- FindStat

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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Description

The number of valleys of the Dyck path.

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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 $\lambda/\mu$, its rotation $(\lambda/\mu)^\natural$ is the skew partition with cells $\{(a-i, b-j)| (i, j) \in \lambda/\mu\}$, where $b$ and $a$ are the first part and the number of parts of $\lambda$ respectively.

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to Dyck path

Description

Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.

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outer shape

Description

The outer shape of the skew partition.