Identifier
-
Mp00311:
Plane partitions
—to partition⟶
Integer partitions
St000228: Integer partitions ⟶ ℤ
Values
[[1]] => [1] => 1
[[1],[1]] => [1,1] => 2
[[2]] => [2] => 2
[[1,1]] => [2] => 2
[[1],[1],[1]] => [1,1,1] => 3
[[2],[1]] => [2,1] => 3
[[1,1],[1]] => [2,1] => 3
[[3]] => [3] => 3
[[2,1]] => [3] => 3
[[1,1,1]] => [3] => 3
[[1],[1],[1],[1]] => [1,1,1,1] => 4
[[2],[1],[1]] => [2,1,1] => 4
[[2],[2]] => [2,2] => 4
[[1,1],[1],[1]] => [2,1,1] => 4
[[1,1],[1,1]] => [2,2] => 4
[[3],[1]] => [3,1] => 4
[[2,1],[1]] => [3,1] => 4
[[1,1,1],[1]] => [3,1] => 4
[[4]] => [4] => 4
[[3,1]] => [4] => 4
[[2,2]] => [4] => 4
[[2,1,1]] => [4] => 4
[[1,1,1,1]] => [4] => 4
[[1],[1],[1],[1],[1]] => [1,1,1,1,1] => 5
[[2],[1],[1],[1]] => [2,1,1,1] => 5
[[2],[2],[1]] => [2,2,1] => 5
[[1,1],[1],[1],[1]] => [2,1,1,1] => 5
[[1,1],[1,1],[1]] => [2,2,1] => 5
[[3],[1],[1]] => [3,1,1] => 5
[[3],[2]] => [3,2] => 5
[[2,1],[1],[1]] => [3,1,1] => 5
[[2,1],[2]] => [3,2] => 5
[[2,1],[1,1]] => [3,2] => 5
[[1,1,1],[1],[1]] => [3,1,1] => 5
[[1,1,1],[1,1]] => [3,2] => 5
[[4],[1]] => [4,1] => 5
[[3,1],[1]] => [4,1] => 5
[[2,2],[1]] => [4,1] => 5
[[2,1,1],[1]] => [4,1] => 5
[[1,1,1,1],[1]] => [4,1] => 5
[[5]] => [5] => 5
[[4,1]] => [5] => 5
[[3,2]] => [5] => 5
[[3,1,1]] => [5] => 5
[[2,2,1]] => [5] => 5
[[2,1,1,1]] => [5] => 5
[[1,1,1,1,1]] => [5] => 5
[[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1] => 6
[[2],[1],[1],[1],[1]] => [2,1,1,1,1] => 6
[[2],[2],[1],[1]] => [2,2,1,1] => 6
[[2],[2],[2]] => [2,2,2] => 6
[[1,1],[1],[1],[1],[1]] => [2,1,1,1,1] => 6
[[1,1],[1,1],[1],[1]] => [2,2,1,1] => 6
[[1,1],[1,1],[1,1]] => [2,2,2] => 6
[[3],[1],[1],[1]] => [3,1,1,1] => 6
[[3],[2],[1]] => [3,2,1] => 6
[[3],[3]] => [3,3] => 6
[[2,1],[1],[1],[1]] => [3,1,1,1] => 6
[[2,1],[2],[1]] => [3,2,1] => 6
[[2,1],[1,1],[1]] => [3,2,1] => 6
[[2,1],[2,1]] => [3,3] => 6
[[1,1,1],[1],[1],[1]] => [3,1,1,1] => 6
[[1,1,1],[1,1],[1]] => [3,2,1] => 6
[[1,1,1],[1,1,1]] => [3,3] => 6
[[4],[1],[1]] => [4,1,1] => 6
[[4],[2]] => [4,2] => 6
[[3,1],[1],[1]] => [4,1,1] => 6
[[3,1],[2]] => [4,2] => 6
[[3,1],[1,1]] => [4,2] => 6
[[2,2],[1],[1]] => [4,1,1] => 6
[[2,2],[2]] => [4,2] => 6
[[2,2],[1,1]] => [4,2] => 6
[[2,1,1],[1],[1]] => [4,1,1] => 6
[[2,1,1],[2]] => [4,2] => 6
[[2,1,1],[1,1]] => [4,2] => 6
[[1,1,1,1],[1],[1]] => [4,1,1] => 6
[[1,1,1,1],[1,1]] => [4,2] => 6
[[5],[1]] => [5,1] => 6
[[4,1],[1]] => [5,1] => 6
[[3,2],[1]] => [5,1] => 6
[[3,1,1],[1]] => [5,1] => 6
[[2,2,1],[1]] => [5,1] => 6
[[2,1,1,1],[1]] => [5,1] => 6
[[1,1,1,1,1],[1]] => [5,1] => 6
[[6]] => [6] => 6
[[5,1]] => [6] => 6
[[4,2]] => [6] => 6
[[4,1,1]] => [6] => 6
[[3,3]] => [6] => 6
[[3,2,1]] => [6] => 6
[[3,1,1,1]] => [6] => 6
[[2,2,2]] => [6] => 6
[[2,2,1,1]] => [6] => 6
[[2,1,1,1,1]] => [6] => 6
[[1,1,1,1,1,1]] => [6] => 6
[[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1] => 7
[[2],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => 7
[[2],[2],[1],[1],[1]] => [2,2,1,1,1] => 7
[[2],[2],[2],[1]] => [2,2,2,1] => 7
[[1,1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => 7
[[1,1],[1,1],[1],[1],[1]] => [2,2,1,1,1] => 7
>>> Load all 1123 entries. <<<[[1,1],[1,1],[1,1],[1]] => [2,2,2,1] => 7
[[3],[1],[1],[1],[1]] => [3,1,1,1,1] => 7
[[3],[2],[1],[1]] => [3,2,1,1] => 7
[[3],[2],[2]] => [3,2,2] => 7
[[3],[3],[1]] => [3,3,1] => 7
[[2,1],[1],[1],[1],[1]] => [3,1,1,1,1] => 7
[[2,1],[2],[1],[1]] => [3,2,1,1] => 7
[[2,1],[2],[2]] => [3,2,2] => 7
[[2,1],[1,1],[1],[1]] => [3,2,1,1] => 7
[[2,1],[1,1],[1,1]] => [3,2,2] => 7
[[2,1],[2,1],[1]] => [3,3,1] => 7
[[1,1,1],[1],[1],[1],[1]] => [3,1,1,1,1] => 7
[[1,1,1],[1,1],[1],[1]] => [3,2,1,1] => 7
[[1,1,1],[1,1],[1,1]] => [3,2,2] => 7
[[1,1,1],[1,1,1],[1]] => [3,3,1] => 7
[[4],[1],[1],[1]] => [4,1,1,1] => 7
[[4],[2],[1]] => [4,2,1] => 7
[[4],[3]] => [4,3] => 7
[[3,1],[1],[1],[1]] => [4,1,1,1] => 7
[[3,1],[2],[1]] => [4,2,1] => 7
[[3,1],[1,1],[1]] => [4,2,1] => 7
[[3,1],[3]] => [4,3] => 7
[[3,1],[2,1]] => [4,3] => 7
[[2,2],[1],[1],[1]] => [4,1,1,1] => 7
[[2,2],[2],[1]] => [4,2,1] => 7
[[2,2],[1,1],[1]] => [4,2,1] => 7
[[2,2],[2,1]] => [4,3] => 7
[[2,1,1],[1],[1],[1]] => [4,1,1,1] => 7
[[2,1,1],[2],[1]] => [4,2,1] => 7
[[2,1,1],[1,1],[1]] => [4,2,1] => 7
[[2,1,1],[2,1]] => [4,3] => 7
[[2,1,1],[1,1,1]] => [4,3] => 7
[[1,1,1,1],[1],[1],[1]] => [4,1,1,1] => 7
[[1,1,1,1],[1,1],[1]] => [4,2,1] => 7
[[1,1,1,1],[1,1,1]] => [4,3] => 7
[[5],[1],[1]] => [5,1,1] => 7
[[5],[2]] => [5,2] => 7
[[4,1],[1],[1]] => [5,1,1] => 7
[[4,1],[2]] => [5,2] => 7
[[4,1],[1,1]] => [5,2] => 7
[[3,2],[1],[1]] => [5,1,1] => 7
[[3,2],[2]] => [5,2] => 7
[[3,2],[1,1]] => [5,2] => 7
[[3,1,1],[1],[1]] => [5,1,1] => 7
[[3,1,1],[2]] => [5,2] => 7
[[3,1,1],[1,1]] => [5,2] => 7
[[2,2,1],[1],[1]] => [5,1,1] => 7
[[2,2,1],[2]] => [5,2] => 7
[[2,2,1],[1,1]] => [5,2] => 7
[[2,1,1,1],[1],[1]] => [5,1,1] => 7
[[2,1,1,1],[2]] => [5,2] => 7
[[2,1,1,1],[1,1]] => [5,2] => 7
[[1,1,1,1,1],[1],[1]] => [5,1,1] => 7
[[1,1,1,1,1],[1,1]] => [5,2] => 7
[[6],[1]] => [6,1] => 7
[[5,1],[1]] => [6,1] => 7
[[4,2],[1]] => [6,1] => 7
[[4,1,1],[1]] => [6,1] => 7
[[3,3],[1]] => [6,1] => 7
[[3,2,1],[1]] => [6,1] => 7
[[3,1,1,1],[1]] => [6,1] => 7
[[2,2,2],[1]] => [6,1] => 7
[[2,2,1,1],[1]] => [6,1] => 7
[[2,1,1,1,1],[1]] => [6,1] => 7
[[1,1,1,1,1,1],[1]] => [6,1] => 7
[[7]] => [7] => 7
[[6,1]] => [7] => 7
[[5,2]] => [7] => 7
[[5,1,1]] => [7] => 7
[[4,3]] => [7] => 7
[[4,2,1]] => [7] => 7
[[4,1,1,1]] => [7] => 7
[[3,3,1]] => [7] => 7
[[3,2,2]] => [7] => 7
[[3,2,1,1]] => [7] => 7
[[3,1,1,1,1]] => [7] => 7
[[2,2,2,1]] => [7] => 7
[[2,2,1,1,1]] => [7] => 7
[[2,1,1,1,1,1]] => [7] => 7
[[1,1,1,1,1,1,1]] => [7] => 7
[[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1] => 8
[[2],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1] => 8
[[2],[2],[1],[1],[1],[1]] => [2,2,1,1,1,1] => 8
[[2],[2],[2],[1],[1]] => [2,2,2,1,1] => 8
[[2],[2],[2],[2]] => [2,2,2,2] => 8
[[1,1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1] => 8
[[1,1],[1,1],[1],[1],[1],[1]] => [2,2,1,1,1,1] => 8
[[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,1,1] => 8
[[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2] => 8
[[3],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => 8
[[3],[2],[1],[1],[1]] => [3,2,1,1,1] => 8
[[3],[2],[2],[1]] => [3,2,2,1] => 8
[[3],[3],[1],[1]] => [3,3,1,1] => 8
[[3],[3],[2]] => [3,3,2] => 8
[[2,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => 8
[[2,1],[2],[1],[1],[1]] => [3,2,1,1,1] => 8
[[2,1],[2],[2],[1]] => [3,2,2,1] => 8
[[2,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => 8
[[2,1],[1,1],[1,1],[1]] => [3,2,2,1] => 8
[[2,1],[2,1],[1],[1]] => [3,3,1,1] => 8
[[2,1],[2,1],[2]] => [3,3,2] => 8
[[2,1],[2,1],[1,1]] => [3,3,2] => 8
[[1,1,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => 8
[[1,1,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => 8
[[1,1,1],[1,1],[1,1],[1]] => [3,2,2,1] => 8
[[1,1,1],[1,1,1],[1],[1]] => [3,3,1,1] => 8
[[1,1,1],[1,1,1],[1,1]] => [3,3,2] => 8
[[4],[1],[1],[1],[1]] => [4,1,1,1,1] => 8
[[4],[2],[1],[1]] => [4,2,1,1] => 8
[[4],[2],[2]] => [4,2,2] => 8
[[4],[3],[1]] => [4,3,1] => 8
[[4],[4]] => [4,4] => 8
[[3,1],[1],[1],[1],[1]] => [4,1,1,1,1] => 8
[[3,1],[2],[1],[1]] => [4,2,1,1] => 8
[[3,1],[2],[2]] => [4,2,2] => 8
[[3,1],[1,1],[1],[1]] => [4,2,1,1] => 8
[[3,1],[1,1],[1,1]] => [4,2,2] => 8
[[3,1],[3],[1]] => [4,3,1] => 8
[[3,1],[2,1],[1]] => [4,3,1] => 8
[[3,1],[3,1]] => [4,4] => 8
[[2,2],[1],[1],[1],[1]] => [4,1,1,1,1] => 8
[[2,2],[2],[1],[1]] => [4,2,1,1] => 8
[[2,2],[2],[2]] => [4,2,2] => 8
[[2,2],[1,1],[1],[1]] => [4,2,1,1] => 8
[[2,2],[1,1],[1,1]] => [4,2,2] => 8
[[2,2],[2,1],[1]] => [4,3,1] => 8
[[2,2],[2,2]] => [4,4] => 8
[[2,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => 8
[[2,1,1],[2],[1],[1]] => [4,2,1,1] => 8
[[2,1,1],[2],[2]] => [4,2,2] => 8
[[2,1,1],[1,1],[1],[1]] => [4,2,1,1] => 8
[[2,1,1],[1,1],[1,1]] => [4,2,2] => 8
[[2,1,1],[2,1],[1]] => [4,3,1] => 8
[[2,1,1],[1,1,1],[1]] => [4,3,1] => 8
[[2,1,1],[2,1,1]] => [4,4] => 8
[[1,1,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => 8
[[1,1,1,1],[1,1],[1],[1]] => [4,2,1,1] => 8
[[1,1,1,1],[1,1],[1,1]] => [4,2,2] => 8
[[1,1,1,1],[1,1,1],[1]] => [4,3,1] => 8
[[1,1,1,1],[1,1,1,1]] => [4,4] => 8
[[5],[1],[1],[1]] => [5,1,1,1] => 8
[[5],[2],[1]] => [5,2,1] => 8
[[5],[3]] => [5,3] => 8
[[4,1],[1],[1],[1]] => [5,1,1,1] => 8
[[4,1],[2],[1]] => [5,2,1] => 8
[[4,1],[1,1],[1]] => [5,2,1] => 8
[[4,1],[3]] => [5,3] => 8
[[4,1],[2,1]] => [5,3] => 8
[[3,2],[1],[1],[1]] => [5,1,1,1] => 8
[[3,2],[2],[1]] => [5,2,1] => 8
[[3,2],[1,1],[1]] => [5,2,1] => 8
[[3,2],[3]] => [5,3] => 8
[[3,2],[2,1]] => [5,3] => 8
[[3,1,1],[1],[1],[1]] => [5,1,1,1] => 8
[[3,1,1],[2],[1]] => [5,2,1] => 8
[[3,1,1],[1,1],[1]] => [5,2,1] => 8
[[3,1,1],[3]] => [5,3] => 8
[[3,1,1],[2,1]] => [5,3] => 8
[[3,1,1],[1,1,1]] => [5,3] => 8
[[2,2,1],[1],[1],[1]] => [5,1,1,1] => 8
[[2,2,1],[2],[1]] => [5,2,1] => 8
[[2,2,1],[1,1],[1]] => [5,2,1] => 8
[[2,2,1],[2,1]] => [5,3] => 8
[[2,2,1],[1,1,1]] => [5,3] => 8
[[2,1,1,1],[1],[1],[1]] => [5,1,1,1] => 8
[[2,1,1,1],[2],[1]] => [5,2,1] => 8
[[2,1,1,1],[1,1],[1]] => [5,2,1] => 8
[[2,1,1,1],[2,1]] => [5,3] => 8
[[2,1,1,1],[1,1,1]] => [5,3] => 8
[[1,1,1,1,1],[1],[1],[1]] => [5,1,1,1] => 8
[[1,1,1,1,1],[1,1],[1]] => [5,2,1] => 8
[[1,1,1,1,1],[1,1,1]] => [5,3] => 8
[[6],[1],[1]] => [6,1,1] => 8
[[6],[2]] => [6,2] => 8
[[5,1],[1],[1]] => [6,1,1] => 8
[[5,1],[2]] => [6,2] => 8
[[5,1],[1,1]] => [6,2] => 8
[[4,2],[1],[1]] => [6,1,1] => 8
[[4,2],[2]] => [6,2] => 8
[[4,2],[1,1]] => [6,2] => 8
[[4,1,1],[1],[1]] => [6,1,1] => 8
[[4,1,1],[2]] => [6,2] => 8
[[4,1,1],[1,1]] => [6,2] => 8
[[3,3],[1],[1]] => [6,1,1] => 8
[[3,3],[2]] => [6,2] => 8
[[3,3],[1,1]] => [6,2] => 8
[[3,2,1],[1],[1]] => [6,1,1] => 8
[[3,2,1],[2]] => [6,2] => 8
[[3,2,1],[1,1]] => [6,2] => 8
[[3,1,1,1],[1],[1]] => [6,1,1] => 8
[[3,1,1,1],[2]] => [6,2] => 8
[[3,1,1,1],[1,1]] => [6,2] => 8
[[2,2,2],[1],[1]] => [6,1,1] => 8
[[2,2,2],[2]] => [6,2] => 8
[[2,2,2],[1,1]] => [6,2] => 8
[[2,2,1,1],[1],[1]] => [6,1,1] => 8
[[2,2,1,1],[2]] => [6,2] => 8
[[2,2,1,1],[1,1]] => [6,2] => 8
[[2,1,1,1,1],[1],[1]] => [6,1,1] => 8
[[2,1,1,1,1],[2]] => [6,2] => 8
[[2,1,1,1,1],[1,1]] => [6,2] => 8
[[1,1,1,1,1,1],[1],[1]] => [6,1,1] => 8
[[1,1,1,1,1,1],[1,1]] => [6,2] => 8
[[7],[1]] => [7,1] => 8
[[6,1],[1]] => [7,1] => 8
[[5,2],[1]] => [7,1] => 8
[[5,1,1],[1]] => [7,1] => 8
[[4,3],[1]] => [7,1] => 8
[[4,2,1],[1]] => [7,1] => 8
[[4,1,1,1],[1]] => [7,1] => 8
[[3,3,1],[1]] => [7,1] => 8
[[3,2,2],[1]] => [7,1] => 8
[[3,2,1,1],[1]] => [7,1] => 8
[[3,1,1,1,1],[1]] => [7,1] => 8
[[2,2,2,1],[1]] => [7,1] => 8
[[2,2,1,1,1],[1]] => [7,1] => 8
[[2,1,1,1,1,1],[1]] => [7,1] => 8
[[1,1,1,1,1,1,1],[1]] => [7,1] => 8
[[8]] => [8] => 8
[[7,1]] => [8] => 8
[[6,2]] => [8] => 8
[[6,1,1]] => [8] => 8
[[5,3]] => [8] => 8
[[5,2,1]] => [8] => 8
[[5,1,1,1]] => [8] => 8
[[4,4]] => [8] => 8
[[4,3,1]] => [8] => 8
[[4,2,2]] => [8] => 8
[[4,2,1,1]] => [8] => 8
[[4,1,1,1,1]] => [8] => 8
[[3,3,2]] => [8] => 8
[[3,3,1,1]] => [8] => 8
[[3,2,2,1]] => [8] => 8
[[3,2,1,1,1]] => [8] => 8
[[3,1,1,1,1,1]] => [8] => 8
[[2,2,2,2]] => [8] => 8
[[2,2,2,1,1]] => [8] => 8
[[2,2,1,1,1,1]] => [8] => 8
[[2,1,1,1,1,1,1]] => [8] => 8
[[1,1,1,1,1,1,1,1]] => [8] => 8
[[1],[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1,1] => 9
[[2],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1] => 9
[[2],[2],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1] => 9
[[2],[2],[2],[1],[1],[1]] => [2,2,2,1,1,1] => 9
[[2],[2],[2],[2],[1]] => [2,2,2,2,1] => 9
[[1,1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1] => 9
[[1,1],[1,1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1] => 9
[[1,1],[1,1],[1,1],[1],[1],[1]] => [2,2,2,1,1,1] => 9
[[1,1],[1,1],[1,1],[1,1],[1]] => [2,2,2,2,1] => 9
[[3],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => 9
[[3],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1] => 9
[[3],[2],[2],[1],[1]] => [3,2,2,1,1] => 9
[[3],[2],[2],[2]] => [3,2,2,2] => 9
[[3],[3],[1],[1],[1]] => [3,3,1,1,1] => 9
[[3],[3],[2],[1]] => [3,3,2,1] => 9
[[3],[3],[3]] => [3,3,3] => 9
[[2,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => 9
[[2,1],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1] => 9
[[2,1],[2],[2],[1],[1]] => [3,2,2,1,1] => 9
[[2,1],[2],[2],[2]] => [3,2,2,2] => 9
[[2,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1] => 9
[[2,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => 9
[[2,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => 9
[[2,1],[2,1],[1],[1],[1]] => [3,3,1,1,1] => 9
[[2,1],[2,1],[2],[1]] => [3,3,2,1] => 9
[[2,1],[2,1],[1,1],[1]] => [3,3,2,1] => 9
[[2,1],[2,1],[2,1]] => [3,3,3] => 9
[[1,1,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => 9
[[1,1,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1] => 9
[[1,1,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => 9
[[1,1,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => 9
[[1,1,1],[1,1,1],[1],[1],[1]] => [3,3,1,1,1] => 9
[[1,1,1],[1,1,1],[1,1],[1]] => [3,3,2,1] => 9
[[1,1,1],[1,1,1],[1,1,1]] => [3,3,3] => 9
[[4],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 9
[[4],[2],[1],[1],[1]] => [4,2,1,1,1] => 9
[[4],[2],[2],[1]] => [4,2,2,1] => 9
[[4],[3],[1],[1]] => [4,3,1,1] => 9
[[4],[3],[2]] => [4,3,2] => 9
[[4],[4],[1]] => [4,4,1] => 9
[[3,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 9
[[3,1],[2],[1],[1],[1]] => [4,2,1,1,1] => 9
[[3,1],[2],[2],[1]] => [4,2,2,1] => 9
[[3,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => 9
[[3,1],[1,1],[1,1],[1]] => [4,2,2,1] => 9
[[3,1],[3],[1],[1]] => [4,3,1,1] => 9
[[3,1],[3],[2]] => [4,3,2] => 9
[[3,1],[2,1],[1],[1]] => [4,3,1,1] => 9
[[3,1],[2,1],[2]] => [4,3,2] => 9
[[3,1],[2,1],[1,1]] => [4,3,2] => 9
[[3,1],[3,1],[1]] => [4,4,1] => 9
[[2,2],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 9
[[2,2],[2],[1],[1],[1]] => [4,2,1,1,1] => 9
[[2,2],[2],[2],[1]] => [4,2,2,1] => 9
[[2,2],[1,1],[1],[1],[1]] => [4,2,1,1,1] => 9
[[2,2],[1,1],[1,1],[1]] => [4,2,2,1] => 9
[[2,2],[2,1],[1],[1]] => [4,3,1,1] => 9
[[2,2],[2,1],[2]] => [4,3,2] => 9
[[2,2],[2,1],[1,1]] => [4,3,2] => 9
[[2,2],[2,2],[1]] => [4,4,1] => 9
[[2,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 9
[[2,1,1],[2],[1],[1],[1]] => [4,2,1,1,1] => 9
[[2,1,1],[2],[2],[1]] => [4,2,2,1] => 9
[[2,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => 9
[[2,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => 9
[[2,1,1],[2,1],[1],[1]] => [4,3,1,1] => 9
[[2,1,1],[2,1],[2]] => [4,3,2] => 9
[[2,1,1],[2,1],[1,1]] => [4,3,2] => 9
[[2,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => 9
[[2,1,1],[1,1,1],[1,1]] => [4,3,2] => 9
[[2,1,1],[2,1,1],[1]] => [4,4,1] => 9
[[1,1,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 9
[[1,1,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => 9
[[1,1,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => 9
[[1,1,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => 9
[[1,1,1,1],[1,1,1],[1,1]] => [4,3,2] => 9
[[1,1,1,1],[1,1,1,1],[1]] => [4,4,1] => 9
[[5],[1],[1],[1],[1]] => [5,1,1,1,1] => 9
[[5],[2],[1],[1]] => [5,2,1,1] => 9
[[5],[2],[2]] => [5,2,2] => 9
[[5],[3],[1]] => [5,3,1] => 9
[[5],[4]] => [5,4] => 9
[[4,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 9
[[4,1],[2],[1],[1]] => [5,2,1,1] => 9
[[4,1],[2],[2]] => [5,2,2] => 9
[[4,1],[1,1],[1],[1]] => [5,2,1,1] => 9
[[4,1],[1,1],[1,1]] => [5,2,2] => 9
[[4,1],[3],[1]] => [5,3,1] => 9
[[4,1],[2,1],[1]] => [5,3,1] => 9
[[4,1],[4]] => [5,4] => 9
[[4,1],[3,1]] => [5,4] => 9
[[3,2],[1],[1],[1],[1]] => [5,1,1,1,1] => 9
[[3,2],[2],[1],[1]] => [5,2,1,1] => 9
[[3,2],[2],[2]] => [5,2,2] => 9
[[3,2],[1,1],[1],[1]] => [5,2,1,1] => 9
[[3,2],[1,1],[1,1]] => [5,2,2] => 9
[[3,2],[3],[1]] => [5,3,1] => 9
[[3,2],[2,1],[1]] => [5,3,1] => 9
[[3,2],[3,1]] => [5,4] => 9
[[3,2],[2,2]] => [5,4] => 9
[[3,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 9
[[3,1,1],[2],[1],[1]] => [5,2,1,1] => 9
[[3,1,1],[2],[2]] => [5,2,2] => 9
[[3,1,1],[1,1],[1],[1]] => [5,2,1,1] => 9
[[3,1,1],[1,1],[1,1]] => [5,2,2] => 9
[[3,1,1],[3],[1]] => [5,3,1] => 9
[[3,1,1],[2,1],[1]] => [5,3,1] => 9
[[3,1,1],[1,1,1],[1]] => [5,3,1] => 9
[[3,1,1],[3,1]] => [5,4] => 9
[[3,1,1],[2,1,1]] => [5,4] => 9
[[2,2,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 9
[[2,2,1],[2],[1],[1]] => [5,2,1,1] => 9
[[2,2,1],[2],[2]] => [5,2,2] => 9
[[2,2,1],[1,1],[1],[1]] => [5,2,1,1] => 9
[[2,2,1],[1,1],[1,1]] => [5,2,2] => 9
[[2,2,1],[2,1],[1]] => [5,3,1] => 9
[[2,2,1],[1,1,1],[1]] => [5,3,1] => 9
[[2,2,1],[2,2]] => [5,4] => 9
[[2,2,1],[2,1,1]] => [5,4] => 9
[[2,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 9
[[2,1,1,1],[2],[1],[1]] => [5,2,1,1] => 9
[[2,1,1,1],[2],[2]] => [5,2,2] => 9
[[2,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => 9
[[2,1,1,1],[1,1],[1,1]] => [5,2,2] => 9
[[2,1,1,1],[2,1],[1]] => [5,3,1] => 9
[[2,1,1,1],[1,1,1],[1]] => [5,3,1] => 9
[[2,1,1,1],[2,1,1]] => [5,4] => 9
[[2,1,1,1],[1,1,1,1]] => [5,4] => 9
[[1,1,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 9
[[1,1,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => 9
[[1,1,1,1,1],[1,1],[1,1]] => [5,2,2] => 9
[[1,1,1,1,1],[1,1,1],[1]] => [5,3,1] => 9
[[1,1,1,1,1],[1,1,1,1]] => [5,4] => 9
[[6],[1],[1],[1]] => [6,1,1,1] => 9
[[6],[2],[1]] => [6,2,1] => 9
[[6],[3]] => [6,3] => 9
[[5,1],[1],[1],[1]] => [6,1,1,1] => 9
[[5,1],[2],[1]] => [6,2,1] => 9
[[5,1],[1,1],[1]] => [6,2,1] => 9
[[5,1],[3]] => [6,3] => 9
[[5,1],[2,1]] => [6,3] => 9
[[4,2],[1],[1],[1]] => [6,1,1,1] => 9
[[4,2],[2],[1]] => [6,2,1] => 9
[[4,2],[1,1],[1]] => [6,2,1] => 9
[[4,2],[3]] => [6,3] => 9
[[4,2],[2,1]] => [6,3] => 9
[[4,1,1],[1],[1],[1]] => [6,1,1,1] => 9
[[4,1,1],[2],[1]] => [6,2,1] => 9
[[4,1,1],[1,1],[1]] => [6,2,1] => 9
[[4,1,1],[3]] => [6,3] => 9
[[4,1,1],[2,1]] => [6,3] => 9
[[4,1,1],[1,1,1]] => [6,3] => 9
[[3,3],[1],[1],[1]] => [6,1,1,1] => 9
[[3,3],[2],[1]] => [6,2,1] => 9
[[3,3],[1,1],[1]] => [6,2,1] => 9
[[3,3],[3]] => [6,3] => 9
[[3,3],[2,1]] => [6,3] => 9
[[3,2,1],[1],[1],[1]] => [6,1,1,1] => 9
[[3,2,1],[2],[1]] => [6,2,1] => 9
[[3,2,1],[1,1],[1]] => [6,2,1] => 9
[[3,2,1],[3]] => [6,3] => 9
[[3,2,1],[2,1]] => [6,3] => 9
[[3,2,1],[1,1,1]] => [6,3] => 9
[[3,1,1,1],[1],[1],[1]] => [6,1,1,1] => 9
[[3,1,1,1],[2],[1]] => [6,2,1] => 9
[[3,1,1,1],[1,1],[1]] => [6,2,1] => 9
[[3,1,1,1],[3]] => [6,3] => 9
[[3,1,1,1],[2,1]] => [6,3] => 9
[[3,1,1,1],[1,1,1]] => [6,3] => 9
[[2,2,2],[1],[1],[1]] => [6,1,1,1] => 9
[[2,2,2],[2],[1]] => [6,2,1] => 9
[[2,2,2],[1,1],[1]] => [6,2,1] => 9
[[2,2,2],[2,1]] => [6,3] => 9
[[2,2,2],[1,1,1]] => [6,3] => 9
[[2,2,1,1],[1],[1],[1]] => [6,1,1,1] => 9
[[2,2,1,1],[2],[1]] => [6,2,1] => 9
[[2,2,1,1],[1,1],[1]] => [6,2,1] => 9
[[2,2,1,1],[2,1]] => [6,3] => 9
[[2,2,1,1],[1,1,1]] => [6,3] => 9
[[2,1,1,1,1],[1],[1],[1]] => [6,1,1,1] => 9
[[2,1,1,1,1],[2],[1]] => [6,2,1] => 9
[[2,1,1,1,1],[1,1],[1]] => [6,2,1] => 9
[[2,1,1,1,1],[2,1]] => [6,3] => 9
[[2,1,1,1,1],[1,1,1]] => [6,3] => 9
[[1,1,1,1,1,1],[1],[1],[1]] => [6,1,1,1] => 9
[[1,1,1,1,1,1],[1,1],[1]] => [6,2,1] => 9
[[1,1,1,1,1,1],[1,1,1]] => [6,3] => 9
[[7],[1],[1]] => [7,1,1] => 9
[[7],[2]] => [7,2] => 9
[[6,1],[1],[1]] => [7,1,1] => 9
[[6,1],[2]] => [7,2] => 9
[[6,1],[1,1]] => [7,2] => 9
[[5,2],[1],[1]] => [7,1,1] => 9
[[5,2],[2]] => [7,2] => 9
[[5,2],[1,1]] => [7,2] => 9
[[5,1,1],[1],[1]] => [7,1,1] => 9
[[5,1,1],[2]] => [7,2] => 9
[[5,1,1],[1,1]] => [7,2] => 9
[[4,3],[1],[1]] => [7,1,1] => 9
[[4,3],[2]] => [7,2] => 9
[[4,3],[1,1]] => [7,2] => 9
[[4,2,1],[1],[1]] => [7,1,1] => 9
[[4,2,1],[2]] => [7,2] => 9
[[4,2,1],[1,1]] => [7,2] => 9
[[4,1,1,1],[1],[1]] => [7,1,1] => 9
[[4,1,1,1],[2]] => [7,2] => 9
[[4,1,1,1],[1,1]] => [7,2] => 9
[[3,3,1],[1],[1]] => [7,1,1] => 9
[[3,3,1],[2]] => [7,2] => 9
[[3,3,1],[1,1]] => [7,2] => 9
[[3,2,2],[1],[1]] => [7,1,1] => 9
[[3,2,2],[2]] => [7,2] => 9
[[3,2,2],[1,1]] => [7,2] => 9
[[3,2,1,1],[1],[1]] => [7,1,1] => 9
[[3,2,1,1],[2]] => [7,2] => 9
[[3,2,1,1],[1,1]] => [7,2] => 9
[[3,1,1,1,1],[1],[1]] => [7,1,1] => 9
[[3,1,1,1,1],[2]] => [7,2] => 9
[[3,1,1,1,1],[1,1]] => [7,2] => 9
[[2,2,2,1],[1],[1]] => [7,1,1] => 9
[[2,2,2,1],[2]] => [7,2] => 9
[[2,2,2,1],[1,1]] => [7,2] => 9
[[2,2,1,1,1],[1],[1]] => [7,1,1] => 9
[[2,2,1,1,1],[2]] => [7,2] => 9
[[2,2,1,1,1],[1,1]] => [7,2] => 9
[[2,1,1,1,1,1],[1],[1]] => [7,1,1] => 9
[[2,1,1,1,1,1],[2]] => [7,2] => 9
[[2,1,1,1,1,1],[1,1]] => [7,2] => 9
[[1,1,1,1,1,1,1],[1],[1]] => [7,1,1] => 9
[[1,1,1,1,1,1,1],[1,1]] => [7,2] => 9
[[8],[1]] => [8,1] => 9
[[7,1],[1]] => [8,1] => 9
[[6,2],[1]] => [8,1] => 9
[[6,1,1],[1]] => [8,1] => 9
[[5,3],[1]] => [8,1] => 9
[[5,2,1],[1]] => [8,1] => 9
[[5,1,1,1],[1]] => [8,1] => 9
[[4,4],[1]] => [8,1] => 9
[[4,3,1],[1]] => [8,1] => 9
[[4,2,2],[1]] => [8,1] => 9
[[4,2,1,1],[1]] => [8,1] => 9
[[4,1,1,1,1],[1]] => [8,1] => 9
[[3,3,2],[1]] => [8,1] => 9
[[3,3,1,1],[1]] => [8,1] => 9
[[3,2,2,1],[1]] => [8,1] => 9
[[3,2,1,1,1],[1]] => [8,1] => 9
[[3,1,1,1,1,1],[1]] => [8,1] => 9
[[2,2,2,2],[1]] => [8,1] => 9
[[2,2,2,1,1],[1]] => [8,1] => 9
[[2,2,1,1,1,1],[1]] => [8,1] => 9
[[2,1,1,1,1,1,1],[1]] => [8,1] => 9
[[1,1,1,1,1,1,1,1],[1]] => [8,1] => 9
[[9]] => [9] => 9
[[8,1]] => [9] => 9
[[7,2]] => [9] => 9
[[7,1,1]] => [9] => 9
[[6,3]] => [9] => 9
[[6,2,1]] => [9] => 9
[[6,1,1,1]] => [9] => 9
[[5,4]] => [9] => 9
[[5,3,1]] => [9] => 9
[[5,2,2]] => [9] => 9
[[5,2,1,1]] => [9] => 9
[[5,1,1,1,1]] => [9] => 9
[[4,4,1]] => [9] => 9
[[4,3,2]] => [9] => 9
[[4,3,1,1]] => [9] => 9
[[4,2,2,1]] => [9] => 9
[[4,2,1,1,1]] => [9] => 9
[[4,1,1,1,1,1]] => [9] => 9
[[3,3,3]] => [9] => 9
[[3,3,2,1]] => [9] => 9
[[3,3,1,1,1]] => [9] => 9
[[3,2,2,2]] => [9] => 9
[[3,2,2,1,1]] => [9] => 9
[[3,2,1,1,1,1]] => [9] => 9
[[3,1,1,1,1,1,1]] => [9] => 9
[[2,2,2,2,1]] => [9] => 9
[[2,2,2,1,1,1]] => [9] => 9
[[2,2,1,1,1,1,1]] => [9] => 9
[[2,1,1,1,1,1,1,1]] => [9] => 9
[[1,1,1,1,1,1,1,1,1]] => [9] => 9
[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1,1,1] => 10
[[2],[1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1,1] => 10
[[2],[2],[1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1,1] => 10
[[2],[2],[2],[1],[1],[1],[1]] => [2,2,2,1,1,1,1] => 10
[[2],[2],[2],[2],[1],[1]] => [2,2,2,2,1,1] => 10
[[2],[2],[2],[2],[2]] => [2,2,2,2,2] => 10
[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1,1] => 10
[[1,1],[1,1],[1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1,1] => 10
[[1,1],[1,1],[1,1],[1],[1],[1],[1]] => [2,2,2,1,1,1,1] => 10
[[1,1],[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,2,1,1] => 10
[[1,1],[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2,2] => 10
[[3],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => 10
[[3],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => 10
[[3],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1] => 10
[[3],[2],[2],[2],[1]] => [3,2,2,2,1] => 10
[[3],[3],[1],[1],[1],[1]] => [3,3,1,1,1,1] => 10
[[3],[3],[2],[1],[1]] => [3,3,2,1,1] => 10
[[3],[3],[2],[2]] => [3,3,2,2] => 10
[[3],[3],[3],[1]] => [3,3,3,1] => 10
[[2,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => 10
[[2,1],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => 10
[[2,1],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1] => 10
[[2,1],[2],[2],[2],[1]] => [3,2,2,2,1] => 10
[[2,1],[1,1],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => 10
[[2,1],[1,1],[1,1],[1],[1],[1]] => [3,2,2,1,1,1] => 10
[[2,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => 10
[[2,1],[2,1],[1],[1],[1],[1]] => [3,3,1,1,1,1] => 10
[[2,1],[2,1],[2],[1],[1]] => [3,3,2,1,1] => 10
[[2,1],[2,1],[2],[2]] => [3,3,2,2] => 10
[[2,1],[2,1],[1,1],[1],[1]] => [3,3,2,1,1] => 10
[[2,1],[2,1],[1,1],[1,1]] => [3,3,2,2] => 10
[[2,1],[2,1],[2,1],[1]] => [3,3,3,1] => 10
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => 10
[[1,1,1],[1,1],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => 10
[[1,1,1],[1,1],[1,1],[1],[1],[1]] => [3,2,2,1,1,1] => 10
[[1,1,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => 10
[[1,1,1],[1,1,1],[1],[1],[1],[1]] => [3,3,1,1,1,1] => 10
[[1,1,1],[1,1,1],[1,1],[1],[1]] => [3,3,2,1,1] => 10
[[1,1,1],[1,1,1],[1,1],[1,1]] => [3,3,2,2] => 10
[[1,1,1],[1,1,1],[1,1,1],[1]] => [3,3,3,1] => 10
[[4],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => 10
[[4],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 10
[[4],[2],[2],[1],[1]] => [4,2,2,1,1] => 10
[[4],[2],[2],[2]] => [4,2,2,2] => 10
[[4],[3],[1],[1],[1]] => [4,3,1,1,1] => 10
[[4],[3],[2],[1]] => [4,3,2,1] => 10
[[4],[3],[3]] => [4,3,3] => 10
[[4],[4],[1],[1]] => [4,4,1,1] => 10
[[4],[4],[2]] => [4,4,2] => 10
[[3,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => 10
[[3,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 10
[[3,1],[2],[2],[1],[1]] => [4,2,2,1,1] => 10
[[3,1],[2],[2],[2]] => [4,2,2,2] => 10
[[3,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 10
[[3,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => 10
[[3,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => 10
[[3,1],[3],[1],[1],[1]] => [4,3,1,1,1] => 10
[[3,1],[3],[2],[1]] => [4,3,2,1] => 10
[[3,1],[3],[3]] => [4,3,3] => 10
[[3,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => 10
[[3,1],[2,1],[2],[1]] => [4,3,2,1] => 10
[[3,1],[2,1],[1,1],[1]] => [4,3,2,1] => 10
[[3,1],[2,1],[2,1]] => [4,3,3] => 10
[[3,1],[3,1],[1],[1]] => [4,4,1,1] => 10
[[3,1],[3,1],[2]] => [4,4,2] => 10
[[3,1],[3,1],[1,1]] => [4,4,2] => 10
[[2,2],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => 10
[[2,2],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 10
[[2,2],[2],[2],[1],[1]] => [4,2,2,1,1] => 10
[[2,2],[2],[2],[2]] => [4,2,2,2] => 10
[[2,2],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 10
[[2,2],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => 10
[[2,2],[1,1],[1,1],[1,1]] => [4,2,2,2] => 10
[[2,2],[2,1],[1],[1],[1]] => [4,3,1,1,1] => 10
[[2,2],[2,1],[2],[1]] => [4,3,2,1] => 10
[[2,2],[2,1],[1,1],[1]] => [4,3,2,1] => 10
[[2,2],[2,1],[2,1]] => [4,3,3] => 10
[[2,2],[2,2],[1],[1]] => [4,4,1,1] => 10
[[2,2],[2,2],[2]] => [4,4,2] => 10
[[2,2],[2,2],[1,1]] => [4,4,2] => 10
[[2,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => 10
[[2,1,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 10
[[2,1,1],[2],[2],[1],[1]] => [4,2,2,1,1] => 10
[[2,1,1],[2],[2],[2]] => [4,2,2,2] => 10
[[2,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 10
[[2,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => 10
[[2,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => 10
[[2,1,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => 10
[[2,1,1],[2,1],[2],[1]] => [4,3,2,1] => 10
[[2,1,1],[2,1],[1,1],[1]] => [4,3,2,1] => 10
[[2,1,1],[2,1],[2,1]] => [4,3,3] => 10
[[2,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => 10
[[2,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => 10
[[2,1,1],[1,1,1],[1,1,1]] => [4,3,3] => 10
[[2,1,1],[2,1,1],[1],[1]] => [4,4,1,1] => 10
[[2,1,1],[2,1,1],[2]] => [4,4,2] => 10
[[2,1,1],[2,1,1],[1,1]] => [4,4,2] => 10
[[1,1,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => 10
[[1,1,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 10
[[1,1,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => 10
[[1,1,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => 10
[[1,1,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => 10
[[1,1,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => 10
[[1,1,1,1],[1,1,1],[1,1,1]] => [4,3,3] => 10
[[1,1,1,1],[1,1,1,1],[1],[1]] => [4,4,1,1] => 10
[[1,1,1,1],[1,1,1,1],[1,1]] => [4,4,2] => 10
[[5],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 10
[[5],[2],[1],[1],[1]] => [5,2,1,1,1] => 10
[[5],[2],[2],[1]] => [5,2,2,1] => 10
[[5],[3],[1],[1]] => [5,3,1,1] => 10
[[5],[3],[2]] => [5,3,2] => 10
[[5],[4],[1]] => [5,4,1] => 10
[[5],[5]] => [5,5] => 10
[[4,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 10
[[4,1],[2],[1],[1],[1]] => [5,2,1,1,1] => 10
[[4,1],[2],[2],[1]] => [5,2,2,1] => 10
[[4,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 10
[[4,1],[1,1],[1,1],[1]] => [5,2,2,1] => 10
[[4,1],[3],[1],[1]] => [5,3,1,1] => 10
[[4,1],[3],[2]] => [5,3,2] => 10
[[4,1],[2,1],[1],[1]] => [5,3,1,1] => 10
[[4,1],[2,1],[2]] => [5,3,2] => 10
[[4,1],[2,1],[1,1]] => [5,3,2] => 10
[[4,1],[4],[1]] => [5,4,1] => 10
[[4,1],[3,1],[1]] => [5,4,1] => 10
[[4,1],[4,1]] => [5,5] => 10
[[3,2],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 10
[[3,2],[2],[1],[1],[1]] => [5,2,1,1,1] => 10
[[3,2],[2],[2],[1]] => [5,2,2,1] => 10
[[3,2],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 10
[[3,2],[1,1],[1,1],[1]] => [5,2,2,1] => 10
[[3,2],[3],[1],[1]] => [5,3,1,1] => 10
[[3,2],[3],[2]] => [5,3,2] => 10
[[3,2],[2,1],[1],[1]] => [5,3,1,1] => 10
[[3,2],[2,1],[2]] => [5,3,2] => 10
[[3,2],[2,1],[1,1]] => [5,3,2] => 10
[[3,2],[3,1],[1]] => [5,4,1] => 10
[[3,2],[2,2],[1]] => [5,4,1] => 10
[[3,2],[3,2]] => [5,5] => 10
[[3,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 10
[[3,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => 10
[[3,1,1],[2],[2],[1]] => [5,2,2,1] => 10
[[3,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 10
[[3,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => 10
[[3,1,1],[3],[1],[1]] => [5,3,1,1] => 10
[[3,1,1],[3],[2]] => [5,3,2] => 10
[[3,1,1],[2,1],[1],[1]] => [5,3,1,1] => 10
[[3,1,1],[2,1],[2]] => [5,3,2] => 10
[[3,1,1],[2,1],[1,1]] => [5,3,2] => 10
[[3,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => 10
[[3,1,1],[1,1,1],[1,1]] => [5,3,2] => 10
[[3,1,1],[3,1],[1]] => [5,4,1] => 10
[[3,1,1],[2,1,1],[1]] => [5,4,1] => 10
[[3,1,1],[3,1,1]] => [5,5] => 10
[[2,2,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 10
[[2,2,1],[2],[1],[1],[1]] => [5,2,1,1,1] => 10
[[2,2,1],[2],[2],[1]] => [5,2,2,1] => 10
[[2,2,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 10
[[2,2,1],[1,1],[1,1],[1]] => [5,2,2,1] => 10
[[2,2,1],[2,1],[1],[1]] => [5,3,1,1] => 10
[[2,2,1],[2,1],[2]] => [5,3,2] => 10
[[2,2,1],[2,1],[1,1]] => [5,3,2] => 10
[[2,2,1],[1,1,1],[1],[1]] => [5,3,1,1] => 10
[[2,2,1],[1,1,1],[1,1]] => [5,3,2] => 10
[[2,2,1],[2,2],[1]] => [5,4,1] => 10
[[2,2,1],[2,1,1],[1]] => [5,4,1] => 10
[[2,2,1],[2,2,1]] => [5,5] => 10
[[2,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 10
[[2,1,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => 10
[[2,1,1,1],[2],[2],[1]] => [5,2,2,1] => 10
[[2,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 10
[[2,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => 10
[[2,1,1,1],[2,1],[1],[1]] => [5,3,1,1] => 10
[[2,1,1,1],[2,1],[2]] => [5,3,2] => 10
[[2,1,1,1],[2,1],[1,1]] => [5,3,2] => 10
[[2,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => 10
[[2,1,1,1],[1,1,1],[1,1]] => [5,3,2] => 10
[[2,1,1,1],[2,1,1],[1]] => [5,4,1] => 10
[[2,1,1,1],[1,1,1,1],[1]] => [5,4,1] => 10
[[2,1,1,1],[2,1,1,1]] => [5,5] => 10
[[1,1,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 10
[[1,1,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 10
[[1,1,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => 10
[[1,1,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => 10
[[1,1,1,1,1],[1,1,1],[1,1]] => [5,3,2] => 10
[[1,1,1,1,1],[1,1,1,1],[1]] => [5,4,1] => 10
[[1,1,1,1,1],[1,1,1,1,1]] => [5,5] => 10
[[6],[1],[1],[1],[1]] => [6,1,1,1,1] => 10
[[6],[2],[1],[1]] => [6,2,1,1] => 10
[[6],[2],[2]] => [6,2,2] => 10
[[6],[3],[1]] => [6,3,1] => 10
[[6],[4]] => [6,4] => 10
[[5,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 10
[[5,1],[2],[1],[1]] => [6,2,1,1] => 10
[[5,1],[2],[2]] => [6,2,2] => 10
[[5,1],[1,1],[1],[1]] => [6,2,1,1] => 10
[[5,1],[1,1],[1,1]] => [6,2,2] => 10
[[5,1],[3],[1]] => [6,3,1] => 10
[[5,1],[2,1],[1]] => [6,3,1] => 10
[[5,1],[4]] => [6,4] => 10
[[5,1],[3,1]] => [6,4] => 10
[[4,2],[1],[1],[1],[1]] => [6,1,1,1,1] => 10
[[4,2],[2],[1],[1]] => [6,2,1,1] => 10
[[4,2],[2],[2]] => [6,2,2] => 10
[[4,2],[1,1],[1],[1]] => [6,2,1,1] => 10
[[4,2],[1,1],[1,1]] => [6,2,2] => 10
[[4,2],[3],[1]] => [6,3,1] => 10
[[4,2],[2,1],[1]] => [6,3,1] => 10
[[4,2],[4]] => [6,4] => 10
[[4,2],[3,1]] => [6,4] => 10
[[4,2],[2,2]] => [6,4] => 10
[[4,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 10
[[4,1,1],[2],[1],[1]] => [6,2,1,1] => 10
[[4,1,1],[2],[2]] => [6,2,2] => 10
[[4,1,1],[1,1],[1],[1]] => [6,2,1,1] => 10
[[4,1,1],[1,1],[1,1]] => [6,2,2] => 10
[[4,1,1],[3],[1]] => [6,3,1] => 10
[[4,1,1],[2,1],[1]] => [6,3,1] => 10
[[4,1,1],[1,1,1],[1]] => [6,3,1] => 10
[[4,1,1],[4]] => [6,4] => 10
[[4,1,1],[3,1]] => [6,4] => 10
[[4,1,1],[2,1,1]] => [6,4] => 10
[[3,3],[1],[1],[1],[1]] => [6,1,1,1,1] => 10
[[3,3],[2],[1],[1]] => [6,2,1,1] => 10
[[3,3],[2],[2]] => [6,2,2] => 10
[[3,3],[1,1],[1],[1]] => [6,2,1,1] => 10
[[3,3],[1,1],[1,1]] => [6,2,2] => 10
[[3,3],[3],[1]] => [6,3,1] => 10
[[3,3],[2,1],[1]] => [6,3,1] => 10
[[3,3],[3,1]] => [6,4] => 10
[[3,3],[2,2]] => [6,4] => 10
[[3,2,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 10
[[3,2,1],[2],[1],[1]] => [6,2,1,1] => 10
[[3,2,1],[2],[2]] => [6,2,2] => 10
[[3,2,1],[1,1],[1],[1]] => [6,2,1,1] => 10
[[3,2,1],[1,1],[1,1]] => [6,2,2] => 10
[[3,2,1],[3],[1]] => [6,3,1] => 10
[[3,2,1],[2,1],[1]] => [6,3,1] => 10
[[3,2,1],[1,1,1],[1]] => [6,3,1] => 10
[[3,2,1],[3,1]] => [6,4] => 10
[[3,2,1],[2,2]] => [6,4] => 10
[[3,2,1],[2,1,1]] => [6,4] => 10
[[3,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 10
[[3,1,1,1],[2],[1],[1]] => [6,2,1,1] => 10
[[3,1,1,1],[2],[2]] => [6,2,2] => 10
[[3,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => 10
[[3,1,1,1],[1,1],[1,1]] => [6,2,2] => 10
[[3,1,1,1],[3],[1]] => [6,3,1] => 10
[[3,1,1,1],[2,1],[1]] => [6,3,1] => 10
[[3,1,1,1],[1,1,1],[1]] => [6,3,1] => 10
[[3,1,1,1],[3,1]] => [6,4] => 10
[[3,1,1,1],[2,1,1]] => [6,4] => 10
[[3,1,1,1],[1,1,1,1]] => [6,4] => 10
[[2,2,2],[1],[1],[1],[1]] => [6,1,1,1,1] => 10
[[2,2,2],[2],[1],[1]] => [6,2,1,1] => 10
[[2,2,2],[2],[2]] => [6,2,2] => 10
[[2,2,2],[1,1],[1],[1]] => [6,2,1,1] => 10
[[2,2,2],[1,1],[1,1]] => [6,2,2] => 10
[[2,2,2],[2,1],[1]] => [6,3,1] => 10
[[2,2,2],[1,1,1],[1]] => [6,3,1] => 10
[[2,2,2],[2,2]] => [6,4] => 10
[[2,2,2],[2,1,1]] => [6,4] => 10
[[2,2,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 10
[[2,2,1,1],[2],[1],[1]] => [6,2,1,1] => 10
[[2,2,1,1],[2],[2]] => [6,2,2] => 10
[[2,2,1,1],[1,1],[1],[1]] => [6,2,1,1] => 10
[[2,2,1,1],[1,1],[1,1]] => [6,2,2] => 10
[[2,2,1,1],[2,1],[1]] => [6,3,1] => 10
[[2,2,1,1],[1,1,1],[1]] => [6,3,1] => 10
[[2,2,1,1],[2,2]] => [6,4] => 10
[[2,2,1,1],[2,1,1]] => [6,4] => 10
[[2,2,1,1],[1,1,1,1]] => [6,4] => 10
[[2,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 10
[[2,1,1,1,1],[2],[1],[1]] => [6,2,1,1] => 10
[[2,1,1,1,1],[2],[2]] => [6,2,2] => 10
[[2,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => 10
[[2,1,1,1,1],[1,1],[1,1]] => [6,2,2] => 10
[[2,1,1,1,1],[2,1],[1]] => [6,3,1] => 10
[[2,1,1,1,1],[1,1,1],[1]] => [6,3,1] => 10
[[2,1,1,1,1],[2,1,1]] => [6,4] => 10
[[2,1,1,1,1],[1,1,1,1]] => [6,4] => 10
[[1,1,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 10
[[1,1,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => 10
[[1,1,1,1,1,1],[1,1],[1,1]] => [6,2,2] => 10
[[1,1,1,1,1,1],[1,1,1],[1]] => [6,3,1] => 10
[[1,1,1,1,1,1],[1,1,1,1]] => [6,4] => 10
[[7],[1],[1],[1]] => [7,1,1,1] => 10
[[7],[2],[1]] => [7,2,1] => 10
[[7],[3]] => [7,3] => 10
[[6,1],[1],[1],[1]] => [7,1,1,1] => 10
[[6,1],[2],[1]] => [7,2,1] => 10
[[6,1],[1,1],[1]] => [7,2,1] => 10
[[6,1],[3]] => [7,3] => 10
[[6,1],[2,1]] => [7,3] => 10
[[5,2],[1],[1],[1]] => [7,1,1,1] => 10
[[5,2],[2],[1]] => [7,2,1] => 10
[[5,2],[1,1],[1]] => [7,2,1] => 10
[[5,2],[3]] => [7,3] => 10
[[5,2],[2,1]] => [7,3] => 10
[[5,1,1],[1],[1],[1]] => [7,1,1,1] => 10
[[5,1,1],[2],[1]] => [7,2,1] => 10
[[5,1,1],[1,1],[1]] => [7,2,1] => 10
[[5,1,1],[3]] => [7,3] => 10
[[5,1,1],[2,1]] => [7,3] => 10
[[5,1,1],[1,1,1]] => [7,3] => 10
[[4,3],[1],[1],[1]] => [7,1,1,1] => 10
[[4,3],[2],[1]] => [7,2,1] => 10
[[4,3],[1,1],[1]] => [7,2,1] => 10
[[4,3],[3]] => [7,3] => 10
[[4,3],[2,1]] => [7,3] => 10
[[4,2,1],[1],[1],[1]] => [7,1,1,1] => 10
[[4,2,1],[2],[1]] => [7,2,1] => 10
[[4,2,1],[1,1],[1]] => [7,2,1] => 10
[[4,2,1],[3]] => [7,3] => 10
[[4,2,1],[2,1]] => [7,3] => 10
[[4,2,1],[1,1,1]] => [7,3] => 10
[[4,1,1,1],[1],[1],[1]] => [7,1,1,1] => 10
[[4,1,1,1],[2],[1]] => [7,2,1] => 10
[[4,1,1,1],[1,1],[1]] => [7,2,1] => 10
[[4,1,1,1],[3]] => [7,3] => 10
[[4,1,1,1],[2,1]] => [7,3] => 10
[[4,1,1,1],[1,1,1]] => [7,3] => 10
[[3,3,1],[1],[1],[1]] => [7,1,1,1] => 10
[[3,3,1],[2],[1]] => [7,2,1] => 10
[[3,3,1],[1,1],[1]] => [7,2,1] => 10
[[3,3,1],[3]] => [7,3] => 10
[[3,3,1],[2,1]] => [7,3] => 10
[[3,3,1],[1,1,1]] => [7,3] => 10
[[3,2,2],[1],[1],[1]] => [7,1,1,1] => 10
[[3,2,2],[2],[1]] => [7,2,1] => 10
[[3,2,2],[1,1],[1]] => [7,2,1] => 10
[[3,2,2],[3]] => [7,3] => 10
[[3,2,2],[2,1]] => [7,3] => 10
[[3,2,2],[1,1,1]] => [7,3] => 10
[[3,2,1,1],[1],[1],[1]] => [7,1,1,1] => 10
[[3,2,1,1],[2],[1]] => [7,2,1] => 10
[[3,2,1,1],[1,1],[1]] => [7,2,1] => 10
[[3,2,1,1],[3]] => [7,3] => 10
[[3,2,1,1],[2,1]] => [7,3] => 10
[[3,2,1,1],[1,1,1]] => [7,3] => 10
[[3,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => 10
[[3,1,1,1,1],[2],[1]] => [7,2,1] => 10
[[3,1,1,1,1],[1,1],[1]] => [7,2,1] => 10
[[3,1,1,1,1],[3]] => [7,3] => 10
[[3,1,1,1,1],[2,1]] => [7,3] => 10
[[3,1,1,1,1],[1,1,1]] => [7,3] => 10
[[2,2,2,1],[1],[1],[1]] => [7,1,1,1] => 10
[[2,2,2,1],[2],[1]] => [7,2,1] => 10
[[2,2,2,1],[1,1],[1]] => [7,2,1] => 10
[[2,2,2,1],[2,1]] => [7,3] => 10
[[2,2,2,1],[1,1,1]] => [7,3] => 10
[[2,2,1,1,1],[1],[1],[1]] => [7,1,1,1] => 10
[[2,2,1,1,1],[2],[1]] => [7,2,1] => 10
[[2,2,1,1,1],[1,1],[1]] => [7,2,1] => 10
[[2,2,1,1,1],[2,1]] => [7,3] => 10
[[2,2,1,1,1],[1,1,1]] => [7,3] => 10
[[2,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => 10
[[2,1,1,1,1,1],[2],[1]] => [7,2,1] => 10
[[2,1,1,1,1,1],[1,1],[1]] => [7,2,1] => 10
[[2,1,1,1,1,1],[2,1]] => [7,3] => 10
[[2,1,1,1,1,1],[1,1,1]] => [7,3] => 10
[[1,1,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => 10
[[1,1,1,1,1,1,1],[1,1],[1]] => [7,2,1] => 10
[[1,1,1,1,1,1,1],[1,1,1]] => [7,3] => 10
[[8],[1],[1]] => [8,1,1] => 10
[[8],[2]] => [8,2] => 10
[[7,1],[1],[1]] => [8,1,1] => 10
[[7,1],[2]] => [8,2] => 10
[[7,1],[1,1]] => [8,2] => 10
[[6,2],[1],[1]] => [8,1,1] => 10
[[6,2],[2]] => [8,2] => 10
[[6,2],[1,1]] => [8,2] => 10
[[6,1,1],[1],[1]] => [8,1,1] => 10
[[6,1,1],[2]] => [8,2] => 10
[[6,1,1],[1,1]] => [8,2] => 10
[[5,3],[1],[1]] => [8,1,1] => 10
[[5,3],[2]] => [8,2] => 10
[[5,3],[1,1]] => [8,2] => 10
[[5,2,1],[1],[1]] => [8,1,1] => 10
[[5,2,1],[2]] => [8,2] => 10
[[5,2,1],[1,1]] => [8,2] => 10
[[5,1,1,1],[1],[1]] => [8,1,1] => 10
[[5,1,1,1],[2]] => [8,2] => 10
[[5,1,1,1],[1,1]] => [8,2] => 10
[[4,4],[1],[1]] => [8,1,1] => 10
[[4,4],[2]] => [8,2] => 10
[[4,4],[1,1]] => [8,2] => 10
[[4,3,1],[1],[1]] => [8,1,1] => 10
[[4,3,1],[2]] => [8,2] => 10
[[4,3,1],[1,1]] => [8,2] => 10
[[4,2,2],[1],[1]] => [8,1,1] => 10
[[4,2,2],[2]] => [8,2] => 10
[[4,2,2],[1,1]] => [8,2] => 10
[[4,2,1,1],[1],[1]] => [8,1,1] => 10
[[4,2,1,1],[2]] => [8,2] => 10
[[4,2,1,1],[1,1]] => [8,2] => 10
[[4,1,1,1,1],[1],[1]] => [8,1,1] => 10
[[4,1,1,1,1],[2]] => [8,2] => 10
[[4,1,1,1,1],[1,1]] => [8,2] => 10
[[3,3,2],[1],[1]] => [8,1,1] => 10
[[3,3,2],[2]] => [8,2] => 10
[[3,3,2],[1,1]] => [8,2] => 10
[[3,3,1,1],[1],[1]] => [8,1,1] => 10
[[3,3,1,1],[2]] => [8,2] => 10
[[3,3,1,1],[1,1]] => [8,2] => 10
[[3,2,2,1],[1],[1]] => [8,1,1] => 10
[[3,2,2,1],[2]] => [8,2] => 10
[[3,2,2,1],[1,1]] => [8,2] => 10
[[3,2,1,1,1],[1],[1]] => [8,1,1] => 10
[[3,2,1,1,1],[2]] => [8,2] => 10
[[3,2,1,1,1],[1,1]] => [8,2] => 10
[[3,1,1,1,1,1],[1],[1]] => [8,1,1] => 10
[[3,1,1,1,1,1],[2]] => [8,2] => 10
[[3,1,1,1,1,1],[1,1]] => [8,2] => 10
[[2,2,2,2],[1],[1]] => [8,1,1] => 10
[[2,2,2,2],[2]] => [8,2] => 10
[[2,2,2,2],[1,1]] => [8,2] => 10
[[2,2,2,1,1],[1],[1]] => [8,1,1] => 10
[[2,2,2,1,1],[2]] => [8,2] => 10
[[2,2,2,1,1],[1,1]] => [8,2] => 10
[[2,2,1,1,1,1],[1],[1]] => [8,1,1] => 10
[[2,2,1,1,1,1],[2]] => [8,2] => 10
[[2,2,1,1,1,1],[1,1]] => [8,2] => 10
[[2,1,1,1,1,1,1],[1],[1]] => [8,1,1] => 10
[[2,1,1,1,1,1,1],[2]] => [8,2] => 10
[[2,1,1,1,1,1,1],[1,1]] => [8,2] => 10
[[1,1,1,1,1,1,1,1],[1],[1]] => [8,1,1] => 10
[[1,1,1,1,1,1,1,1],[1,1]] => [8,2] => 10
[[9],[1]] => [9,1] => 10
[[8,1],[1]] => [9,1] => 10
[[7,2],[1]] => [9,1] => 10
[[7,1,1],[1]] => [9,1] => 10
[[6,3],[1]] => [9,1] => 10
[[6,2,1],[1]] => [9,1] => 10
[[6,1,1,1],[1]] => [9,1] => 10
[[5,4],[1]] => [9,1] => 10
[[5,3,1],[1]] => [9,1] => 10
[[5,2,2],[1]] => [9,1] => 10
[[5,2,1,1],[1]] => [9,1] => 10
[[5,1,1,1,1],[1]] => [9,1] => 10
[[4,4,1],[1]] => [9,1] => 10
[[4,3,2],[1]] => [9,1] => 10
[[4,3,1,1],[1]] => [9,1] => 10
[[4,2,2,1],[1]] => [9,1] => 10
[[4,2,1,1,1],[1]] => [9,1] => 10
[[4,1,1,1,1,1],[1]] => [9,1] => 10
[[3,3,3],[1]] => [9,1] => 10
[[3,3,2,1],[1]] => [9,1] => 10
[[3,3,1,1,1],[1]] => [9,1] => 10
[[3,2,2,2],[1]] => [9,1] => 10
[[3,2,2,1,1],[1]] => [9,1] => 10
[[3,2,1,1,1,1],[1]] => [9,1] => 10
[[3,1,1,1,1,1,1],[1]] => [9,1] => 10
[[2,2,2,2,1],[1]] => [9,1] => 10
[[2,2,2,1,1,1],[1]] => [9,1] => 10
[[2,2,1,1,1,1,1],[1]] => [9,1] => 10
[[2,1,1,1,1,1,1,1],[1]] => [9,1] => 10
[[1,1,1,1,1,1,1,1,1],[1]] => [9,1] => 10
[[10]] => [10] => 10
[[9,1]] => [10] => 10
[[8,2]] => [10] => 10
[[8,1,1]] => [10] => 10
[[7,3]] => [10] => 10
[[7,2,1]] => [10] => 10
[[7,1,1,1]] => [10] => 10
[[6,4]] => [10] => 10
[[6,3,1]] => [10] => 10
[[6,2,2]] => [10] => 10
[[6,2,1,1]] => [10] => 10
[[6,1,1,1,1]] => [10] => 10
[[5,5]] => [10] => 10
[[5,4,1]] => [10] => 10
[[5,3,2]] => [10] => 10
[[5,3,1,1]] => [10] => 10
[[5,2,2,1]] => [10] => 10
[[5,2,1,1,1]] => [10] => 10
[[5,1,1,1,1,1]] => [10] => 10
[[4,4,2]] => [10] => 10
[[4,4,1,1]] => [10] => 10
[[4,3,3]] => [10] => 10
[[4,3,2,1]] => [10] => 10
[[4,3,1,1,1]] => [10] => 10
[[4,2,2,2]] => [10] => 10
[[4,2,2,1,1]] => [10] => 10
[[4,2,1,1,1,1]] => [10] => 10
[[4,1,1,1,1,1,1]] => [10] => 10
[[3,3,3,1]] => [10] => 10
[[3,3,2,2]] => [10] => 10
[[3,3,2,1,1]] => [10] => 10
[[3,3,1,1,1,1]] => [10] => 10
[[3,2,2,2,1]] => [10] => 10
[[3,2,2,1,1,1]] => [10] => 10
[[3,2,1,1,1,1,1]] => [10] => 10
[[3,1,1,1,1,1,1,1]] => [10] => 10
[[2,2,2,2,2]] => [10] => 10
[[2,2,2,2,1,1]] => [10] => 10
[[2,2,2,1,1,1,1]] => [10] => 10
[[2,2,1,1,1,1,1,1]] => [10] => 10
[[2,1,1,1,1,1,1,1,1]] => [10] => 10
[[1,1,1,1,1,1,1,1,1,1]] => [10] => 10
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
$F_{1} = q$
$F_{2} = 3\ q^{2}$
$F_{3} = 6\ q^{3}$
$F_{4} = 13\ q^{4}$
$F_{5} = 24\ q^{5}$
$F_{6} = 48\ q^{6}$
$F_{7} = 86\ q^{7}$
$F_{8} = 160\ q^{8}$
$F_{9} = 282\ q^{9}$
$F_{10} = 500\ q^{10}$
Description
The size of a partition.
This statistic is the constant statistic of the level sets.
This statistic is the constant statistic of the level sets.
Map
to partition
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.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!