]] => [[4,3,3,3],[2,2,2]] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[[5,3,3,2],[2,2,2]] => [[5,3,3,3],[3,2,2]] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[[5,3,2,2],[2,2,1]] => [[5,4,3,3],[3,3,2]] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[[6,4,3,2],[3,3,2]] => [[6,4,3,3],[4,3,2]] => [6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3
[[5,2,2,2],[2,1,1]] => [[5,4,4,3],[3,3,3]] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[[6,3,3,2],[3,2,2]] => [[6,4,4,3],[4,3,3]] => [6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
[[6,3,2,2],[3,2,1]] => [[6,5,4,3],[4,4,3]] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[[5,5],[3]] => [[5,2],[]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[[6,5],[4]] => [[6,2],[1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[[4,4,1],[2]] => [[4,4,2],[3]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[5,5,1],[3,1]] => [[5,4,2],[4]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[5,4,1],[3]] => [[5,5,2],[4,1]] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[[6,5,1],[4,1]] => [[6,5,2],[5,1]] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[[3,3,2],[1]] => [[3,3,2],[1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[4,4,2],[2,1]] => [[4,3,2],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[5,5,2],[3,2]] => [[5,3,2],[3]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[4,3,2],[2]] => [[4,4,2],[2,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[5,4,2],[3,1]] => [[5,4,2],[3,1]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[6,5,2],[4,2]] => [[6,4,2],[4,1]] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[[5,3,2],[3]] => [[5,5,2],[3,2]] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[[6,4,2],[4,1]] => [[6,5,2],[4,2]] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[[3,3,1,1],[1]] => [[3,3,3,2],[2,2]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[4,4,2,1],[2,1,1]] => [[4,3,3,2],[3,2]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[4,4,1,1],[2,1]] => [[4,4,3,2],[3,3]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[5,5,2,1],[3,2,1]] => [[5,4,3,2],[4,3]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[4,3,1,1],[2]] => [[4,4,4,2],[3,3,1]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[5,4,2,1],[3,1,1]] => [[5,4,4,2],[4,3,1]] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[[5,4,1,1],[3,1]] => [[5,5,4,2],[4,4,1]] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[[6,5,2,1],[4,2,1]] => [[6,5,4,2],[5,4,1]] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[[3,3,3],[1,1]] => [[3,2,2],[]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 2
[[4,4,3],[2,2]] => [[4,2,2],[1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[[5,5,3],[3,3]] => [[5,2,2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[[4,3,3],[2,1]] => [[4,3,2],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[5,4,3],[3,2]] => [[5,3,2],[2,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[6,5,3],[4,3]] => [[6,3,2],[3,1]] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[[5,3,3],[3,1]] => [[5,4,2],[2,2]] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[6,4,3],[4,2]] => [[6,4,2],[3,2]] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[[2,2,2,1],[]] => [[2,2,2,2],[1]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[3,3,3,1],[1,1,1]] => [[3,2,2,2],[2]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[3,3,2,1],[1,1]] => [[3,3,2,2],[2,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,3,1],[2,2,1]] => [[4,3,2,2],[3,1]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[4,4,2,1],[2,2]] => [[4,4,2,2],[3,2]] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[5,5,3,1],[3,3,1]] => [[5,4,2,2],[4,2]] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[3,2,2,1],[1]] => [[3,3,3,2],[2,1,1]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[4,3,3,1],[2,1,1]] => [[4,3,3,2],[3,1,1]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[4,3,2,1],[2,1]] => [[4,4,3,2],[3,2,1]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[5,4,3,1],[3,2,1]] => [[5,4,3,2],[4,2,1]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[5,4,2,1],[3,2]] => [[5,5,3,2],[4,3,1]] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[[6,5,3,1],[4,3,1]] => [[6,5,3,2],[5,3,1]] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[[4,2,2,1],[2]] => [[4,4,4,2],[3,2,2]] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[5,3,3,1],[3,1,1]] => [[5,4,4,2],[4,2,2]] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[[5,3,2,1],[3,1]] => [[5,5,4,2],[4,3,2]] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[[6,4,3,1],[4,2,1]] => [[6,5,4,2],[5,3,2]] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[[3,3,2,2],[1,1,1]] => [[3,2,2,2],[1,1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[4,4,3,2],[2,2,2]] => [[4,2,2,2],[2,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[[4,4,2,2],[2,2,1]] => [[4,3,2,2],[2,2]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[5,5,3,2],[3,3,2]] => [[5,3,2,2],[3,2]] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[[4,3,2,2],[2,1,1]] => [[4,3,3,2],[2,2,1]] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[5,4,3,2],[3,2,2]] => [[5,3,3,2],[3,2,1]] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[[5,4,2,2],[3,2,1]] => [[5,4,3,2],[3,3,1]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[6,5,3,2],[4,3,2]] => [[6,4,3,2],[4,3,1]] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[[5,3,2,2],[3,1,1]] => [[5,4,4,2],[3,3,2]] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[[6,4,3,2],[4,2,2]] => [[6,4,4,2],[4,3,2]] => [6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[[6,4,2,2],[4,2,1]] => [[6,5,4,2],[4,4,2]] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[[2,2,1,1,1],[]] => [[2,2,2,2,2],[1,1,1]] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[3,3,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1]] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[[3,3,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1]] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[[4,4,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1]] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[[3,3,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2]] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[[4,4,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2]] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[[4,4,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2]] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[[5,5,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2]] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[[3,2,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,1]] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[[4,3,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,1]] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[[4,3,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,1]] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[[5,4,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,1]] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[[4,3,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,1]] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[[5,4,2,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,3,1]] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[[5,4,2,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,3,1]] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[[6,5,3,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,3,1]] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[[5,4,4],[3,3]] => [[5,2,2],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[[6,5,4],[4,4]] => [[6,2,2],[2,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[[6,4,4],[4,3]] => [[6,3,2],[2,2]] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[[4,3,3,1],[2,2]] => [[4,4,2,2],[3,1,1]] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[5,4,4,1],[3,3,1]] => [[5,4,2,2],[4,1,1]] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[5,4,3,1],[3,3]] => [[5,5,2,2],[4,2,1]] => [5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[[6,5,4,1],[4,4,1]] => [[6,5,2,2],[5,2,1]] => [6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3
[[5,3,3,1],[3,2]] => [[5,5,3,2],[4,2,2]] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[[6,4,4,1],[4,3,1]] => [[6,5,3,2],[5,2,2]] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[[3,2,2,2],[1,1]] => [[3,3,2,2],[1,1,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,3,3,2],[2,2,1]] => [[4,3,2,2],[2,1,1]] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[5,4,4,2],[3,3,2]] => [[5,3,2,2],[3,1,1]] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[[4,3,2,2],[2,2]] => [[4,4,2,2],[2,2,1]] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[5,4,3,2],[3,3,1]] => [[5,4,2,2],[3,2,1]] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[6,5,4,2],[4,4,2]] => [[6,4,2,2],[4,2,1]] => [6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[[4,2,2,2],[2,1]] => [[4,4,3,2],[2,2,2]] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[5,3,3,2],[3,2,1]] => [[5,4,3,2],[3,2,2]] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[6,4,4,2],[4,3,2]] => [[6,4,3,2],[4,2,2]] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[[5,3,2,2],[3,2]] => [[5,5,3,2],[3,3,2]] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[[6,4,3,2],[4,3,1]] => [[6,5,3,2],[4,3,2]] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[[3,2,2,1,1],[1,1]] => [[3,3,3,2,2],[2,2,1,1]] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[[4,3,3,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,1,1]] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[[4,3,3,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,1,1]] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[[5,4,4,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,1,1]] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[[4,3,2,1,1],[2,2]] => [[4,4,4,2,2],[3,3,2,1]] => [4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[[5,4,3,2,1],[3,3,1,1]] => [[5,4,4,2,2],[4,3,2,1]] => [5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3
[[5,4,3,1,1],[3,3,1]] => [[5,5,4,2,2],[4,4,2,1]] => [5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[[6,5,4,2,1],[4,4,2,1]] => [[6,5,4,2,2],[5,4,2,1]] => [6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[[4,2,2,1,1],[2,1]] => [[4,4,4,3,2],[3,3,2,2]] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[[5,3,3,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,2,2]] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[[5,3,3,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,2,2]] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[[6,4,4,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,2,2]] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[[4,3,3,3],[2,2,2]] => [[4,2,2,2],[1,1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[[5,4,4,3],[3,3,3]] => [[5,2,2,2],[2,1,1]] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[5,4,3,3],[3,3,2]] => [[5,3,2,2],[2,2,1]] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[[6,5,4,3],[4,4,3]] => [[6,3,2,2],[3,2,1]] => [6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[[5,3,3,3],[3,2,2]] => [[5,3,3,2],[2,2,2]] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[[6,4,4,3],[4,3,3]] => [[6,3,3,2],[3,2,2]] => [6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 3
[[6,4,3,3],[4,3,2]] => [[6,4,3,2],[3,3,2]] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[[3,2,2,2,1],[1,1,1]] => [[3,3,2,2,2],[2,1,1,1]] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[[4,3,3,3,1],[2,2,2,1]] => [[4,3,2,2,2],[3,1,1,1]] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[[4,3,3,2,1],[2,2,2]] => [[4,4,2,2,2],[3,2,1,1]] => [4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[[5,4,4,3,1],[3,3,3,1]] => [[5,4,2,2,2],[4,2,1,1]] => [5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3
[[4,3,2,2,1],[2,2,1]] => [[4,4,3,2,2],[3,2,2,1]] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[[5,4,3,3,1],[3,3,2,1]] => [[5,4,3,2,2],[4,2,2,1]] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[3,3,2]] => [[5,5,3,2,2],[4,3,2,1]] => [5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 3
[[6,5,4,3,1],[4,4,3,1]] => [[6,5,3,2,2],[5,3,2,1]] => [6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[[4,2,2,2,1],[2,1,1]] => [[4,4,3,3,2],[3,2,2,2]] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[[5,3,3,3,1],[3,2,2,1]] => [[5,4,3,3,2],[4,2,2,2]] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[[5,3,3,2,1],[3,2,2]] => [[5,5,3,3,2],[4,3,2,2]] => [5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[[6,4,4,3,1],[4,3,3,1]] => [[6,5,3,3,2],[5,3,2,2]] => [6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4
[[5,3,2,2,1],[3,2,1]] => [[5,5,4,3,2],[4,3,3,2]] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[[6,4,3,3,1],[4,3,2,1]] => [[6,5,4,3,2],[5,3,3,2]] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[[3,2,2,2,2],[1,1,1,1]] => [[3,2,2,2,2],[1,1,1,1]] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[[4,3,3,3,2],[2,2,2,2]] => [[4,2,2,2,2],[2,1,1,1]] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[[4,3,3,2,2],[2,2,2,1]] => [[4,3,2,2,2],[2,2,1,1]] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[[5,4,4,3,2],[3,3,3,2]] => [[5,3,2,2,2],[3,2,1,1]] => [5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[[4,3,2,2,2],[2,2,1,1]] => [[4,3,3,2,2],[2,2,2,1]] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[[5,4,3,3,2],[3,3,2,2]] => [[5,3,3,2,2],[3,2,2,1]] => [5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 3
[[5,4,3,2,2],[3,3,2,1]] => [[5,4,3,2,2],[3,3,2,1]] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[[6,5,4,3,2],[4,4,3,2]] => [[6,4,3,2,2],[4,3,2,1]] => [6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[[4,2,2,2,2],[2,1,1,1]] => [[4,3,3,3,2],[2,2,2,2]] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[[5,3,3,3,2],[3,2,2,2]] => [[5,3,3,3,2],[3,2,2,2]] => [5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[[5,3,3,2,2],[3,2,2,1]] => [[5,4,3,3,2],[3,3,2,2]] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[[6,4,4,3,2],[4,3,3,2]] => [[6,4,3,3,2],[4,3,2,2]] => [6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[[5,3,2,2,2],[3,2,1,1]] => [[5,4,4,3,2],[3,3,3,2]] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[[6,4,3,3,2],[4,3,2,2]] => [[6,4,4,3,2],[4,3,3,2]] => [6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
[[6,4,3,2,2],[4,3,2,1]] => [[6,5,4,3,2],[4,4,3,2]] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[[6,6],[5]] => [[6,1],[]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[[5,5,1],[4]] => [[5,5,1],[4]] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[[6,6,1],[5,1]] => [[6,5,1],[5]] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[[4,4,2],[3]] => [[4,4,1],[2]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[5,5,2],[4,1]] => [[5,4,1],[3]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[[6,6,2],[5,2]] => [[6,4,1],[4]] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[[5,4,2],[4]] => [[5,5,1],[3,1]] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[[6,5,2],[5,1]] => [[6,5,1],[4,1]] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[[4,4,1,1],[3]] => [[4,4,4,1],[3,3]] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[[5,5,2,1],[4,1,1]] => [[5,4,4,1],[4,3]] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[[5,5,1,1],[4,1]] => [[5,5,4,1],[4,4]] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[[6,6,2,1],[5,2,1]] => [[6,5,4,1],[5,4]] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[[3,3,3],[2]] => [[3,3,1],[]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 2
[[4,4,3],[3,1]] => [[4,3,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[5,5,3],[4,2]] => [[5,3,1],[2]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[[6,6,3],[5,3]] => [[6,3,1],[3]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[[4,3,3],[3]] => [[4,4,1],[1,1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[5,4,3],[4,1]] => [[5,4,1],[2,1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[[6,5,3],[5,2]] => [[6,4,1],[3,1]] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[[3,3,2,1],[2]] => [[3,3,3,1],[2,1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[4,4,3,1],[3,1,1]] => [[4,3,3,1],[3,1]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[4,4,2,1],[3,1]] => [[4,4,3,1],[3,2]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[5,5,3,1],[4,2,1]] => [[5,4,3,1],[4,2]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[5,5,2,1],[4,2]] => [[5,5,3,1],[4,3]] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3
[[6,6,3,1],[5,3,1]] => [[6,5,3,1],[5,3]] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4
[[4,3,2,1],[3]] => [[4,4,4,1],[3,2,1]] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[[5,4,3,1],[4,1,1]] => [[5,4,4,1],[4,2,1]] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[[5,4,2,1],[4,1]] => [[5,5,4,1],[4,3,1]] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[[6,5,3,1],[5,2,1]] => [[6,5,4,1],[5,3,1]] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[[4,4,2,2],[3,1,1]] => [[4,3,3,1],[2,2]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[5,5,3,2],[4,2,2]] => [[5,3,3,1],[3,2]] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[[5,5,2,2],[4,2,1]] => [[5,4,3,1],[3,3]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[6,6,3,2],[5,3,2]] => [[6,4,3,1],[4,3]] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[[5,4,2,2],[4,1,1]] => [[5,4,4,1],[3,3,1]] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[[6,5,3,2],[5,2,2]] => [[6,4,4,1],[4,3,1]] => [6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 3
[[6,5,2,2],[5,2,1]] => [[6,5,4,1],[4,4,1]] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[[3,3,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2]] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[[4,4,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2]] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[[4,4,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2]] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 3
[[5,5,3,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,2]] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4
[[4,4,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3]] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[[5,5,2,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,3]] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[[5,5,2,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,3]] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[[6,6,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3]] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[[4,4,4],[3,2]] => [[4,2,1],[]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 3
[[5,5,4],[4,3]] => [[5,2,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[[6,6,4],[5,4]] => [[6,2,1],[2]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3
[[5,4,4],[4,2]] => [[5,3,1],[1,1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[[6,5,4],[5,3]] => [[6,3,1],[2,1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[[3,3,3,1],[2,1]] => [[3,3,2,1],[2]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[4,4,4,1],[3,2,1]] => [[4,3,2,1],[3]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[4,4,3,1],[3,2]] => [[4,4,2,1],[3,1]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[5,5,4,1],[4,3,1]] => [[5,4,2,1],[4,1]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[5,5,3,1],[4,3]] => [[5,5,2,1],[4,2]] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[[6,6,4,1],[5,4,1]] => [[6,5,2,1],[5,2]] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[[4,3,3,1],[3,1]] => [[4,4,3,1],[3,1,1]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[5,4,4,1],[4,2,1]] => [[5,4,3,1],[4,1,1]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[5,4,3,1],[4,2]] => [[5,5,3,1],[4,2,1]] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3
[[6,5,4,1],[5,3,1]] => [[6,5,3,1],[5,2,1]] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4
[[2,2,2,2],[1]] => [[2,2,2,1],[]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 2
[[3,3,3,2],[2,1,1]] => [[3,2,2,1],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[4,4,4,2],[3,2,2]] => [[4,2,2,1],[2]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[[3,3,2,2],[2,1]] => [[3,3,2,1],[1,1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[4,4,3,2],[3,2,1]] => [[4,3,2,1],[2,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[5,5,4,2],[4,3,2]] => [[5,3,2,1],[3,1]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[4,4,2,2],[3,2]] => [[4,4,2,1],[2,2]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[5,5,3,2],[4,3,1]] => [[5,4,2,1],[3,2]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[6,6,4,2],[5,4,2]] => [[6,4,2,1],[4,2]] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[[3,2,2,2],[2]] => [[3,3,3,1],[1,1,1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[4,3,3,2],[3,1,1]] => [[4,3,3,1],[2,1,1]] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[5,4,4,2],[4,2,2]] => [[5,3,3,1],[3,1,1]] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[[4,3,2,2],[3,1]] => [[4,4,3,1],[2,2,1]] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[5,4,3,2],[4,2,1]] => [[5,4,3,1],[3,2,1]] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[6,5,4,2],[5,3,2]] => [[6,4,3,1],[4,2,1]] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[[5,4,2,2],[4,2]] => [[5,5,3,1],[3,3,1]] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3
[[6,5,3,2],[5,3,1]] => [[6,5,3,1],[4,3,1]] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4
[[2,2,2,1,1],[1]] => [[2,2,2,2,1],[1,1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[3,3,3,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[3,3,3,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[4,4,4,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[3,3,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[4,4,3,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[4,4,3,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[5,5,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[4,4,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2]] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[[5,5,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2]] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[[5,5,3,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,2]] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[[6,6,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2]] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[[3,2,2,1,1],[2]] => [[3,3,3,3,1],[2,2,1,1]] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[[4,3,3,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,1,1]] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[[4,3,3,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,1,1]] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 3
[[5,4,4,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,1,1]] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4
[[4,3,2,1,1],[3,1]] => [[4,4,4,3,1],[3,3,2,1]] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[[5,4,3,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,2,1]] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[[5,4,3,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,2,1]] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[[6,5,4,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,2,1]] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[[4,4,3,3],[3,2,2]] => [[4,2,2,1],[1,1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[[5,5,4,3],[4,3,3]] => [[5,2,2,1],[2,1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[[5,5,3,3],[4,3,2]] => [[5,3,2,1],[2,2]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[6,6,4,3],[5,4,3]] => [[6,3,2,1],[3,2]] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[[5,4,3,3],[4,2,2]] => [[5,3,3,1],[2,2,1]] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[[6,5,4,3],[5,3,3]] => [[6,3,3,1],[3,2,1]] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 3
[[6,5,3,3],[5,3,2]] => [[6,4,3,1],[3,3,1]] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[[3,3,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[4,4,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[4,4,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1]] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[[5,5,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1]] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[[4,4,2,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,2]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[5,5,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[5,5,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2]] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[[6,6,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2]] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[[4,3,2,2,1],[3,1,1]] => [[4,4,3,3,1],[3,2,2,1]] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 3
[[5,4,3,3,1],[4,2,2,1]] => [[5,4,3,3,1],[4,2,2,1]] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4
[[5,4,3,2,1],[4,2,2]] => [[5,5,3,3,1],[4,3,2,1]] => [5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 3
[[6,5,4,3,1],[5,3,3,1]] => [[6,5,3,3,1],[5,3,2,1]] => [6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[[5,4,2,2,1],[4,2,1]] => [[5,5,4,3,1],[4,3,3,1]] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[[6,5,3,3,1],[5,3,2,1]] => [[6,5,4,3,1],[5,3,3,1]] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[[3,3,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[4,4,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1]] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[4,4,3,2,2],[3,2,2,1]] => [[4,3,2,2,1],[2,2,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[5,5,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1]] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[[4,4,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[5,5,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2]] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[[5,5,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[6,6,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2]] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[[4,3,2,2,2],[3,1,1,1]] => [[4,3,3,3,1],[2,2,2,1]] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[[5,4,3,3,2],[4,2,2,2]] => [[5,3,3,3,1],[3,2,2,1]] => [5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 3
[[5,4,3,2,2],[4,2,2,1]] => [[5,4,3,3,1],[3,3,2,1]] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4
[[6,5,4,3,2],[5,3,3,2]] => [[6,4,3,3,1],[4,3,2,1]] => [6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[[5,4,2,2,2],[4,2,1,1]] => [[5,4,4,3,1],[3,3,3,1]] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[[6,5,3,3,2],[5,3,2,2]] => [[6,4,4,3,1],[4,3,3,1]] => [6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 4
[[6,5,3,2,2],[5,3,2,1]] => [[6,5,4,3,1],[4,4,3,1]] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[[2,2,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1]] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[3,3,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1]] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[3,3,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1]] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[4,4,3,3,2,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,2,1,1]] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[[3,3,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1]] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[4,4,3,2,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,2,1]] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4
[[4,4,3,2,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,2,1]] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[[5,5,4,3,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1]] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[3,3,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2]] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[[4,4,2,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,2]] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[[4,4,2,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,2]] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[[5,5,3,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,2]] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[[4,4,2,1,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,3,2]] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[[5,5,3,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,2]] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[5,5,3,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,2]] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[6,6,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2]] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[5,5,5],[4,4]] => [[5,1,1],[]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[[6,6,5],[5,5]] => [[6,1,1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[[6,5,5],[5,4]] => [[6,2,1],[1,1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3
[[4,4,4,1],[3,3]] => [[4,4,1,1],[3]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[[5,5,5,1],[4,4,1]] => [[5,4,1,1],[4]] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[[5,5,4,1],[4,4]] => [[5,5,1,1],[4,1]] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 2
[[6,6,5,1],[5,5,1]] => [[6,5,1,1],[5,1]] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[[5,4,4,1],[4,3]] => [[5,5,2,1],[4,1,1]] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[[6,5,5,1],[5,4,1]] => [[6,5,2,1],[5,1,1]] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[[3,3,3,2],[2,2]] => [[3,3,1,1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[[4,4,4,2],[3,3,1]] => [[4,3,1,1],[2]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[[5,5,5,2],[4,4,2]] => [[5,3,1,1],[3]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[[4,4,3,2],[3,3]] => [[4,4,1,1],[2,1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[[5,5,4,2],[4,4,1]] => [[5,4,1,1],[3,1]] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[[6,6,5,2],[5,5,2]] => [[6,4,1,1],[4,1]] => [6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3
[[4,3,3,2],[3,2]] => [[4,4,2,1],[2,1,1]] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[5,4,4,2],[4,3,1]] => [[5,4,2,1],[3,1,1]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[6,5,5,2],[5,4,2]] => [[6,4,2,1],[4,1,1]] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[[5,4,3,2],[4,3]] => [[5,5,2,1],[3,2,1]] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[[6,5,4,2],[5,4,1]] => [[6,5,2,1],[4,2,1]] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[[3,3,3,1,1],[2,2]] => [[3,3,3,1,1],[2,2]] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[[4,4,4,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2]] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[[4,4,4,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3]] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[[5,5,5,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3]] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[[4,4,3,1,1],[3,3]] => [[4,4,4,1,1],[3,3,1]] => [4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 2
[[5,5,4,2,1],[4,4,1,1]] => [[5,4,4,1,1],[4,3,1]] => [5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 3
[[5,5,4,1,1],[4,4,1]] => [[5,5,4,1,1],[4,4,1]] => [5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 3
[[6,6,5,2,1],[5,5,2,1]] => [[6,5,4,1,1],[5,4,1]] => [6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[[4,3,3,1,1],[3,2]] => [[4,4,4,2,1],[3,3,1,1]] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[[5,4,4,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,1,1]] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[[5,4,4,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,1,1]] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[[6,5,5,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,1,1]] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[[3,3,3,3],[2,2,1]] => [[3,2,1,1],[]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 3
[[4,4,4,3],[3,3,2]] => [[4,2,1,1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 3
[[5,5,5,3],[4,4,3]] => [[5,2,1,1],[2]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[[4,4,3,3],[3,3,1]] => [[4,3,1,1],[1,1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[[5,5,4,3],[4,4,2]] => [[5,3,1,1],[2,1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[[6,6,5,3],[5,5,3]] => [[6,3,1,1],[3,1]] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3
[[4,3,3,3],[3,2,1]] => [[4,3,2,1],[1,1,1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[5,4,4,3],[4,3,2]] => [[5,3,2,1],[2,1,1]] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[6,5,5,3],[5,4,3]] => [[6,3,2,1],[3,1,1]] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[[5,4,3,3],[4,3,1]] => [[5,4,2,1],[2,2,1]] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[6,5,4,3],[5,4,2]] => [[6,4,2,1],[3,2,1]] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[[2,2,2,2,1],[1,1]] => [[2,2,2,1,1],[1]] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[[3,3,3,3,1],[2,2,1,1]] => [[3,2,2,1,1],[2]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[3,3,3,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,4,3,1],[3,3,2,1]] => [[4,3,2,1,1],[3,1]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[4,4,4,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2]] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[[5,5,5,3,1],[4,4,3,1]] => [[5,4,2,1,1],[4,2]] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[[3,3,2,2,1],[2,2]] => [[3,3,3,1,1],[2,1,1]] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[[4,4,3,3,1],[3,3,1,1]] => [[4,3,3,1,1],[3,1,1]] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[[4,4,3,2,1],[3,3,1]] => [[4,4,3,1,1],[3,2,1]] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[[5,5,4,3,1],[4,4,2,1]] => [[5,4,3,1,1],[4,2,1]] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[[5,5,4,2,1],[4,4,2]] => [[5,5,3,1,1],[4,3,1]] => [5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 3
[[6,6,5,3,1],[5,5,3,1]] => [[6,5,3,1,1],[5,3,1]] => [6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[[3,2,2,2,1],[2,1]] => [[3,3,3,2,1],[2,1,1,1]] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[4,3,3,3,1],[3,2,1,1]] => [[4,3,3,2,1],[3,1,1,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[4,3,3,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,1,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[5,4,4,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,1,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[5,4,4,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,1,1]] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[[6,5,5,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,1,1]] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[[4,3,2,2,1],[3,2]] => [[4,4,4,2,1],[3,2,2,1]] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[[5,4,3,3,1],[4,3,1,1]] => [[5,4,4,2,1],[4,2,2,1]] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[[5,4,3,2,1],[4,3,1]] => [[5,5,4,2,1],[4,3,2,1]] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[[6,5,4,3,1],[5,4,2,1]] => [[6,5,4,2,1],[5,3,2,1]] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[[3,3,3,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[4,4,4,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[[4,4,4,2,2],[3,3,2,1]] => [[4,3,2,1,1],[2,2]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[5,5,5,3,2],[4,4,3,2]] => [[5,3,2,1,1],[3,2]] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[4,4,3,2,2],[3,3,1,1]] => [[4,3,3,1,1],[2,2,1]] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[[5,5,4,3,2],[4,4,2,2]] => [[5,3,3,1,1],[3,2,1]] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[[5,5,4,2,2],[4,4,2,1]] => [[5,4,3,1,1],[3,3,1]] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[[6,6,5,3,2],[5,5,3,2]] => [[6,4,3,1,1],[4,3,1]] => [6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4
[[4,3,3,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,1,1]] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[5,4,4,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,1,1]] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[[5,4,4,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,1,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[6,5,5,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,1,1]] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[[5,4,3,2,2],[4,3,1,1]] => [[5,4,4,2,1],[3,3,2,1]] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[[6,5,4,3,2],[5,4,2,2]] => [[6,4,4,2,1],[4,3,2,1]] => [6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[[6,5,4,2,2],[5,4,2,1]] => [[6,5,4,2,1],[4,4,2,1]] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[[2,2,2,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1]] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[3,3,3,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1]] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[3,3,3,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1]] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,4,4,3,2,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,2,1]] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[3,3,3,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2]] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[4,4,4,2,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,2]] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[4,4,4,2,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,2]] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[5,5,5,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2]] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[3,3,2,1,1,1],[2,2]] => [[3,3,3,3,1,1],[2,2,2,1]] => [3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[4,4,3,2,2,1],[3,3,1,1,1]] => [[4,3,3,3,1,1],[3,2,2,1]] => [4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[[4,4,3,2,1,1],[3,3,1,1]] => [[4,4,3,3,1,1],[3,3,2,1]] => [4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 3
[[5,5,4,3,2,1],[4,4,2,2,1]] => [[5,4,3,3,1,1],[4,3,2,1]] => [5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[[4,4,3,1,1,1],[3,3,1]] => [[4,4,4,3,1,1],[3,3,3,1]] => [4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[[5,5,4,2,2,1],[4,4,2,1,1]] => [[5,4,4,3,1,1],[4,3,3,1]] => [5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[[5,5,4,2,1,1],[4,4,2,1]] => [[5,5,4,3,1,1],[4,4,3,1]] => [5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4
[[6,6,5,3,2,1],[5,5,3,2,1]] => [[6,5,4,3,1,1],[5,4,3,1]] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5
[[3,2,2,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,1,1]] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[[4,3,3,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,1,1]] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[[4,3,3,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,1,1]] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[[5,4,4,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,1,1]] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[[4,3,3,1,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,3,1,1]] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[[5,4,4,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,1,1]] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[5,4,4,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,1,1]] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[6,5,5,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,1,1]] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[4,4,4,4],[3,3,3]] => [[4,1,1,1],[]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[[5,5,5,4],[4,4,4]] => [[5,1,1,1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[[5,5,4,4],[4,4,3]] => [[5,2,1,1],[1,1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[[6,6,5,4],[5,5,4]] => [[6,2,1,1],[2,1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[[5,4,4,4],[4,3,3]] => [[5,2,2,1],[1,1,1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[[6,5,5,4],[5,4,4]] => [[6,2,2,1],[2,1,1]] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3
[[6,5,4,4],[5,4,3]] => [[6,3,2,1],[2,2,1]] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[[3,3,3,3,1],[2,2,2]] => [[3,3,1,1,1],[2]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,4,4,1],[3,3,3,1]] => [[4,3,1,1,1],[3]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[4,4,4,3,1],[3,3,3]] => [[4,4,1,1,1],[3,1]] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[[5,5,5,4,1],[4,4,4,1]] => [[5,4,1,1,1],[4,1]] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[[4,4,3,3,1],[3,3,2]] => [[4,4,2,1,1],[3,1,1]] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[[5,5,4,4,1],[4,4,3,1]] => [[5,4,2,1,1],[4,1,1]] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[[5,5,4,3,1],[4,4,3]] => [[5,5,2,1,1],[4,2,1]] => [5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 3
[[6,6,5,4,1],[5,5,4,1]] => [[6,5,2,1,1],[5,2,1]] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4
[[4,3,3,3,1],[3,2,2]] => [[4,4,2,2,1],[3,1,1,1]] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[[5,4,4,4,1],[4,3,3,1]] => [[5,4,2,2,1],[4,1,1,1]] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[[5,4,4,3,1],[4,3,3]] => [[5,5,2,2,1],[4,2,1,1]] => [5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 3
[[6,5,5,4,1],[5,4,4,1]] => [[6,5,2,2,1],[5,2,1,1]] => [6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 4
[[5,4,3,3,1],[4,3,2]] => [[5,5,3,2,1],[4,2,2,1]] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[[6,5,4,4,1],[5,4,3,1]] => [[6,5,3,2,1],[5,2,2,1]] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[[2,2,2,2,2],[1,1,1]] => [[2,2,1,1,1],[]] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[3,3,3,3,2],[2,2,2,1]] => [[3,2,1,1,1],[1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[4,4,4,4,2],[3,3,3,2]] => [[4,2,1,1,1],[2]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[3,3,3,2,2],[2,2,2]] => [[3,3,1,1,1],[1,1]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[[4,4,4,3,2],[3,3,3,1]] => [[4,3,1,1,1],[2,1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[5,5,5,4,2],[4,4,4,2]] => [[5,3,1,1,1],[3,1]] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[[3,3,2,2,2],[2,2,1]] => [[3,3,2,1,1],[1,1,1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[4,4,3,3,2],[3,3,2,1]] => [[4,3,2,1,1],[2,1,1]] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[5,5,4,4,2],[4,4,3,2]] => [[5,3,2,1,1],[3,1,1]] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[4,4,3,2,2],[3,3,2]] => [[4,4,2,1,1],[2,2,1]] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[[5,5,4,3,2],[4,4,3,1]] => [[5,4,2,1,1],[3,2,1]] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[[6,6,5,4,2],[5,5,4,2]] => [[6,4,2,1,1],[4,2,1]] => [6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4
[[3,2,2,2,2],[2,1,1]] => [[3,3,2,2,1],[1,1,1,1]] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[4,3,3,3,2],[3,2,2,1]] => [[4,3,2,2,1],[2,1,1,1]] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[5,4,4,4,2],[4,3,3,2]] => [[5,3,2,2,1],[3,1,1,1]] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[[4,3,3,2,2],[3,2,2]] => [[4,4,2,2,1],[2,2,1,1]] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[[5,4,4,3,2],[4,3,3,1]] => [[5,4,2,2,1],[3,2,1,1]] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[[6,5,5,4,2],[5,4,4,2]] => [[6,4,2,2,1],[4,2,1,1]] => [6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4
[[4,3,2,2,2],[3,2,1]] => [[4,4,3,2,1],[2,2,2,1]] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[5,4,3,3,2],[4,3,2,1]] => [[5,4,3,2,1],[3,2,2,1]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[6,5,4,4,2],[5,4,3,2]] => [[6,4,3,2,1],[4,2,2,1]] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[[5,4,3,2,2],[4,3,2]] => [[5,5,3,2,1],[3,3,2,1]] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[[6,5,4,3,2],[5,4,3,1]] => [[6,5,3,2,1],[4,3,2,1]] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[[2,2,2,2,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1]] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[[3,3,3,3,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1]] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[3,3,3,3,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2]] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[4,4,4,4,2,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,2]] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[[3,3,3,2,1,1],[2,2,2]] => [[3,3,3,1,1,1],[2,2,1]] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[4,4,4,3,2,1],[3,3,3,1,1]] => [[4,3,3,1,1,1],[3,2,1]] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[4,4,4,3,1,1],[3,3,3,1]] => [[4,4,3,1,1,1],[3,3,1]] => [4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[5,5,5,4,2,1],[4,4,4,2,1]] => [[5,4,3,1,1,1],[4,3,1]] => [5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[3,3,2,2,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,1,1]] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[4,4,3,3,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,1,1]] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[4,4,3,3,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,1,1]] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[5,5,4,4,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,1,1]] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[4,4,3,2,1,1],[3,3,2]] => [[4,4,4,2,1,1],[3,3,2,1]] => [4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[[5,5,4,3,2,1],[4,4,3,1,1]] => [[5,4,4,2,1,1],[4,3,2,1]] => [5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[[5,5,4,3,1,1],[4,4,3,1]] => [[5,5,4,2,1,1],[4,4,2,1]] => [5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[[6,6,5,4,2,1],[5,5,4,2,1]] => [[6,5,4,2,1,1],[5,4,2,1]] => [6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[[3,2,2,2,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,1,1,1]] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[4,3,3,3,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,1,1,1]] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4
[[4,3,3,3,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,1,1,1]] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[[5,4,4,4,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,1,1,1]] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[4,3,3,2,1,1],[3,2,2]] => [[4,4,4,2,2,1],[3,3,2,1,1]] => [4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[[5,4,4,3,2,1],[4,3,3,1,1]] => [[5,4,4,2,2,1],[4,3,2,1,1]] => [5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[[5,4,4,3,1,1],[4,3,3,1]] => [[5,5,4,2,2,1],[4,4,2,1,1]] => [5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4
[[6,5,5,4,2,1],[5,4,4,2,1]] => [[6,5,4,2,2,1],[5,4,2,1,1]] => [6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 5
[[4,3,2,2,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,2,2,1]] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[[5,4,3,3,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,2,2,1]] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[5,4,3,3,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,2,2,1]] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[6,5,4,4,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,2,2,1]] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[3,3,3,3,3],[2,2,2,2]] => [[3,1,1,1,1],[]] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[[4,4,4,4,3],[3,3,3,3]] => [[4,1,1,1,1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[[4,4,4,3,3],[3,3,3,2]] => [[4,2,1,1,1],[1,1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[5,5,5,4,3],[4,4,4,3]] => [[5,2,1,1,1],[2,1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3
[[4,4,3,3,3],[3,3,2,2]] => [[4,2,2,1,1],[1,1,1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[[5,5,4,4,3],[4,4,3,3]] => [[5,2,2,1,1],[2,1,1]] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[[5,5,4,3,3],[4,4,3,2]] => [[5,3,2,1,1],[2,2,1]] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[6,6,5,4,3],[5,5,4,3]] => [[6,3,2,1,1],[3,2,1]] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4
[[4,3,3,3,3],[3,2,2,2]] => [[4,2,2,2,1],[1,1,1,1]] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[5,4,4,4,3],[4,3,3,3]] => [[5,2,2,2,1],[2,1,1,1]] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[[5,4,4,3,3],[4,3,3,2]] => [[5,3,2,2,1],[2,2,1,1]] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[[6,5,5,4,3],[5,4,4,3]] => [[6,3,2,2,1],[3,2,1,1]] => [6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 4
[[5,4,3,3,3],[4,3,2,2]] => [[5,3,3,2,1],[2,2,2,1]] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[[6,5,4,4,3],[5,4,3,3]] => [[6,3,3,2,1],[3,2,2,1]] => [6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 4
[[6,5,4,3,3],[5,4,3,2]] => [[6,4,3,2,1],[3,3,2,1]] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[[2,2,2,2,2,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1]] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[[3,3,3,3,3,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2]] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[[3,3,3,3,2,1],[2,2,2,2]] => [[3,3,1,1,1,1],[2,1]] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[[4,4,4,4,3,1],[3,3,3,3,1]] => [[4,3,1,1,1,1],[3,1]] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3
[[3,3,3,2,2,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,1,1]] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[4,4,4,3,3,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,1,1]] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[[4,4,4,3,2,1],[3,3,3,2]] => [[4,4,2,1,1,1],[3,2,1]] => [4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[5,5,5,4,3,1],[4,4,4,3,1]] => [[5,4,2,1,1,1],[4,2,1]] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[3,3,2,2,2,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,1,1,1]] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[4,4,3,3,3,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,1,1,1]] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[4,4,3,3,2,1],[3,3,2,2]] => [[4,4,2,2,1,1],[3,2,1,1]] => [4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3
[[5,5,4,4,3,1],[4,4,3,3,1]] => [[5,4,2,2,1,1],[4,2,1,1]] => [5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4
[[4,4,3,2,2,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,2,2,1]] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[5,5,4,3,3,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,2,2,1]] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[5,5,4,3,2,1],[4,4,3,2]] => [[5,5,3,2,1,1],[4,3,2,1]] => [5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[[6,6,5,4,3,1],[5,5,4,3,1]] => [[6,5,3,2,1,1],[5,3,2,1]] => [6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5
[[3,2,2,2,2,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,1,1,1,1]] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[[4,3,3,3,3,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,1,1,1,1]] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[[4,3,3,3,2,1],[3,2,2,2]] => [[4,4,2,2,2,1],[3,2,1,1,1]] => [4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[[5,4,4,4,3,1],[4,3,3,3,1]] => [[5,4,2,2,2,1],[4,2,1,1,1]] => [5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[[4,3,3,2,2,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,2,2,1,1]] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[[5,4,4,3,3,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,2,2,1,1]] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[5,4,4,3,2,1],[4,3,3,2]] => [[5,5,3,2,2,1],[4,3,2,1,1]] => [5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[[6,5,5,4,3,1],[5,4,4,3,1]] => [[6,5,3,2,2,1],[5,3,2,1,1]] => [6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5
[[4,3,2,2,2,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,2,2,2,1]] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[[5,4,3,3,3,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,2,2,2,1]] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[[5,4,3,3,2,1],[4,3,2,2]] => [[5,5,3,3,2,1],[4,3,2,2,1]] => [5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4
[[6,5,4,4,3,1],[5,4,3,3,1]] => [[6,5,3,3,2,1],[5,3,2,2,1]] => [6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 5
[[5,4,3,2,2,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,3,3,2,1]] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[6,5,4,3,3,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,3,3,2,1]] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[2,2,2,2,2,2],[1,1,1,1,1]] => [[2,1,1,1,1,1],[]] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[[3,3,3,3,3,2],[2,2,2,2,2]] => [[3,1,1,1,1,1],[1]] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[[3,3,3,3,2,2],[2,2,2,2,1]] => [[3,2,1,1,1,1],[1,1]] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[[4,4,4,4,3,2],[3,3,3,3,2]] => [[4,2,1,1,1,1],[2,1]] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3
[[3,3,3,2,2,2],[2,2,2,1,1]] => [[3,2,2,1,1,1],[1,1,1]] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[4,4,4,3,3,2],[3,3,3,2,2]] => [[4,2,2,1,1,1],[2,1,1]] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[[4,4,4,3,2,2],[3,3,3,2,1]] => [[4,3,2,1,1,1],[2,2,1]] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[[5,5,5,4,3,2],[4,4,4,3,2]] => [[5,3,2,1,1,1],[3,2,1]] => [5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[3,3,2,2,2,2],[2,2,1,1,1]] => [[3,2,2,2,1,1],[1,1,1,1]] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[4,4,3,3,3,2],[3,3,2,2,2]] => [[4,2,2,2,1,1],[2,1,1,1]] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[4,4,3,3,2,2],[3,3,2,2,1]] => [[4,3,2,2,1,1],[2,2,1,1]] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[5,5,4,4,3,2],[4,4,3,3,2]] => [[5,3,2,2,1,1],[3,2,1,1]] => [5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 4
[[4,4,3,2,2,2],[3,3,2,1,1]] => [[4,3,3,2,1,1],[2,2,2,1]] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[5,5,4,3,3,2],[4,4,3,2,2]] => [[5,3,3,2,1,1],[3,2,2,1]] => [5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4
[[5,5,4,3,2,2],[4,4,3,2,1]] => [[5,4,3,2,1,1],[3,3,2,1]] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[6,6,5,4,3,2],[5,5,4,3,2]] => [[6,4,3,2,1,1],[4,3,2,1]] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[[3,2,2,2,2,2],[2,1,1,1,1]] => [[3,2,2,2,2,1],[1,1,1,1,1]] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[4,3,3,3,3,2],[3,2,2,2,2]] => [[4,2,2,2,2,1],[2,1,1,1,1]] => [4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3
[[4,3,3,3,2,2],[3,2,2,2,1]] => [[4,3,2,2,2,1],[2,2,1,1,1]] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[[5,4,4,4,3,2],[4,3,3,3,2]] => [[5,3,2,2,2,1],[3,2,1,1,1]] => [5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 4
[[4,3,3,2,2,2],[3,2,2,1,1]] => [[4,3,3,2,2,1],[2,2,2,1,1]] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4
[[5,4,4,3,3,2],[4,3,3,2,2]] => [[5,3,3,2,2,1],[3,2,2,1,1]] => [5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[[5,4,4,3,2,2],[4,3,3,2,1]] => [[5,4,3,2,2,1],[3,3,2,1,1]] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[6,5,5,4,3,2],[5,4,4,3,2]] => [[6,4,3,2,2,1],[4,3,2,1,1]] => [6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 5
[[4,3,2,2,2,2],[3,2,1,1,1]] => [[4,3,3,3,2,1],[2,2,2,2,1]] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[[5,4,3,3,3,2],[4,3,2,2,2]] => [[5,3,3,3,2,1],[3,2,2,2,1]] => [5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[[5,4,3,3,2,2],[4,3,2,2,1]] => [[5,4,3,3,2,1],[3,3,2,2,1]] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[[6,5,4,4,3,2],[5,4,3,3,2]] => [[6,4,3,3,2,1],[4,3,2,2,1]] => [6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5
[[5,4,3,2,2,2],[4,3,2,1,1]] => [[5,4,4,3,2,1],[3,3,3,2,1]] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[6,5,4,3,3,2],[5,4,3,2,2]] => [[6,4,4,3,2,1],[4,3,3,2,1]] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5
[[6,5,4,3,2,2],[5,4,3,2,1]] => [[6,5,4,3,2,1],[4,4,3,2,1]] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[5,3],[]] => [[5,5],[2]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[4,4],[]] => [[4,4],[]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[4,3,1],[]] => [[4,4,4],[3,1]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[4,2,2],[]] => [[4,4,4],[2,2]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[3,3,2],[]] => [[3,3,3],[1]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[3,3,1,1],[]] => [[3,3,3,3],[2,2]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[2,2,2,2],[]] => [[2,2,2,2],[]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[2,2,2,1,1],[]] => [[2,2,2,2,2],[1,1]] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[5,4],[]] => [[5,5],[1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[4,4,1],[]] => [[4,4,4],[3]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[4,3,2],[]] => [[4,4,4],[2,1]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[3,3,3],[]] => [[3,3,3],[]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[2,2,2,2,1],[]] => [[2,2,2,2,2],[1]] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[5,5],[]] => [[5,5],[]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[4,4,2],[]] => [[4,4,4],[2]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[4,3,3],[]] => [[4,4,4],[1,1]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[3,3,3,1],[]] => [[3,3,3,3],[2]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[2,2,2,2,2],[]] => [[2,2,2,2,2],[]] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[4,4,3],[]] => [[4,4,4],[1]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[3,3,3,2],[]] => [[3,3,3,3],[1]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[4,4,4],[]] => [[4,4,4],[]] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[3,3,3,3],[]] => [[3,3,3,3],[]] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[3,3,3],[1]] => [[3,3,2],[]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[3,3,3,1],[1,1]] => [[3,3,2,2],[2]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,1],[1]] => [[4,4,3],[3]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[3,3,2,1],[1]] => [[3,3,3,2],[2,1]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[2,2,2,2,1],[1]] => [[2,2,2,2,1],[1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[3,3,3,1],[2]] => [[3,3,3,1],[2]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[3,3,3,1],[1]] => [[3,3,3,2],[2]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[3,3,3,2],[1,1,1]] => [[3,2,2,2],[1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[4,4,2],[1,1]] => [[4,3,3],[2]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[4,4,4],[2,2]] => [[4,2,2],[]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[[5,5],[2]] => [[5,3],[]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[4,4,3],[2,1]] => [[4,3,2],[1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[3,3,3,3],[2,1,1]] => [[3,2,2,1],[]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[4,3,3],[1,1]] => [[4,3,3],[1,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[3,3,3,3],[1,1,1]] => [[3,2,2,2],[]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[4,4,3],[1,1]] => [[4,3,3],[1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[4,4,4],[3,1]] => [[4,3,1],[]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 3
[[5,4],[1]] => [[5,4],[1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[4,4,4],[2,1]] => [[4,3,2],[]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 3
[[5,5],[1]] => [[5,4],[]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[4,4,4],[1,1]] => [[4,3,3],[]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[3,3,2,2],[1,1]] => [[3,3,2,2],[1,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,2],[2]] => [[4,4,2],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[3,3,3,2],[2,1]] => [[3,3,2,1],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[4,3,2],[1]] => [[4,4,3],[2,1]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[3,3,3,2],[1,1]] => [[3,3,2,2],[1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,2],[1]] => [[4,4,3],[2]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[2,2,2,2,2],[1,1]] => [[2,2,2,1,1],[]] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[[3,2,2,2],[1]] => [[3,3,3,2],[1,1,1]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[3,3,2,2],[2]] => [[3,3,3,1],[1,1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[3,3,2,2],[1]] => [[3,3,3,2],[1,1]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[2,2,2,2,2],[1]] => [[2,2,2,2,1],[]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[3,3,3,2],[2]] => [[3,3,3,1],[1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[3,3,3,2],[1]] => [[3,3,3,2],[1]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[3,3,3,3],[2,2]] => [[3,3,1,1],[]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[[4,3,3],[2]] => [[4,4,2],[1,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[4,4,3],[3]] => [[4,4,1],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[4,4,3],[2]] => [[4,4,2],[1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[3,3,3,3],[2,1]] => [[3,3,2,1],[]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[4,3,3],[1]] => [[4,4,3],[1,1]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[3,3,3,3],[1,1]] => [[3,3,2,2],[]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[4,4,3],[1]] => [[4,4,3],[1]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[4,4,4],[3]] => [[4,4,1],[]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[4,4,4],[2]] => [[4,4,2],[]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[4,4,4],[1]] => [[4,4,3],[]] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[3,3,3,3],[2]] => [[3,3,3,1],[]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[3,3,3,3],[1]] => [[3,3,3,2],[]] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,1 3,5,1 5,14,8,1 7,34,34,11,1 11,71,112,63,14,1
F1=q
F2=2 q+q2
F3=3 q+5 q2+q3
F4=5 q+14 q2+8 q3+q4
F5=7 q+34 q2+34 q3+11 q4+q5
F6=11 q+71 q2+112 q3+63 q4+14 q5+q6
Description
The number of valleys of the Dyck path.
Map
outer shape
Description
The outer shape of the skew partition.
Map
rotate
Description
The rotation of a skew partition.
This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition λ/μ, its rotation (λ/μ)♮ is the skew partition with cells {(a−i,b−j)|(i,j)∈λ/μ}, where b and a are the first part and the number of parts of λ respectively.
This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition λ/μ, its rotation (λ/μ)♮ is the skew partition with cells {(a−i,b−j)|(i,j)∈λ/μ}, where b and a are the first part and the number of parts of λ respectively.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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