Identifier
-
Mp00311:
Plane partitions
—to partition⟶
Integer partitions
St000318: Integer partitions ⟶ ℤ (values match St000159The number of distinct parts of the integer partition., St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition.)
Values
[[1]] => [1] => 2
[[1],[1]] => [1,1] => 2
[[2]] => [2] => 2
[[1,1]] => [2] => 2
[[1],[1],[1]] => [1,1,1] => 2
[[2],[1]] => [2,1] => 3
[[1,1],[1]] => [2,1] => 3
[[3]] => [3] => 2
[[2,1]] => [3] => 2
[[1,1,1]] => [3] => 2
[[1],[1],[1],[1]] => [1,1,1,1] => 2
[[2],[1],[1]] => [2,1,1] => 3
[[2],[2]] => [2,2] => 2
[[1,1],[1],[1]] => [2,1,1] => 3
[[1,1],[1,1]] => [2,2] => 2
[[3],[1]] => [3,1] => 3
[[2,1],[1]] => [3,1] => 3
[[1,1,1],[1]] => [3,1] => 3
[[4]] => [4] => 2
[[3,1]] => [4] => 2
[[2,2]] => [4] => 2
[[2,1,1]] => [4] => 2
[[1,1,1,1]] => [4] => 2
[[1],[1],[1],[1],[1]] => [1,1,1,1,1] => 2
[[2],[1],[1],[1]] => [2,1,1,1] => 3
[[2],[2],[1]] => [2,2,1] => 3
[[1,1],[1],[1],[1]] => [2,1,1,1] => 3
[[1,1],[1,1],[1]] => [2,2,1] => 3
[[3],[1],[1]] => [3,1,1] => 3
[[3],[2]] => [3,2] => 3
[[2,1],[1],[1]] => [3,1,1] => 3
[[2,1],[2]] => [3,2] => 3
[[2,1],[1,1]] => [3,2] => 3
[[1,1,1],[1],[1]] => [3,1,1] => 3
[[1,1,1],[1,1]] => [3,2] => 3
[[4],[1]] => [4,1] => 3
[[3,1],[1]] => [4,1] => 3
[[2,2],[1]] => [4,1] => 3
[[2,1,1],[1]] => [4,1] => 3
[[1,1,1,1],[1]] => [4,1] => 3
[[5]] => [5] => 2
[[4,1]] => [5] => 2
[[3,2]] => [5] => 2
[[3,1,1]] => [5] => 2
[[2,2,1]] => [5] => 2
[[2,1,1,1]] => [5] => 2
[[1,1,1,1,1]] => [5] => 2
[[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1] => 2
[[2],[1],[1],[1],[1]] => [2,1,1,1,1] => 3
[[2],[2],[1],[1]] => [2,2,1,1] => 3
[[2],[2],[2]] => [2,2,2] => 2
[[1,1],[1],[1],[1],[1]] => [2,1,1,1,1] => 3
[[1,1],[1,1],[1],[1]] => [2,2,1,1] => 3
[[1,1],[1,1],[1,1]] => [2,2,2] => 2
[[3],[1],[1],[1]] => [3,1,1,1] => 3
[[3],[2],[1]] => [3,2,1] => 4
[[3],[3]] => [3,3] => 2
[[2,1],[1],[1],[1]] => [3,1,1,1] => 3
[[2,1],[2],[1]] => [3,2,1] => 4
[[2,1],[1,1],[1]] => [3,2,1] => 4
[[2,1],[2,1]] => [3,3] => 2
[[1,1,1],[1],[1],[1]] => [3,1,1,1] => 3
[[1,1,1],[1,1],[1]] => [3,2,1] => 4
[[1,1,1],[1,1,1]] => [3,3] => 2
[[4],[1],[1]] => [4,1,1] => 3
[[4],[2]] => [4,2] => 3
[[3,1],[1],[1]] => [4,1,1] => 3
[[3,1],[2]] => [4,2] => 3
[[3,1],[1,1]] => [4,2] => 3
[[2,2],[1],[1]] => [4,1,1] => 3
[[2,2],[2]] => [4,2] => 3
[[2,2],[1,1]] => [4,2] => 3
[[2,1,1],[1],[1]] => [4,1,1] => 3
[[2,1,1],[2]] => [4,2] => 3
[[2,1,1],[1,1]] => [4,2] => 3
[[1,1,1,1],[1],[1]] => [4,1,1] => 3
[[1,1,1,1],[1,1]] => [4,2] => 3
[[5],[1]] => [5,1] => 3
[[4,1],[1]] => [5,1] => 3
[[3,2],[1]] => [5,1] => 3
[[3,1,1],[1]] => [5,1] => 3
[[2,2,1],[1]] => [5,1] => 3
[[2,1,1,1],[1]] => [5,1] => 3
[[1,1,1,1,1],[1]] => [5,1] => 3
[[6]] => [6] => 2
[[5,1]] => [6] => 2
[[4,2]] => [6] => 2
[[4,1,1]] => [6] => 2
[[3,3]] => [6] => 2
[[3,2,1]] => [6] => 2
[[3,1,1,1]] => [6] => 2
[[2,2,2]] => [6] => 2
[[2,2,1,1]] => [6] => 2
[[2,1,1,1,1]] => [6] => 2
[[1,1,1,1,1,1]] => [6] => 2
[[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1] => 2
[[2],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => 3
[[2],[2],[1],[1],[1]] => [2,2,1,1,1] => 3
[[2],[2],[2],[1]] => [2,2,2,1] => 3
[[1,1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => 3
[[1,1],[1,1],[1],[1],[1]] => [2,2,1,1,1] => 3
>>> Load all 1123 entries. <<<[[1,1],[1,1],[1,1],[1]] => [2,2,2,1] => 3
[[3],[1],[1],[1],[1]] => [3,1,1,1,1] => 3
[[3],[2],[1],[1]] => [3,2,1,1] => 4
[[3],[2],[2]] => [3,2,2] => 3
[[3],[3],[1]] => [3,3,1] => 3
[[2,1],[1],[1],[1],[1]] => [3,1,1,1,1] => 3
[[2,1],[2],[1],[1]] => [3,2,1,1] => 4
[[2,1],[2],[2]] => [3,2,2] => 3
[[2,1],[1,1],[1],[1]] => [3,2,1,1] => 4
[[2,1],[1,1],[1,1]] => [3,2,2] => 3
[[2,1],[2,1],[1]] => [3,3,1] => 3
[[1,1,1],[1],[1],[1],[1]] => [3,1,1,1,1] => 3
[[1,1,1],[1,1],[1],[1]] => [3,2,1,1] => 4
[[1,1,1],[1,1],[1,1]] => [3,2,2] => 3
[[1,1,1],[1,1,1],[1]] => [3,3,1] => 3
[[4],[1],[1],[1]] => [4,1,1,1] => 3
[[4],[2],[1]] => [4,2,1] => 4
[[4],[3]] => [4,3] => 3
[[3,1],[1],[1],[1]] => [4,1,1,1] => 3
[[3,1],[2],[1]] => [4,2,1] => 4
[[3,1],[1,1],[1]] => [4,2,1] => 4
[[3,1],[3]] => [4,3] => 3
[[3,1],[2,1]] => [4,3] => 3
[[2,2],[1],[1],[1]] => [4,1,1,1] => 3
[[2,2],[2],[1]] => [4,2,1] => 4
[[2,2],[1,1],[1]] => [4,2,1] => 4
[[2,2],[2,1]] => [4,3] => 3
[[2,1,1],[1],[1],[1]] => [4,1,1,1] => 3
[[2,1,1],[2],[1]] => [4,2,1] => 4
[[2,1,1],[1,1],[1]] => [4,2,1] => 4
[[2,1,1],[2,1]] => [4,3] => 3
[[2,1,1],[1,1,1]] => [4,3] => 3
[[1,1,1,1],[1],[1],[1]] => [4,1,1,1] => 3
[[1,1,1,1],[1,1],[1]] => [4,2,1] => 4
[[1,1,1,1],[1,1,1]] => [4,3] => 3
[[5],[1],[1]] => [5,1,1] => 3
[[5],[2]] => [5,2] => 3
[[4,1],[1],[1]] => [5,1,1] => 3
[[4,1],[2]] => [5,2] => 3
[[4,1],[1,1]] => [5,2] => 3
[[3,2],[1],[1]] => [5,1,1] => 3
[[3,2],[2]] => [5,2] => 3
[[3,2],[1,1]] => [5,2] => 3
[[3,1,1],[1],[1]] => [5,1,1] => 3
[[3,1,1],[2]] => [5,2] => 3
[[3,1,1],[1,1]] => [5,2] => 3
[[2,2,1],[1],[1]] => [5,1,1] => 3
[[2,2,1],[2]] => [5,2] => 3
[[2,2,1],[1,1]] => [5,2] => 3
[[2,1,1,1],[1],[1]] => [5,1,1] => 3
[[2,1,1,1],[2]] => [5,2] => 3
[[2,1,1,1],[1,1]] => [5,2] => 3
[[1,1,1,1,1],[1],[1]] => [5,1,1] => 3
[[1,1,1,1,1],[1,1]] => [5,2] => 3
[[6],[1]] => [6,1] => 3
[[5,1],[1]] => [6,1] => 3
[[4,2],[1]] => [6,1] => 3
[[4,1,1],[1]] => [6,1] => 3
[[3,3],[1]] => [6,1] => 3
[[3,2,1],[1]] => [6,1] => 3
[[3,1,1,1],[1]] => [6,1] => 3
[[2,2,2],[1]] => [6,1] => 3
[[2,2,1,1],[1]] => [6,1] => 3
[[2,1,1,1,1],[1]] => [6,1] => 3
[[1,1,1,1,1,1],[1]] => [6,1] => 3
[[7]] => [7] => 2
[[6,1]] => [7] => 2
[[5,2]] => [7] => 2
[[5,1,1]] => [7] => 2
[[4,3]] => [7] => 2
[[4,2,1]] => [7] => 2
[[4,1,1,1]] => [7] => 2
[[3,3,1]] => [7] => 2
[[3,2,2]] => [7] => 2
[[3,2,1,1]] => [7] => 2
[[3,1,1,1,1]] => [7] => 2
[[2,2,2,1]] => [7] => 2
[[2,2,1,1,1]] => [7] => 2
[[2,1,1,1,1,1]] => [7] => 2
[[1,1,1,1,1,1,1]] => [7] => 2
[[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1] => 2
[[2],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1] => 3
[[2],[2],[1],[1],[1],[1]] => [2,2,1,1,1,1] => 3
[[2],[2],[2],[1],[1]] => [2,2,2,1,1] => 3
[[2],[2],[2],[2]] => [2,2,2,2] => 2
[[1,1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1] => 3
[[1,1],[1,1],[1],[1],[1],[1]] => [2,2,1,1,1,1] => 3
[[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,1,1] => 3
[[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2] => 2
[[3],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => 3
[[3],[2],[1],[1],[1]] => [3,2,1,1,1] => 4
[[3],[2],[2],[1]] => [3,2,2,1] => 4
[[3],[3],[1],[1]] => [3,3,1,1] => 3
[[3],[3],[2]] => [3,3,2] => 3
[[2,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => 3
[[2,1],[2],[1],[1],[1]] => [3,2,1,1,1] => 4
[[2,1],[2],[2],[1]] => [3,2,2,1] => 4
[[2,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => 4
[[2,1],[1,1],[1,1],[1]] => [3,2,2,1] => 4
[[2,1],[2,1],[1],[1]] => [3,3,1,1] => 3
[[2,1],[2,1],[2]] => [3,3,2] => 3
[[2,1],[2,1],[1,1]] => [3,3,2] => 3
[[1,1,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => 3
[[1,1,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => 4
[[1,1,1],[1,1],[1,1],[1]] => [3,2,2,1] => 4
[[1,1,1],[1,1,1],[1],[1]] => [3,3,1,1] => 3
[[1,1,1],[1,1,1],[1,1]] => [3,3,2] => 3
[[4],[1],[1],[1],[1]] => [4,1,1,1,1] => 3
[[4],[2],[1],[1]] => [4,2,1,1] => 4
[[4],[2],[2]] => [4,2,2] => 3
[[4],[3],[1]] => [4,3,1] => 4
[[4],[4]] => [4,4] => 2
[[3,1],[1],[1],[1],[1]] => [4,1,1,1,1] => 3
[[3,1],[2],[1],[1]] => [4,2,1,1] => 4
[[3,1],[2],[2]] => [4,2,2] => 3
[[3,1],[1,1],[1],[1]] => [4,2,1,1] => 4
[[3,1],[1,1],[1,1]] => [4,2,2] => 3
[[3,1],[3],[1]] => [4,3,1] => 4
[[3,1],[2,1],[1]] => [4,3,1] => 4
[[3,1],[3,1]] => [4,4] => 2
[[2,2],[1],[1],[1],[1]] => [4,1,1,1,1] => 3
[[2,2],[2],[1],[1]] => [4,2,1,1] => 4
[[2,2],[2],[2]] => [4,2,2] => 3
[[2,2],[1,1],[1],[1]] => [4,2,1,1] => 4
[[2,2],[1,1],[1,1]] => [4,2,2] => 3
[[2,2],[2,1],[1]] => [4,3,1] => 4
[[2,2],[2,2]] => [4,4] => 2
[[2,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => 3
[[2,1,1],[2],[1],[1]] => [4,2,1,1] => 4
[[2,1,1],[2],[2]] => [4,2,2] => 3
[[2,1,1],[1,1],[1],[1]] => [4,2,1,1] => 4
[[2,1,1],[1,1],[1,1]] => [4,2,2] => 3
[[2,1,1],[2,1],[1]] => [4,3,1] => 4
[[2,1,1],[1,1,1],[1]] => [4,3,1] => 4
[[2,1,1],[2,1,1]] => [4,4] => 2
[[1,1,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => 3
[[1,1,1,1],[1,1],[1],[1]] => [4,2,1,1] => 4
[[1,1,1,1],[1,1],[1,1]] => [4,2,2] => 3
[[1,1,1,1],[1,1,1],[1]] => [4,3,1] => 4
[[1,1,1,1],[1,1,1,1]] => [4,4] => 2
[[5],[1],[1],[1]] => [5,1,1,1] => 3
[[5],[2],[1]] => [5,2,1] => 4
[[5],[3]] => [5,3] => 3
[[4,1],[1],[1],[1]] => [5,1,1,1] => 3
[[4,1],[2],[1]] => [5,2,1] => 4
[[4,1],[1,1],[1]] => [5,2,1] => 4
[[4,1],[3]] => [5,3] => 3
[[4,1],[2,1]] => [5,3] => 3
[[3,2],[1],[1],[1]] => [5,1,1,1] => 3
[[3,2],[2],[1]] => [5,2,1] => 4
[[3,2],[1,1],[1]] => [5,2,1] => 4
[[3,2],[3]] => [5,3] => 3
[[3,2],[2,1]] => [5,3] => 3
[[3,1,1],[1],[1],[1]] => [5,1,1,1] => 3
[[3,1,1],[2],[1]] => [5,2,1] => 4
[[3,1,1],[1,1],[1]] => [5,2,1] => 4
[[3,1,1],[3]] => [5,3] => 3
[[3,1,1],[2,1]] => [5,3] => 3
[[3,1,1],[1,1,1]] => [5,3] => 3
[[2,2,1],[1],[1],[1]] => [5,1,1,1] => 3
[[2,2,1],[2],[1]] => [5,2,1] => 4
[[2,2,1],[1,1],[1]] => [5,2,1] => 4
[[2,2,1],[2,1]] => [5,3] => 3
[[2,2,1],[1,1,1]] => [5,3] => 3
[[2,1,1,1],[1],[1],[1]] => [5,1,1,1] => 3
[[2,1,1,1],[2],[1]] => [5,2,1] => 4
[[2,1,1,1],[1,1],[1]] => [5,2,1] => 4
[[2,1,1,1],[2,1]] => [5,3] => 3
[[2,1,1,1],[1,1,1]] => [5,3] => 3
[[1,1,1,1,1],[1],[1],[1]] => [5,1,1,1] => 3
[[1,1,1,1,1],[1,1],[1]] => [5,2,1] => 4
[[1,1,1,1,1],[1,1,1]] => [5,3] => 3
[[6],[1],[1]] => [6,1,1] => 3
[[6],[2]] => [6,2] => 3
[[5,1],[1],[1]] => [6,1,1] => 3
[[5,1],[2]] => [6,2] => 3
[[5,1],[1,1]] => [6,2] => 3
[[4,2],[1],[1]] => [6,1,1] => 3
[[4,2],[2]] => [6,2] => 3
[[4,2],[1,1]] => [6,2] => 3
[[4,1,1],[1],[1]] => [6,1,1] => 3
[[4,1,1],[2]] => [6,2] => 3
[[4,1,1],[1,1]] => [6,2] => 3
[[3,3],[1],[1]] => [6,1,1] => 3
[[3,3],[2]] => [6,2] => 3
[[3,3],[1,1]] => [6,2] => 3
[[3,2,1],[1],[1]] => [6,1,1] => 3
[[3,2,1],[2]] => [6,2] => 3
[[3,2,1],[1,1]] => [6,2] => 3
[[3,1,1,1],[1],[1]] => [6,1,1] => 3
[[3,1,1,1],[2]] => [6,2] => 3
[[3,1,1,1],[1,1]] => [6,2] => 3
[[2,2,2],[1],[1]] => [6,1,1] => 3
[[2,2,2],[2]] => [6,2] => 3
[[2,2,2],[1,1]] => [6,2] => 3
[[2,2,1,1],[1],[1]] => [6,1,1] => 3
[[2,2,1,1],[2]] => [6,2] => 3
[[2,2,1,1],[1,1]] => [6,2] => 3
[[2,1,1,1,1],[1],[1]] => [6,1,1] => 3
[[2,1,1,1,1],[2]] => [6,2] => 3
[[2,1,1,1,1],[1,1]] => [6,2] => 3
[[1,1,1,1,1,1],[1],[1]] => [6,1,1] => 3
[[1,1,1,1,1,1],[1,1]] => [6,2] => 3
[[7],[1]] => [7,1] => 3
[[6,1],[1]] => [7,1] => 3
[[5,2],[1]] => [7,1] => 3
[[5,1,1],[1]] => [7,1] => 3
[[4,3],[1]] => [7,1] => 3
[[4,2,1],[1]] => [7,1] => 3
[[4,1,1,1],[1]] => [7,1] => 3
[[3,3,1],[1]] => [7,1] => 3
[[3,2,2],[1]] => [7,1] => 3
[[3,2,1,1],[1]] => [7,1] => 3
[[3,1,1,1,1],[1]] => [7,1] => 3
[[2,2,2,1],[1]] => [7,1] => 3
[[2,2,1,1,1],[1]] => [7,1] => 3
[[2,1,1,1,1,1],[1]] => [7,1] => 3
[[1,1,1,1,1,1,1],[1]] => [7,1] => 3
[[8]] => [8] => 2
[[7,1]] => [8] => 2
[[6,2]] => [8] => 2
[[6,1,1]] => [8] => 2
[[5,3]] => [8] => 2
[[5,2,1]] => [8] => 2
[[5,1,1,1]] => [8] => 2
[[4,4]] => [8] => 2
[[4,3,1]] => [8] => 2
[[4,2,2]] => [8] => 2
[[4,2,1,1]] => [8] => 2
[[4,1,1,1,1]] => [8] => 2
[[3,3,2]] => [8] => 2
[[3,3,1,1]] => [8] => 2
[[3,2,2,1]] => [8] => 2
[[3,2,1,1,1]] => [8] => 2
[[3,1,1,1,1,1]] => [8] => 2
[[2,2,2,2]] => [8] => 2
[[2,2,2,1,1]] => [8] => 2
[[2,2,1,1,1,1]] => [8] => 2
[[2,1,1,1,1,1,1]] => [8] => 2
[[1,1,1,1,1,1,1,1]] => [8] => 2
[[1],[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1,1] => 2
[[2],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1] => 3
[[2],[2],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1] => 3
[[2],[2],[2],[1],[1],[1]] => [2,2,2,1,1,1] => 3
[[2],[2],[2],[2],[1]] => [2,2,2,2,1] => 3
[[1,1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1] => 3
[[1,1],[1,1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1] => 3
[[1,1],[1,1],[1,1],[1],[1],[1]] => [2,2,2,1,1,1] => 3
[[1,1],[1,1],[1,1],[1,1],[1]] => [2,2,2,2,1] => 3
[[3],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => 3
[[3],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1] => 4
[[3],[2],[2],[1],[1]] => [3,2,2,1,1] => 4
[[3],[2],[2],[2]] => [3,2,2,2] => 3
[[3],[3],[1],[1],[1]] => [3,3,1,1,1] => 3
[[3],[3],[2],[1]] => [3,3,2,1] => 4
[[3],[3],[3]] => [3,3,3] => 2
[[2,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => 3
[[2,1],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1] => 4
[[2,1],[2],[2],[1],[1]] => [3,2,2,1,1] => 4
[[2,1],[2],[2],[2]] => [3,2,2,2] => 3
[[2,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1] => 4
[[2,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => 4
[[2,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => 3
[[2,1],[2,1],[1],[1],[1]] => [3,3,1,1,1] => 3
[[2,1],[2,1],[2],[1]] => [3,3,2,1] => 4
[[2,1],[2,1],[1,1],[1]] => [3,3,2,1] => 4
[[2,1],[2,1],[2,1]] => [3,3,3] => 2
[[1,1,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => 3
[[1,1,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1] => 4
[[1,1,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => 4
[[1,1,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => 3
[[1,1,1],[1,1,1],[1],[1],[1]] => [3,3,1,1,1] => 3
[[1,1,1],[1,1,1],[1,1],[1]] => [3,3,2,1] => 4
[[1,1,1],[1,1,1],[1,1,1]] => [3,3,3] => 2
[[4],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 3
[[4],[2],[1],[1],[1]] => [4,2,1,1,1] => 4
[[4],[2],[2],[1]] => [4,2,2,1] => 4
[[4],[3],[1],[1]] => [4,3,1,1] => 4
[[4],[3],[2]] => [4,3,2] => 4
[[4],[4],[1]] => [4,4,1] => 3
[[3,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 3
[[3,1],[2],[1],[1],[1]] => [4,2,1,1,1] => 4
[[3,1],[2],[2],[1]] => [4,2,2,1] => 4
[[3,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => 4
[[3,1],[1,1],[1,1],[1]] => [4,2,2,1] => 4
[[3,1],[3],[1],[1]] => [4,3,1,1] => 4
[[3,1],[3],[2]] => [4,3,2] => 4
[[3,1],[2,1],[1],[1]] => [4,3,1,1] => 4
[[3,1],[2,1],[2]] => [4,3,2] => 4
[[3,1],[2,1],[1,1]] => [4,3,2] => 4
[[3,1],[3,1],[1]] => [4,4,1] => 3
[[2,2],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 3
[[2,2],[2],[1],[1],[1]] => [4,2,1,1,1] => 4
[[2,2],[2],[2],[1]] => [4,2,2,1] => 4
[[2,2],[1,1],[1],[1],[1]] => [4,2,1,1,1] => 4
[[2,2],[1,1],[1,1],[1]] => [4,2,2,1] => 4
[[2,2],[2,1],[1],[1]] => [4,3,1,1] => 4
[[2,2],[2,1],[2]] => [4,3,2] => 4
[[2,2],[2,1],[1,1]] => [4,3,2] => 4
[[2,2],[2,2],[1]] => [4,4,1] => 3
[[2,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 3
[[2,1,1],[2],[1],[1],[1]] => [4,2,1,1,1] => 4
[[2,1,1],[2],[2],[1]] => [4,2,2,1] => 4
[[2,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => 4
[[2,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => 4
[[2,1,1],[2,1],[1],[1]] => [4,3,1,1] => 4
[[2,1,1],[2,1],[2]] => [4,3,2] => 4
[[2,1,1],[2,1],[1,1]] => [4,3,2] => 4
[[2,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => 4
[[2,1,1],[1,1,1],[1,1]] => [4,3,2] => 4
[[2,1,1],[2,1,1],[1]] => [4,4,1] => 3
[[1,1,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 3
[[1,1,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => 4
[[1,1,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => 4
[[1,1,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => 4
[[1,1,1,1],[1,1,1],[1,1]] => [4,3,2] => 4
[[1,1,1,1],[1,1,1,1],[1]] => [4,4,1] => 3
[[5],[1],[1],[1],[1]] => [5,1,1,1,1] => 3
[[5],[2],[1],[1]] => [5,2,1,1] => 4
[[5],[2],[2]] => [5,2,2] => 3
[[5],[3],[1]] => [5,3,1] => 4
[[5],[4]] => [5,4] => 3
[[4,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 3
[[4,1],[2],[1],[1]] => [5,2,1,1] => 4
[[4,1],[2],[2]] => [5,2,2] => 3
[[4,1],[1,1],[1],[1]] => [5,2,1,1] => 4
[[4,1],[1,1],[1,1]] => [5,2,2] => 3
[[4,1],[3],[1]] => [5,3,1] => 4
[[4,1],[2,1],[1]] => [5,3,1] => 4
[[4,1],[4]] => [5,4] => 3
[[4,1],[3,1]] => [5,4] => 3
[[3,2],[1],[1],[1],[1]] => [5,1,1,1,1] => 3
[[3,2],[2],[1],[1]] => [5,2,1,1] => 4
[[3,2],[2],[2]] => [5,2,2] => 3
[[3,2],[1,1],[1],[1]] => [5,2,1,1] => 4
[[3,2],[1,1],[1,1]] => [5,2,2] => 3
[[3,2],[3],[1]] => [5,3,1] => 4
[[3,2],[2,1],[1]] => [5,3,1] => 4
[[3,2],[3,1]] => [5,4] => 3
[[3,2],[2,2]] => [5,4] => 3
[[3,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 3
[[3,1,1],[2],[1],[1]] => [5,2,1,1] => 4
[[3,1,1],[2],[2]] => [5,2,2] => 3
[[3,1,1],[1,1],[1],[1]] => [5,2,1,1] => 4
[[3,1,1],[1,1],[1,1]] => [5,2,2] => 3
[[3,1,1],[3],[1]] => [5,3,1] => 4
[[3,1,1],[2,1],[1]] => [5,3,1] => 4
[[3,1,1],[1,1,1],[1]] => [5,3,1] => 4
[[3,1,1],[3,1]] => [5,4] => 3
[[3,1,1],[2,1,1]] => [5,4] => 3
[[2,2,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 3
[[2,2,1],[2],[1],[1]] => [5,2,1,1] => 4
[[2,2,1],[2],[2]] => [5,2,2] => 3
[[2,2,1],[1,1],[1],[1]] => [5,2,1,1] => 4
[[2,2,1],[1,1],[1,1]] => [5,2,2] => 3
[[2,2,1],[2,1],[1]] => [5,3,1] => 4
[[2,2,1],[1,1,1],[1]] => [5,3,1] => 4
[[2,2,1],[2,2]] => [5,4] => 3
[[2,2,1],[2,1,1]] => [5,4] => 3
[[2,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 3
[[2,1,1,1],[2],[1],[1]] => [5,2,1,1] => 4
[[2,1,1,1],[2],[2]] => [5,2,2] => 3
[[2,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => 4
[[2,1,1,1],[1,1],[1,1]] => [5,2,2] => 3
[[2,1,1,1],[2,1],[1]] => [5,3,1] => 4
[[2,1,1,1],[1,1,1],[1]] => [5,3,1] => 4
[[2,1,1,1],[2,1,1]] => [5,4] => 3
[[2,1,1,1],[1,1,1,1]] => [5,4] => 3
[[1,1,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 3
[[1,1,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => 4
[[1,1,1,1,1],[1,1],[1,1]] => [5,2,2] => 3
[[1,1,1,1,1],[1,1,1],[1]] => [5,3,1] => 4
[[1,1,1,1,1],[1,1,1,1]] => [5,4] => 3
[[6],[1],[1],[1]] => [6,1,1,1] => 3
[[6],[2],[1]] => [6,2,1] => 4
[[6],[3]] => [6,3] => 3
[[5,1],[1],[1],[1]] => [6,1,1,1] => 3
[[5,1],[2],[1]] => [6,2,1] => 4
[[5,1],[1,1],[1]] => [6,2,1] => 4
[[5,1],[3]] => [6,3] => 3
[[5,1],[2,1]] => [6,3] => 3
[[4,2],[1],[1],[1]] => [6,1,1,1] => 3
[[4,2],[2],[1]] => [6,2,1] => 4
[[4,2],[1,1],[1]] => [6,2,1] => 4
[[4,2],[3]] => [6,3] => 3
[[4,2],[2,1]] => [6,3] => 3
[[4,1,1],[1],[1],[1]] => [6,1,1,1] => 3
[[4,1,1],[2],[1]] => [6,2,1] => 4
[[4,1,1],[1,1],[1]] => [6,2,1] => 4
[[4,1,1],[3]] => [6,3] => 3
[[4,1,1],[2,1]] => [6,3] => 3
[[4,1,1],[1,1,1]] => [6,3] => 3
[[3,3],[1],[1],[1]] => [6,1,1,1] => 3
[[3,3],[2],[1]] => [6,2,1] => 4
[[3,3],[1,1],[1]] => [6,2,1] => 4
[[3,3],[3]] => [6,3] => 3
[[3,3],[2,1]] => [6,3] => 3
[[3,2,1],[1],[1],[1]] => [6,1,1,1] => 3
[[3,2,1],[2],[1]] => [6,2,1] => 4
[[3,2,1],[1,1],[1]] => [6,2,1] => 4
[[3,2,1],[3]] => [6,3] => 3
[[3,2,1],[2,1]] => [6,3] => 3
[[3,2,1],[1,1,1]] => [6,3] => 3
[[3,1,1,1],[1],[1],[1]] => [6,1,1,1] => 3
[[3,1,1,1],[2],[1]] => [6,2,1] => 4
[[3,1,1,1],[1,1],[1]] => [6,2,1] => 4
[[3,1,1,1],[3]] => [6,3] => 3
[[3,1,1,1],[2,1]] => [6,3] => 3
[[3,1,1,1],[1,1,1]] => [6,3] => 3
[[2,2,2],[1],[1],[1]] => [6,1,1,1] => 3
[[2,2,2],[2],[1]] => [6,2,1] => 4
[[2,2,2],[1,1],[1]] => [6,2,1] => 4
[[2,2,2],[2,1]] => [6,3] => 3
[[2,2,2],[1,1,1]] => [6,3] => 3
[[2,2,1,1],[1],[1],[1]] => [6,1,1,1] => 3
[[2,2,1,1],[2],[1]] => [6,2,1] => 4
[[2,2,1,1],[1,1],[1]] => [6,2,1] => 4
[[2,2,1,1],[2,1]] => [6,3] => 3
[[2,2,1,1],[1,1,1]] => [6,3] => 3
[[2,1,1,1,1],[1],[1],[1]] => [6,1,1,1] => 3
[[2,1,1,1,1],[2],[1]] => [6,2,1] => 4
[[2,1,1,1,1],[1,1],[1]] => [6,2,1] => 4
[[2,1,1,1,1],[2,1]] => [6,3] => 3
[[2,1,1,1,1],[1,1,1]] => [6,3] => 3
[[1,1,1,1,1,1],[1],[1],[1]] => [6,1,1,1] => 3
[[1,1,1,1,1,1],[1,1],[1]] => [6,2,1] => 4
[[1,1,1,1,1,1],[1,1,1]] => [6,3] => 3
[[7],[1],[1]] => [7,1,1] => 3
[[7],[2]] => [7,2] => 3
[[6,1],[1],[1]] => [7,1,1] => 3
[[6,1],[2]] => [7,2] => 3
[[6,1],[1,1]] => [7,2] => 3
[[5,2],[1],[1]] => [7,1,1] => 3
[[5,2],[2]] => [7,2] => 3
[[5,2],[1,1]] => [7,2] => 3
[[5,1,1],[1],[1]] => [7,1,1] => 3
[[5,1,1],[2]] => [7,2] => 3
[[5,1,1],[1,1]] => [7,2] => 3
[[4,3],[1],[1]] => [7,1,1] => 3
[[4,3],[2]] => [7,2] => 3
[[4,3],[1,1]] => [7,2] => 3
[[4,2,1],[1],[1]] => [7,1,1] => 3
[[4,2,1],[2]] => [7,2] => 3
[[4,2,1],[1,1]] => [7,2] => 3
[[4,1,1,1],[1],[1]] => [7,1,1] => 3
[[4,1,1,1],[2]] => [7,2] => 3
[[4,1,1,1],[1,1]] => [7,2] => 3
[[3,3,1],[1],[1]] => [7,1,1] => 3
[[3,3,1],[2]] => [7,2] => 3
[[3,3,1],[1,1]] => [7,2] => 3
[[3,2,2],[1],[1]] => [7,1,1] => 3
[[3,2,2],[2]] => [7,2] => 3
[[3,2,2],[1,1]] => [7,2] => 3
[[3,2,1,1],[1],[1]] => [7,1,1] => 3
[[3,2,1,1],[2]] => [7,2] => 3
[[3,2,1,1],[1,1]] => [7,2] => 3
[[3,1,1,1,1],[1],[1]] => [7,1,1] => 3
[[3,1,1,1,1],[2]] => [7,2] => 3
[[3,1,1,1,1],[1,1]] => [7,2] => 3
[[2,2,2,1],[1],[1]] => [7,1,1] => 3
[[2,2,2,1],[2]] => [7,2] => 3
[[2,2,2,1],[1,1]] => [7,2] => 3
[[2,2,1,1,1],[1],[1]] => [7,1,1] => 3
[[2,2,1,1,1],[2]] => [7,2] => 3
[[2,2,1,1,1],[1,1]] => [7,2] => 3
[[2,1,1,1,1,1],[1],[1]] => [7,1,1] => 3
[[2,1,1,1,1,1],[2]] => [7,2] => 3
[[2,1,1,1,1,1],[1,1]] => [7,2] => 3
[[1,1,1,1,1,1,1],[1],[1]] => [7,1,1] => 3
[[1,1,1,1,1,1,1],[1,1]] => [7,2] => 3
[[8],[1]] => [8,1] => 3
[[7,1],[1]] => [8,1] => 3
[[6,2],[1]] => [8,1] => 3
[[6,1,1],[1]] => [8,1] => 3
[[5,3],[1]] => [8,1] => 3
[[5,2,1],[1]] => [8,1] => 3
[[5,1,1,1],[1]] => [8,1] => 3
[[4,4],[1]] => [8,1] => 3
[[4,3,1],[1]] => [8,1] => 3
[[4,2,2],[1]] => [8,1] => 3
[[4,2,1,1],[1]] => [8,1] => 3
[[4,1,1,1,1],[1]] => [8,1] => 3
[[3,3,2],[1]] => [8,1] => 3
[[3,3,1,1],[1]] => [8,1] => 3
[[3,2,2,1],[1]] => [8,1] => 3
[[3,2,1,1,1],[1]] => [8,1] => 3
[[3,1,1,1,1,1],[1]] => [8,1] => 3
[[2,2,2,2],[1]] => [8,1] => 3
[[2,2,2,1,1],[1]] => [8,1] => 3
[[2,2,1,1,1,1],[1]] => [8,1] => 3
[[2,1,1,1,1,1,1],[1]] => [8,1] => 3
[[1,1,1,1,1,1,1,1],[1]] => [8,1] => 3
[[9]] => [9] => 2
[[8,1]] => [9] => 2
[[7,2]] => [9] => 2
[[7,1,1]] => [9] => 2
[[6,3]] => [9] => 2
[[6,2,1]] => [9] => 2
[[6,1,1,1]] => [9] => 2
[[5,4]] => [9] => 2
[[5,3,1]] => [9] => 2
[[5,2,2]] => [9] => 2
[[5,2,1,1]] => [9] => 2
[[5,1,1,1,1]] => [9] => 2
[[4,4,1]] => [9] => 2
[[4,3,2]] => [9] => 2
[[4,3,1,1]] => [9] => 2
[[4,2,2,1]] => [9] => 2
[[4,2,1,1,1]] => [9] => 2
[[4,1,1,1,1,1]] => [9] => 2
[[3,3,3]] => [9] => 2
[[3,3,2,1]] => [9] => 2
[[3,3,1,1,1]] => [9] => 2
[[3,2,2,2]] => [9] => 2
[[3,2,2,1,1]] => [9] => 2
[[3,2,1,1,1,1]] => [9] => 2
[[3,1,1,1,1,1,1]] => [9] => 2
[[2,2,2,2,1]] => [9] => 2
[[2,2,2,1,1,1]] => [9] => 2
[[2,2,1,1,1,1,1]] => [9] => 2
[[2,1,1,1,1,1,1,1]] => [9] => 2
[[1,1,1,1,1,1,1,1,1]] => [9] => 2
[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1,1,1] => 2
[[2],[1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1,1] => 3
[[2],[2],[1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1,1] => 3
[[2],[2],[2],[1],[1],[1],[1]] => [2,2,2,1,1,1,1] => 3
[[2],[2],[2],[2],[1],[1]] => [2,2,2,2,1,1] => 3
[[2],[2],[2],[2],[2]] => [2,2,2,2,2] => 2
[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1,1] => 3
[[1,1],[1,1],[1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1,1] => 3
[[1,1],[1,1],[1,1],[1],[1],[1],[1]] => [2,2,2,1,1,1,1] => 3
[[1,1],[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,2,1,1] => 3
[[1,1],[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2,2] => 2
[[3],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => 3
[[3],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => 4
[[3],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1] => 4
[[3],[2],[2],[2],[1]] => [3,2,2,2,1] => 4
[[3],[3],[1],[1],[1],[1]] => [3,3,1,1,1,1] => 3
[[3],[3],[2],[1],[1]] => [3,3,2,1,1] => 4
[[3],[3],[2],[2]] => [3,3,2,2] => 3
[[3],[3],[3],[1]] => [3,3,3,1] => 3
[[2,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => 3
[[2,1],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => 4
[[2,1],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1] => 4
[[2,1],[2],[2],[2],[1]] => [3,2,2,2,1] => 4
[[2,1],[1,1],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => 4
[[2,1],[1,1],[1,1],[1],[1],[1]] => [3,2,2,1,1,1] => 4
[[2,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => 4
[[2,1],[2,1],[1],[1],[1],[1]] => [3,3,1,1,1,1] => 3
[[2,1],[2,1],[2],[1],[1]] => [3,3,2,1,1] => 4
[[2,1],[2,1],[2],[2]] => [3,3,2,2] => 3
[[2,1],[2,1],[1,1],[1],[1]] => [3,3,2,1,1] => 4
[[2,1],[2,1],[1,1],[1,1]] => [3,3,2,2] => 3
[[2,1],[2,1],[2,1],[1]] => [3,3,3,1] => 3
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => 3
[[1,1,1],[1,1],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => 4
[[1,1,1],[1,1],[1,1],[1],[1],[1]] => [3,2,2,1,1,1] => 4
[[1,1,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => 4
[[1,1,1],[1,1,1],[1],[1],[1],[1]] => [3,3,1,1,1,1] => 3
[[1,1,1],[1,1,1],[1,1],[1],[1]] => [3,3,2,1,1] => 4
[[1,1,1],[1,1,1],[1,1],[1,1]] => [3,3,2,2] => 3
[[1,1,1],[1,1,1],[1,1,1],[1]] => [3,3,3,1] => 3
[[4],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => 3
[[4],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 4
[[4],[2],[2],[1],[1]] => [4,2,2,1,1] => 4
[[4],[2],[2],[2]] => [4,2,2,2] => 3
[[4],[3],[1],[1],[1]] => [4,3,1,1,1] => 4
[[4],[3],[2],[1]] => [4,3,2,1] => 5
[[4],[3],[3]] => [4,3,3] => 3
[[4],[4],[1],[1]] => [4,4,1,1] => 3
[[4],[4],[2]] => [4,4,2] => 3
[[3,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => 3
[[3,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 4
[[3,1],[2],[2],[1],[1]] => [4,2,2,1,1] => 4
[[3,1],[2],[2],[2]] => [4,2,2,2] => 3
[[3,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 4
[[3,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => 4
[[3,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => 3
[[3,1],[3],[1],[1],[1]] => [4,3,1,1,1] => 4
[[3,1],[3],[2],[1]] => [4,3,2,1] => 5
[[3,1],[3],[3]] => [4,3,3] => 3
[[3,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => 4
[[3,1],[2,1],[2],[1]] => [4,3,2,1] => 5
[[3,1],[2,1],[1,1],[1]] => [4,3,2,1] => 5
[[3,1],[2,1],[2,1]] => [4,3,3] => 3
[[3,1],[3,1],[1],[1]] => [4,4,1,1] => 3
[[3,1],[3,1],[2]] => [4,4,2] => 3
[[3,1],[3,1],[1,1]] => [4,4,2] => 3
[[2,2],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => 3
[[2,2],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 4
[[2,2],[2],[2],[1],[1]] => [4,2,2,1,1] => 4
[[2,2],[2],[2],[2]] => [4,2,2,2] => 3
[[2,2],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 4
[[2,2],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => 4
[[2,2],[1,1],[1,1],[1,1]] => [4,2,2,2] => 3
[[2,2],[2,1],[1],[1],[1]] => [4,3,1,1,1] => 4
[[2,2],[2,1],[2],[1]] => [4,3,2,1] => 5
[[2,2],[2,1],[1,1],[1]] => [4,3,2,1] => 5
[[2,2],[2,1],[2,1]] => [4,3,3] => 3
[[2,2],[2,2],[1],[1]] => [4,4,1,1] => 3
[[2,2],[2,2],[2]] => [4,4,2] => 3
[[2,2],[2,2],[1,1]] => [4,4,2] => 3
[[2,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => 3
[[2,1,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 4
[[2,1,1],[2],[2],[1],[1]] => [4,2,2,1,1] => 4
[[2,1,1],[2],[2],[2]] => [4,2,2,2] => 3
[[2,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 4
[[2,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => 4
[[2,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => 3
[[2,1,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => 4
[[2,1,1],[2,1],[2],[1]] => [4,3,2,1] => 5
[[2,1,1],[2,1],[1,1],[1]] => [4,3,2,1] => 5
[[2,1,1],[2,1],[2,1]] => [4,3,3] => 3
[[2,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => 4
[[2,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => 5
[[2,1,1],[1,1,1],[1,1,1]] => [4,3,3] => 3
[[2,1,1],[2,1,1],[1],[1]] => [4,4,1,1] => 3
[[2,1,1],[2,1,1],[2]] => [4,4,2] => 3
[[2,1,1],[2,1,1],[1,1]] => [4,4,2] => 3
[[1,1,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => 3
[[1,1,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 4
[[1,1,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => 4
[[1,1,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => 3
[[1,1,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => 4
[[1,1,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => 5
[[1,1,1,1],[1,1,1],[1,1,1]] => [4,3,3] => 3
[[1,1,1,1],[1,1,1,1],[1],[1]] => [4,4,1,1] => 3
[[1,1,1,1],[1,1,1,1],[1,1]] => [4,4,2] => 3
[[5],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 3
[[5],[2],[1],[1],[1]] => [5,2,1,1,1] => 4
[[5],[2],[2],[1]] => [5,2,2,1] => 4
[[5],[3],[1],[1]] => [5,3,1,1] => 4
[[5],[3],[2]] => [5,3,2] => 4
[[5],[4],[1]] => [5,4,1] => 4
[[5],[5]] => [5,5] => 2
[[4,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 3
[[4,1],[2],[1],[1],[1]] => [5,2,1,1,1] => 4
[[4,1],[2],[2],[1]] => [5,2,2,1] => 4
[[4,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 4
[[4,1],[1,1],[1,1],[1]] => [5,2,2,1] => 4
[[4,1],[3],[1],[1]] => [5,3,1,1] => 4
[[4,1],[3],[2]] => [5,3,2] => 4
[[4,1],[2,1],[1],[1]] => [5,3,1,1] => 4
[[4,1],[2,1],[2]] => [5,3,2] => 4
[[4,1],[2,1],[1,1]] => [5,3,2] => 4
[[4,1],[4],[1]] => [5,4,1] => 4
[[4,1],[3,1],[1]] => [5,4,1] => 4
[[4,1],[4,1]] => [5,5] => 2
[[3,2],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 3
[[3,2],[2],[1],[1],[1]] => [5,2,1,1,1] => 4
[[3,2],[2],[2],[1]] => [5,2,2,1] => 4
[[3,2],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 4
[[3,2],[1,1],[1,1],[1]] => [5,2,2,1] => 4
[[3,2],[3],[1],[1]] => [5,3,1,1] => 4
[[3,2],[3],[2]] => [5,3,2] => 4
[[3,2],[2,1],[1],[1]] => [5,3,1,1] => 4
[[3,2],[2,1],[2]] => [5,3,2] => 4
[[3,2],[2,1],[1,1]] => [5,3,2] => 4
[[3,2],[3,1],[1]] => [5,4,1] => 4
[[3,2],[2,2],[1]] => [5,4,1] => 4
[[3,2],[3,2]] => [5,5] => 2
[[3,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 3
[[3,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => 4
[[3,1,1],[2],[2],[1]] => [5,2,2,1] => 4
[[3,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 4
[[3,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => 4
[[3,1,1],[3],[1],[1]] => [5,3,1,1] => 4
[[3,1,1],[3],[2]] => [5,3,2] => 4
[[3,1,1],[2,1],[1],[1]] => [5,3,1,1] => 4
[[3,1,1],[2,1],[2]] => [5,3,2] => 4
[[3,1,1],[2,1],[1,1]] => [5,3,2] => 4
[[3,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => 4
[[3,1,1],[1,1,1],[1,1]] => [5,3,2] => 4
[[3,1,1],[3,1],[1]] => [5,4,1] => 4
[[3,1,1],[2,1,1],[1]] => [5,4,1] => 4
[[3,1,1],[3,1,1]] => [5,5] => 2
[[2,2,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 3
[[2,2,1],[2],[1],[1],[1]] => [5,2,1,1,1] => 4
[[2,2,1],[2],[2],[1]] => [5,2,2,1] => 4
[[2,2,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 4
[[2,2,1],[1,1],[1,1],[1]] => [5,2,2,1] => 4
[[2,2,1],[2,1],[1],[1]] => [5,3,1,1] => 4
[[2,2,1],[2,1],[2]] => [5,3,2] => 4
[[2,2,1],[2,1],[1,1]] => [5,3,2] => 4
[[2,2,1],[1,1,1],[1],[1]] => [5,3,1,1] => 4
[[2,2,1],[1,1,1],[1,1]] => [5,3,2] => 4
[[2,2,1],[2,2],[1]] => [5,4,1] => 4
[[2,2,1],[2,1,1],[1]] => [5,4,1] => 4
[[2,2,1],[2,2,1]] => [5,5] => 2
[[2,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 3
[[2,1,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => 4
[[2,1,1,1],[2],[2],[1]] => [5,2,2,1] => 4
[[2,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 4
[[2,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => 4
[[2,1,1,1],[2,1],[1],[1]] => [5,3,1,1] => 4
[[2,1,1,1],[2,1],[2]] => [5,3,2] => 4
[[2,1,1,1],[2,1],[1,1]] => [5,3,2] => 4
[[2,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => 4
[[2,1,1,1],[1,1,1],[1,1]] => [5,3,2] => 4
[[2,1,1,1],[2,1,1],[1]] => [5,4,1] => 4
[[2,1,1,1],[1,1,1,1],[1]] => [5,4,1] => 4
[[2,1,1,1],[2,1,1,1]] => [5,5] => 2
[[1,1,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 3
[[1,1,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 4
[[1,1,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => 4
[[1,1,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => 4
[[1,1,1,1,1],[1,1,1],[1,1]] => [5,3,2] => 4
[[1,1,1,1,1],[1,1,1,1],[1]] => [5,4,1] => 4
[[1,1,1,1,1],[1,1,1,1,1]] => [5,5] => 2
[[6],[1],[1],[1],[1]] => [6,1,1,1,1] => 3
[[6],[2],[1],[1]] => [6,2,1,1] => 4
[[6],[2],[2]] => [6,2,2] => 3
[[6],[3],[1]] => [6,3,1] => 4
[[6],[4]] => [6,4] => 3
[[5,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 3
[[5,1],[2],[1],[1]] => [6,2,1,1] => 4
[[5,1],[2],[2]] => [6,2,2] => 3
[[5,1],[1,1],[1],[1]] => [6,2,1,1] => 4
[[5,1],[1,1],[1,1]] => [6,2,2] => 3
[[5,1],[3],[1]] => [6,3,1] => 4
[[5,1],[2,1],[1]] => [6,3,1] => 4
[[5,1],[4]] => [6,4] => 3
[[5,1],[3,1]] => [6,4] => 3
[[4,2],[1],[1],[1],[1]] => [6,1,1,1,1] => 3
[[4,2],[2],[1],[1]] => [6,2,1,1] => 4
[[4,2],[2],[2]] => [6,2,2] => 3
[[4,2],[1,1],[1],[1]] => [6,2,1,1] => 4
[[4,2],[1,1],[1,1]] => [6,2,2] => 3
[[4,2],[3],[1]] => [6,3,1] => 4
[[4,2],[2,1],[1]] => [6,3,1] => 4
[[4,2],[4]] => [6,4] => 3
[[4,2],[3,1]] => [6,4] => 3
[[4,2],[2,2]] => [6,4] => 3
[[4,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 3
[[4,1,1],[2],[1],[1]] => [6,2,1,1] => 4
[[4,1,1],[2],[2]] => [6,2,2] => 3
[[4,1,1],[1,1],[1],[1]] => [6,2,1,1] => 4
[[4,1,1],[1,1],[1,1]] => [6,2,2] => 3
[[4,1,1],[3],[1]] => [6,3,1] => 4
[[4,1,1],[2,1],[1]] => [6,3,1] => 4
[[4,1,1],[1,1,1],[1]] => [6,3,1] => 4
[[4,1,1],[4]] => [6,4] => 3
[[4,1,1],[3,1]] => [6,4] => 3
[[4,1,1],[2,1,1]] => [6,4] => 3
[[3,3],[1],[1],[1],[1]] => [6,1,1,1,1] => 3
[[3,3],[2],[1],[1]] => [6,2,1,1] => 4
[[3,3],[2],[2]] => [6,2,2] => 3
[[3,3],[1,1],[1],[1]] => [6,2,1,1] => 4
[[3,3],[1,1],[1,1]] => [6,2,2] => 3
[[3,3],[3],[1]] => [6,3,1] => 4
[[3,3],[2,1],[1]] => [6,3,1] => 4
[[3,3],[3,1]] => [6,4] => 3
[[3,3],[2,2]] => [6,4] => 3
[[3,2,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 3
[[3,2,1],[2],[1],[1]] => [6,2,1,1] => 4
[[3,2,1],[2],[2]] => [6,2,2] => 3
[[3,2,1],[1,1],[1],[1]] => [6,2,1,1] => 4
[[3,2,1],[1,1],[1,1]] => [6,2,2] => 3
[[3,2,1],[3],[1]] => [6,3,1] => 4
[[3,2,1],[2,1],[1]] => [6,3,1] => 4
[[3,2,1],[1,1,1],[1]] => [6,3,1] => 4
[[3,2,1],[3,1]] => [6,4] => 3
[[3,2,1],[2,2]] => [6,4] => 3
[[3,2,1],[2,1,1]] => [6,4] => 3
[[3,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 3
[[3,1,1,1],[2],[1],[1]] => [6,2,1,1] => 4
[[3,1,1,1],[2],[2]] => [6,2,2] => 3
[[3,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => 4
[[3,1,1,1],[1,1],[1,1]] => [6,2,2] => 3
[[3,1,1,1],[3],[1]] => [6,3,1] => 4
[[3,1,1,1],[2,1],[1]] => [6,3,1] => 4
[[3,1,1,1],[1,1,1],[1]] => [6,3,1] => 4
[[3,1,1,1],[3,1]] => [6,4] => 3
[[3,1,1,1],[2,1,1]] => [6,4] => 3
[[3,1,1,1],[1,1,1,1]] => [6,4] => 3
[[2,2,2],[1],[1],[1],[1]] => [6,1,1,1,1] => 3
[[2,2,2],[2],[1],[1]] => [6,2,1,1] => 4
[[2,2,2],[2],[2]] => [6,2,2] => 3
[[2,2,2],[1,1],[1],[1]] => [6,2,1,1] => 4
[[2,2,2],[1,1],[1,1]] => [6,2,2] => 3
[[2,2,2],[2,1],[1]] => [6,3,1] => 4
[[2,2,2],[1,1,1],[1]] => [6,3,1] => 4
[[2,2,2],[2,2]] => [6,4] => 3
[[2,2,2],[2,1,1]] => [6,4] => 3
[[2,2,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 3
[[2,2,1,1],[2],[1],[1]] => [6,2,1,1] => 4
[[2,2,1,1],[2],[2]] => [6,2,2] => 3
[[2,2,1,1],[1,1],[1],[1]] => [6,2,1,1] => 4
[[2,2,1,1],[1,1],[1,1]] => [6,2,2] => 3
[[2,2,1,1],[2,1],[1]] => [6,3,1] => 4
[[2,2,1,1],[1,1,1],[1]] => [6,3,1] => 4
[[2,2,1,1],[2,2]] => [6,4] => 3
[[2,2,1,1],[2,1,1]] => [6,4] => 3
[[2,2,1,1],[1,1,1,1]] => [6,4] => 3
[[2,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 3
[[2,1,1,1,1],[2],[1],[1]] => [6,2,1,1] => 4
[[2,1,1,1,1],[2],[2]] => [6,2,2] => 3
[[2,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => 4
[[2,1,1,1,1],[1,1],[1,1]] => [6,2,2] => 3
[[2,1,1,1,1],[2,1],[1]] => [6,3,1] => 4
[[2,1,1,1,1],[1,1,1],[1]] => [6,3,1] => 4
[[2,1,1,1,1],[2,1,1]] => [6,4] => 3
[[2,1,1,1,1],[1,1,1,1]] => [6,4] => 3
[[1,1,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 3
[[1,1,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => 4
[[1,1,1,1,1,1],[1,1],[1,1]] => [6,2,2] => 3
[[1,1,1,1,1,1],[1,1,1],[1]] => [6,3,1] => 4
[[1,1,1,1,1,1],[1,1,1,1]] => [6,4] => 3
[[7],[1],[1],[1]] => [7,1,1,1] => 3
[[7],[2],[1]] => [7,2,1] => 4
[[7],[3]] => [7,3] => 3
[[6,1],[1],[1],[1]] => [7,1,1,1] => 3
[[6,1],[2],[1]] => [7,2,1] => 4
[[6,1],[1,1],[1]] => [7,2,1] => 4
[[6,1],[3]] => [7,3] => 3
[[6,1],[2,1]] => [7,3] => 3
[[5,2],[1],[1],[1]] => [7,1,1,1] => 3
[[5,2],[2],[1]] => [7,2,1] => 4
[[5,2],[1,1],[1]] => [7,2,1] => 4
[[5,2],[3]] => [7,3] => 3
[[5,2],[2,1]] => [7,3] => 3
[[5,1,1],[1],[1],[1]] => [7,1,1,1] => 3
[[5,1,1],[2],[1]] => [7,2,1] => 4
[[5,1,1],[1,1],[1]] => [7,2,1] => 4
[[5,1,1],[3]] => [7,3] => 3
[[5,1,1],[2,1]] => [7,3] => 3
[[5,1,1],[1,1,1]] => [7,3] => 3
[[4,3],[1],[1],[1]] => [7,1,1,1] => 3
[[4,3],[2],[1]] => [7,2,1] => 4
[[4,3],[1,1],[1]] => [7,2,1] => 4
[[4,3],[3]] => [7,3] => 3
[[4,3],[2,1]] => [7,3] => 3
[[4,2,1],[1],[1],[1]] => [7,1,1,1] => 3
[[4,2,1],[2],[1]] => [7,2,1] => 4
[[4,2,1],[1,1],[1]] => [7,2,1] => 4
[[4,2,1],[3]] => [7,3] => 3
[[4,2,1],[2,1]] => [7,3] => 3
[[4,2,1],[1,1,1]] => [7,3] => 3
[[4,1,1,1],[1],[1],[1]] => [7,1,1,1] => 3
[[4,1,1,1],[2],[1]] => [7,2,1] => 4
[[4,1,1,1],[1,1],[1]] => [7,2,1] => 4
[[4,1,1,1],[3]] => [7,3] => 3
[[4,1,1,1],[2,1]] => [7,3] => 3
[[4,1,1,1],[1,1,1]] => [7,3] => 3
[[3,3,1],[1],[1],[1]] => [7,1,1,1] => 3
[[3,3,1],[2],[1]] => [7,2,1] => 4
[[3,3,1],[1,1],[1]] => [7,2,1] => 4
[[3,3,1],[3]] => [7,3] => 3
[[3,3,1],[2,1]] => [7,3] => 3
[[3,3,1],[1,1,1]] => [7,3] => 3
[[3,2,2],[1],[1],[1]] => [7,1,1,1] => 3
[[3,2,2],[2],[1]] => [7,2,1] => 4
[[3,2,2],[1,1],[1]] => [7,2,1] => 4
[[3,2,2],[3]] => [7,3] => 3
[[3,2,2],[2,1]] => [7,3] => 3
[[3,2,2],[1,1,1]] => [7,3] => 3
[[3,2,1,1],[1],[1],[1]] => [7,1,1,1] => 3
[[3,2,1,1],[2],[1]] => [7,2,1] => 4
[[3,2,1,1],[1,1],[1]] => [7,2,1] => 4
[[3,2,1,1],[3]] => [7,3] => 3
[[3,2,1,1],[2,1]] => [7,3] => 3
[[3,2,1,1],[1,1,1]] => [7,3] => 3
[[3,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => 3
[[3,1,1,1,1],[2],[1]] => [7,2,1] => 4
[[3,1,1,1,1],[1,1],[1]] => [7,2,1] => 4
[[3,1,1,1,1],[3]] => [7,3] => 3
[[3,1,1,1,1],[2,1]] => [7,3] => 3
[[3,1,1,1,1],[1,1,1]] => [7,3] => 3
[[2,2,2,1],[1],[1],[1]] => [7,1,1,1] => 3
[[2,2,2,1],[2],[1]] => [7,2,1] => 4
[[2,2,2,1],[1,1],[1]] => [7,2,1] => 4
[[2,2,2,1],[2,1]] => [7,3] => 3
[[2,2,2,1],[1,1,1]] => [7,3] => 3
[[2,2,1,1,1],[1],[1],[1]] => [7,1,1,1] => 3
[[2,2,1,1,1],[2],[1]] => [7,2,1] => 4
[[2,2,1,1,1],[1,1],[1]] => [7,2,1] => 4
[[2,2,1,1,1],[2,1]] => [7,3] => 3
[[2,2,1,1,1],[1,1,1]] => [7,3] => 3
[[2,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => 3
[[2,1,1,1,1,1],[2],[1]] => [7,2,1] => 4
[[2,1,1,1,1,1],[1,1],[1]] => [7,2,1] => 4
[[2,1,1,1,1,1],[2,1]] => [7,3] => 3
[[2,1,1,1,1,1],[1,1,1]] => [7,3] => 3
[[1,1,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => 3
[[1,1,1,1,1,1,1],[1,1],[1]] => [7,2,1] => 4
[[1,1,1,1,1,1,1],[1,1,1]] => [7,3] => 3
[[8],[1],[1]] => [8,1,1] => 3
[[8],[2]] => [8,2] => 3
[[7,1],[1],[1]] => [8,1,1] => 3
[[7,1],[2]] => [8,2] => 3
[[7,1],[1,1]] => [8,2] => 3
[[6,2],[1],[1]] => [8,1,1] => 3
[[6,2],[2]] => [8,2] => 3
[[6,2],[1,1]] => [8,2] => 3
[[6,1,1],[1],[1]] => [8,1,1] => 3
[[6,1,1],[2]] => [8,2] => 3
[[6,1,1],[1,1]] => [8,2] => 3
[[5,3],[1],[1]] => [8,1,1] => 3
[[5,3],[2]] => [8,2] => 3
[[5,3],[1,1]] => [8,2] => 3
[[5,2,1],[1],[1]] => [8,1,1] => 3
[[5,2,1],[2]] => [8,2] => 3
[[5,2,1],[1,1]] => [8,2] => 3
[[5,1,1,1],[1],[1]] => [8,1,1] => 3
[[5,1,1,1],[2]] => [8,2] => 3
[[5,1,1,1],[1,1]] => [8,2] => 3
[[4,4],[1],[1]] => [8,1,1] => 3
[[4,4],[2]] => [8,2] => 3
[[4,4],[1,1]] => [8,2] => 3
[[4,3,1],[1],[1]] => [8,1,1] => 3
[[4,3,1],[2]] => [8,2] => 3
[[4,3,1],[1,1]] => [8,2] => 3
[[4,2,2],[1],[1]] => [8,1,1] => 3
[[4,2,2],[2]] => [8,2] => 3
[[4,2,2],[1,1]] => [8,2] => 3
[[4,2,1,1],[1],[1]] => [8,1,1] => 3
[[4,2,1,1],[2]] => [8,2] => 3
[[4,2,1,1],[1,1]] => [8,2] => 3
[[4,1,1,1,1],[1],[1]] => [8,1,1] => 3
[[4,1,1,1,1],[2]] => [8,2] => 3
[[4,1,1,1,1],[1,1]] => [8,2] => 3
[[3,3,2],[1],[1]] => [8,1,1] => 3
[[3,3,2],[2]] => [8,2] => 3
[[3,3,2],[1,1]] => [8,2] => 3
[[3,3,1,1],[1],[1]] => [8,1,1] => 3
[[3,3,1,1],[2]] => [8,2] => 3
[[3,3,1,1],[1,1]] => [8,2] => 3
[[3,2,2,1],[1],[1]] => [8,1,1] => 3
[[3,2,2,1],[2]] => [8,2] => 3
[[3,2,2,1],[1,1]] => [8,2] => 3
[[3,2,1,1,1],[1],[1]] => [8,1,1] => 3
[[3,2,1,1,1],[2]] => [8,2] => 3
[[3,2,1,1,1],[1,1]] => [8,2] => 3
[[3,1,1,1,1,1],[1],[1]] => [8,1,1] => 3
[[3,1,1,1,1,1],[2]] => [8,2] => 3
[[3,1,1,1,1,1],[1,1]] => [8,2] => 3
[[2,2,2,2],[1],[1]] => [8,1,1] => 3
[[2,2,2,2],[2]] => [8,2] => 3
[[2,2,2,2],[1,1]] => [8,2] => 3
[[2,2,2,1,1],[1],[1]] => [8,1,1] => 3
[[2,2,2,1,1],[2]] => [8,2] => 3
[[2,2,2,1,1],[1,1]] => [8,2] => 3
[[2,2,1,1,1,1],[1],[1]] => [8,1,1] => 3
[[2,2,1,1,1,1],[2]] => [8,2] => 3
[[2,2,1,1,1,1],[1,1]] => [8,2] => 3
[[2,1,1,1,1,1,1],[1],[1]] => [8,1,1] => 3
[[2,1,1,1,1,1,1],[2]] => [8,2] => 3
[[2,1,1,1,1,1,1],[1,1]] => [8,2] => 3
[[1,1,1,1,1,1,1,1],[1],[1]] => [8,1,1] => 3
[[1,1,1,1,1,1,1,1],[1,1]] => [8,2] => 3
[[9],[1]] => [9,1] => 3
[[8,1],[1]] => [9,1] => 3
[[7,2],[1]] => [9,1] => 3
[[7,1,1],[1]] => [9,1] => 3
[[6,3],[1]] => [9,1] => 3
[[6,2,1],[1]] => [9,1] => 3
[[6,1,1,1],[1]] => [9,1] => 3
[[5,4],[1]] => [9,1] => 3
[[5,3,1],[1]] => [9,1] => 3
[[5,2,2],[1]] => [9,1] => 3
[[5,2,1,1],[1]] => [9,1] => 3
[[5,1,1,1,1],[1]] => [9,1] => 3
[[4,4,1],[1]] => [9,1] => 3
[[4,3,2],[1]] => [9,1] => 3
[[4,3,1,1],[1]] => [9,1] => 3
[[4,2,2,1],[1]] => [9,1] => 3
[[4,2,1,1,1],[1]] => [9,1] => 3
[[4,1,1,1,1,1],[1]] => [9,1] => 3
[[3,3,3],[1]] => [9,1] => 3
[[3,3,2,1],[1]] => [9,1] => 3
[[3,3,1,1,1],[1]] => [9,1] => 3
[[3,2,2,2],[1]] => [9,1] => 3
[[3,2,2,1,1],[1]] => [9,1] => 3
[[3,2,1,1,1,1],[1]] => [9,1] => 3
[[3,1,1,1,1,1,1],[1]] => [9,1] => 3
[[2,2,2,2,1],[1]] => [9,1] => 3
[[2,2,2,1,1,1],[1]] => [9,1] => 3
[[2,2,1,1,1,1,1],[1]] => [9,1] => 3
[[2,1,1,1,1,1,1,1],[1]] => [9,1] => 3
[[1,1,1,1,1,1,1,1,1],[1]] => [9,1] => 3
[[10]] => [10] => 2
[[9,1]] => [10] => 2
[[8,2]] => [10] => 2
[[8,1,1]] => [10] => 2
[[7,3]] => [10] => 2
[[7,2,1]] => [10] => 2
[[7,1,1,1]] => [10] => 2
[[6,4]] => [10] => 2
[[6,3,1]] => [10] => 2
[[6,2,2]] => [10] => 2
[[6,2,1,1]] => [10] => 2
[[6,1,1,1,1]] => [10] => 2
[[5,5]] => [10] => 2
[[5,4,1]] => [10] => 2
[[5,3,2]] => [10] => 2
[[5,3,1,1]] => [10] => 2
[[5,2,2,1]] => [10] => 2
[[5,2,1,1,1]] => [10] => 2
[[5,1,1,1,1,1]] => [10] => 2
[[4,4,2]] => [10] => 2
[[4,4,1,1]] => [10] => 2
[[4,3,3]] => [10] => 2
[[4,3,2,1]] => [10] => 2
[[4,3,1,1,1]] => [10] => 2
[[4,2,2,2]] => [10] => 2
[[4,2,2,1,1]] => [10] => 2
[[4,2,1,1,1,1]] => [10] => 2
[[4,1,1,1,1,1,1]] => [10] => 2
[[3,3,3,1]] => [10] => 2
[[3,3,2,2]] => [10] => 2
[[3,3,2,1,1]] => [10] => 2
[[3,3,1,1,1,1]] => [10] => 2
[[3,2,2,2,1]] => [10] => 2
[[3,2,2,1,1,1]] => [10] => 2
[[3,2,1,1,1,1,1]] => [10] => 2
[[3,1,1,1,1,1,1,1]] => [10] => 2
[[2,2,2,2,2]] => [10] => 2
[[2,2,2,2,1,1]] => [10] => 2
[[2,2,2,1,1,1,1]] => [10] => 2
[[2,2,1,1,1,1,1,1]] => [10] => 2
[[2,1,1,1,1,1,1,1,1]] => [10] => 2
[[1,1,1,1,1,1,1,1,1,1]] => [10] => 2
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,2 8,5 8,16 17,27,4 16,58,12 30,95,35 34,158,90 52,261,177,10
F1=q2
F2=3 q2
F3=4 q2+2 q3
F4=8 q2+5 q3
F5=8 q2+16 q3
F6=17 q2+27 q3+4 q4
F7=16 q2+58 q3+12 q4
F8=30 q2+95 q3+35 q4
F9=34 q2+158 q3+90 q4
F10=52 q2+261 q3+177 q4+10 q5
Description
The number of addable cells of the Ferrers diagram of an integer partition.
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Description
The underlying integer partition of a plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.
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