Identifier
-
Mp00189:
Skew partitions
—rotate⟶
Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St000228: Integer partitions ⟶ ℤ
Values
[[1],[]] => [[1],[]] => [] => 0
[[2],[]] => [[2],[]] => [] => 0
[[1,1],[]] => [[1,1],[]] => [] => 0
[[2,1],[1]] => [[2,1],[1]] => [1] => 1
[[3],[]] => [[3],[]] => [] => 0
[[2,1],[]] => [[2,2],[1]] => [1] => 1
[[3,1],[1]] => [[3,2],[2]] => [2] => 2
[[2,2],[1]] => [[2,1],[]] => [] => 0
[[3,2],[2]] => [[3,1],[1]] => [1] => 1
[[1,1,1],[]] => [[1,1,1],[]] => [] => 0
[[2,2,1],[1,1]] => [[2,1,1],[1]] => [1] => 1
[[2,1,1],[1]] => [[2,2,1],[1,1]] => [1,1] => 2
[[3,2,1],[2,1]] => [[3,2,1],[2,1]] => [2,1] => 3
[[4],[]] => [[4],[]] => [] => 0
[[3,1],[]] => [[3,3],[2]] => [2] => 2
[[4,1],[1]] => [[4,3],[3]] => [3] => 3
[[2,2],[]] => [[2,2],[]] => [] => 0
[[3,2],[1]] => [[3,2],[1]] => [1] => 1
[[4,2],[2]] => [[4,2],[2]] => [2] => 2
[[2,1,1],[]] => [[2,2,2],[1,1]] => [1,1] => 2
[[3,2,1],[1,1]] => [[3,2,2],[2,1]] => [2,1] => 3
[[3,1,1],[1]] => [[3,3,2],[2,2]] => [2,2] => 4
[[4,2,1],[2,1]] => [[4,3,2],[3,2]] => [3,2] => 5
[[3,3],[2]] => [[3,1],[]] => [] => 0
[[4,3],[3]] => [[4,1],[1]] => [1] => 1
[[2,2,1],[1]] => [[2,2,1],[1]] => [1] => 1
[[3,3,1],[2,1]] => [[3,2,1],[2]] => [2] => 2
[[3,2,1],[2]] => [[3,3,1],[2,1]] => [2,1] => 3
[[4,3,1],[3,1]] => [[4,3,1],[3,1]] => [3,1] => 4
[[2,2,2],[1,1]] => [[2,1,1],[]] => [] => 0
[[3,3,2],[2,2]] => [[3,1,1],[1]] => [1] => 1
[[3,2,2],[2,1]] => [[3,2,1],[1,1]] => [1,1] => 2
[[4,3,2],[3,2]] => [[4,2,1],[2,1]] => [2,1] => 3
[[1,1,1,1],[]] => [[1,1,1,1],[]] => [] => 0
[[2,2,2,1],[1,1,1]] => [[2,1,1,1],[1]] => [1] => 1
[[2,2,1,1],[1,1]] => [[2,2,1,1],[1,1]] => [1,1] => 2
[[3,3,2,1],[2,2,1]] => [[3,2,1,1],[2,1]] => [2,1] => 3
[[2,1,1,1],[1]] => [[2,2,2,1],[1,1,1]] => [1,1,1] => 3
[[3,2,2,1],[2,1,1]] => [[3,2,2,1],[2,1,1]] => [2,1,1] => 4
[[3,2,1,1],[2,1]] => [[3,3,2,1],[2,2,1]] => [2,2,1] => 5
[[4,3,2,1],[3,2,1]] => [[4,3,2,1],[3,2,1]] => [3,2,1] => 6
[[5],[]] => [[5],[]] => [] => 0
[[4,1],[]] => [[4,4],[3]] => [3] => 3
[[5,1],[1]] => [[5,4],[4]] => [4] => 4
[[3,2],[]] => [[3,3],[1]] => [1] => 1
[[4,2],[1]] => [[4,3],[2]] => [2] => 2
[[5,2],[2]] => [[5,3],[3]] => [3] => 3
[[3,1,1],[]] => [[3,3,3],[2,2]] => [2,2] => 4
[[4,2,1],[1,1]] => [[4,3,3],[3,2]] => [3,2] => 5
[[4,1,1],[1]] => [[4,4,3],[3,3]] => [3,3] => 6
[[5,2,1],[2,1]] => [[5,4,3],[4,3]] => [4,3] => 7
[[3,3],[1]] => [[3,2],[]] => [] => 0
[[4,3],[2]] => [[4,2],[1]] => [1] => 1
[[5,3],[3]] => [[5,2],[2]] => [2] => 2
[[2,2,1],[]] => [[2,2,2],[1]] => [1] => 1
[[3,3,1],[1,1]] => [[3,2,2],[2]] => [2] => 2
[[3,2,1],[1]] => [[3,3,2],[2,1]] => [2,1] => 3
[[4,3,1],[2,1]] => [[4,3,2],[3,1]] => [3,1] => 4
[[4,2,1],[2]] => [[4,4,2],[3,2]] => [3,2] => 5
[[5,3,1],[3,1]] => [[5,4,2],[4,2]] => [4,2] => 6
[[3,2,2],[1,1]] => [[3,2,2],[1,1]] => [1,1] => 2
[[4,3,2],[2,2]] => [[4,2,2],[2,1]] => [2,1] => 3
[[4,2,2],[2,1]] => [[4,3,2],[2,2]] => [2,2] => 4
[[5,3,2],[3,2]] => [[5,3,2],[3,2]] => [3,2] => 5
[[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 3
[[3,2,2,1],[1,1,1]] => [[3,2,2,2],[2,1,1]] => [2,1,1] => 4
[[3,2,1,1],[1,1]] => [[3,3,2,2],[2,2,1]] => [2,2,1] => 5
[[4,3,2,1],[2,2,1]] => [[4,3,2,2],[3,2,1]] => [3,2,1] => 6
[[3,1,1,1],[1]] => [[3,3,3,2],[2,2,2]] => [2,2,2] => 6
[[4,2,2,1],[2,1,1]] => [[4,3,3,2],[3,2,2]] => [3,2,2] => 7
[[4,2,1,1],[2,1]] => [[4,4,3,2],[3,3,2]] => [3,3,2] => 8
[[5,3,2,1],[3,2,1]] => [[5,4,3,2],[4,3,2]] => [4,3,2] => 9
[[4,4],[3]] => [[4,1],[]] => [] => 0
[[5,4],[4]] => [[5,1],[1]] => [1] => 1
[[3,3,1],[2]] => [[3,3,1],[2]] => [2] => 2
[[4,4,1],[3,1]] => [[4,3,1],[3]] => [3] => 3
[[4,3,1],[3]] => [[4,4,1],[3,1]] => [3,1] => 4
[[5,4,1],[4,1]] => [[5,4,1],[4,1]] => [4,1] => 5
[[2,2,2],[1]] => [[2,2,1],[]] => [] => 0
[[3,3,2],[2,1]] => [[3,2,1],[1]] => [1] => 1
[[4,4,2],[3,2]] => [[4,2,1],[2]] => [2] => 2
[[3,2,2],[2]] => [[3,3,1],[1,1]] => [1,1] => 2
[[4,3,2],[3,1]] => [[4,3,1],[2,1]] => [2,1] => 3
[[5,4,2],[4,2]] => [[5,3,1],[3,1]] => [3,1] => 4
[[2,2,1,1],[1]] => [[2,2,2,1],[1,1]] => [1,1] => 2
[[3,3,2,1],[2,1,1]] => [[3,2,2,1],[2,1]] => [2,1] => 3
[[3,3,1,1],[2,1]] => [[3,3,2,1],[2,2]] => [2,2] => 4
[[4,4,2,1],[3,2,1]] => [[4,3,2,1],[3,2]] => [3,2] => 5
[[3,2,1,1],[2]] => [[3,3,3,1],[2,2,1]] => [2,2,1] => 5
[[4,3,2,1],[3,1,1]] => [[4,3,3,1],[3,2,1]] => [3,2,1] => 6
[[4,3,1,1],[3,1]] => [[4,4,3,1],[3,3,1]] => [3,3,1] => 7
[[5,4,2,1],[4,2,1]] => [[5,4,3,1],[4,3,1]] => [4,3,1] => 8
[[3,3,3],[2,2]] => [[3,1,1],[]] => [] => 0
[[4,4,3],[3,3]] => [[4,1,1],[1]] => [1] => 1
[[4,3,3],[3,2]] => [[4,2,1],[1,1]] => [1,1] => 2
[[5,4,3],[4,3]] => [[5,2,1],[2,1]] => [2,1] => 3
[[2,2,2,1],[1,1]] => [[2,2,1,1],[1]] => [1] => 1
[[3,3,3,1],[2,2,1]] => [[3,2,1,1],[2]] => [2] => 2
[[3,3,2,1],[2,2]] => [[3,3,1,1],[2,1]] => [2,1] => 3
[[4,4,3,1],[3,3,1]] => [[4,3,1,1],[3,1]] => [3,1] => 4
[[3,2,2,1],[2,1]] => [[3,3,2,1],[2,1,1]] => [2,1,1] => 4
>>> Load all 1183 entries. <<<[[4,3,3,1],[3,2,1]] => [[4,3,2,1],[3,1,1]] => [3,1,1] => 5
[[4,3,2,1],[3,2]] => [[4,4,2,1],[3,2,1]] => [3,2,1] => 6
[[5,4,3,1],[4,3,1]] => [[5,4,2,1],[4,2,1]] => [4,2,1] => 7
[[2,2,2,2],[1,1,1]] => [[2,1,1,1],[]] => [] => 0
[[3,3,3,2],[2,2,2]] => [[3,1,1,1],[1]] => [1] => 1
[[3,3,2,2],[2,2,1]] => [[3,2,1,1],[1,1]] => [1,1] => 2
[[4,4,3,2],[3,3,2]] => [[4,2,1,1],[2,1]] => [2,1] => 3
[[3,2,2,2],[2,1,1]] => [[3,2,2,1],[1,1,1]] => [1,1,1] => 3
[[4,3,3,2],[3,2,2]] => [[4,2,2,1],[2,1,1]] => [2,1,1] => 4
[[4,3,2,2],[3,2,1]] => [[4,3,2,1],[2,2,1]] => [2,2,1] => 5
[[5,4,3,2],[4,3,2]] => [[5,3,2,1],[3,2,1]] => [3,2,1] => 6
[[1,1,1,1,1],[]] => [[1,1,1,1,1],[]] => [] => 0
[[2,2,2,2,1],[1,1,1,1]] => [[2,1,1,1,1],[1]] => [1] => 1
[[2,2,2,1,1],[1,1,1]] => [[2,2,1,1,1],[1,1]] => [1,1] => 2
[[3,3,3,2,1],[2,2,2,1]] => [[3,2,1,1,1],[2,1]] => [2,1] => 3
[[2,2,1,1,1],[1,1]] => [[2,2,2,1,1],[1,1,1]] => [1,1,1] => 3
[[3,3,2,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1,1]] => [2,1,1] => 4
[[3,3,2,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2,1]] => [2,2,1] => 5
[[4,4,3,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2,1]] => [3,2,1] => 6
[[2,1,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 4
[[3,2,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 5
[[3,2,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 6
[[4,3,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => 7
[[3,2,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 7
[[4,3,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => 8
[[4,3,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => 9
[[5,4,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => 10
[[6],[]] => [[6],[]] => [] => 0
[[5,1],[]] => [[5,5],[4]] => [4] => 4
[[6,1],[1]] => [[6,5],[5]] => [5] => 5
[[4,2],[]] => [[4,4],[2]] => [2] => 2
[[5,2],[1]] => [[5,4],[3]] => [3] => 3
[[6,2],[2]] => [[6,4],[4]] => [4] => 4
[[4,1,1],[]] => [[4,4,4],[3,3]] => [3,3] => 6
[[5,2,1],[1,1]] => [[5,4,4],[4,3]] => [4,3] => 7
[[5,1,1],[1]] => [[5,5,4],[4,4]] => [4,4] => 8
[[6,2,1],[2,1]] => [[6,5,4],[5,4]] => [5,4] => 9
[[3,3],[]] => [[3,3],[]] => [] => 0
[[4,3],[1]] => [[4,3],[1]] => [1] => 1
[[5,3],[2]] => [[5,3],[2]] => [2] => 2
[[6,3],[3]] => [[6,3],[3]] => [3] => 3
[[3,2,1],[]] => [[3,3,3],[2,1]] => [2,1] => 3
[[4,3,1],[1,1]] => [[4,3,3],[3,1]] => [3,1] => 4
[[4,2,1],[1]] => [[4,4,3],[3,2]] => [3,2] => 5
[[5,3,1],[2,1]] => [[5,4,3],[4,2]] => [4,2] => 6
[[5,2,1],[2]] => [[5,5,3],[4,3]] => [4,3] => 7
[[6,3,1],[3,1]] => [[6,5,3],[5,3]] => [5,3] => 8
[[4,2,2],[1,1]] => [[4,3,3],[2,2]] => [2,2] => 4
[[5,3,2],[2,2]] => [[5,3,3],[3,2]] => [3,2] => 5
[[5,2,2],[2,1]] => [[5,4,3],[3,3]] => [3,3] => 6
[[6,3,2],[3,2]] => [[6,4,3],[4,3]] => [4,3] => 7
[[3,1,1,1],[]] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 6
[[4,2,2,1],[1,1,1]] => [[4,3,3,3],[3,2,2]] => [3,2,2] => 7
[[4,2,1,1],[1,1]] => [[4,4,3,3],[3,3,2]] => [3,3,2] => 8
[[5,3,2,1],[2,2,1]] => [[5,4,3,3],[4,3,2]] => [4,3,2] => 9
[[4,1,1,1],[1]] => [[4,4,4,3],[3,3,3]] => [3,3,3] => 9
[[5,2,2,1],[2,1,1]] => [[5,4,4,3],[4,3,3]] => [4,3,3] => 10
[[4,4],[2]] => [[4,2],[]] => [] => 0
[[5,4],[3]] => [[5,2],[1]] => [1] => 1
[[6,4],[4]] => [[6,2],[2]] => [2] => 2
[[3,3,1],[1]] => [[3,3,2],[2]] => [2] => 2
[[4,4,1],[2,1]] => [[4,3,2],[3]] => [3] => 3
[[4,3,1],[2]] => [[4,4,2],[3,1]] => [3,1] => 4
[[5,4,1],[3,1]] => [[5,4,2],[4,1]] => [4,1] => 5
[[5,3,1],[3]] => [[5,5,2],[4,2]] => [4,2] => 6
[[6,4,1],[4,1]] => [[6,5,2],[5,2]] => [5,2] => 7
[[2,2,2],[]] => [[2,2,2],[]] => [] => 0
[[3,3,2],[1,1]] => [[3,2,2],[1]] => [1] => 1
[[4,4,2],[2,2]] => [[4,2,2],[2]] => [2] => 2
[[3,2,2],[1]] => [[3,3,2],[1,1]] => [1,1] => 2
[[4,3,2],[2,1]] => [[4,3,2],[2,1]] => [2,1] => 3
[[5,4,2],[3,2]] => [[5,3,2],[3,1]] => [3,1] => 4
[[4,2,2],[2]] => [[4,4,2],[2,2]] => [2,2] => 4
[[5,3,2],[3,1]] => [[5,4,2],[3,2]] => [3,2] => 5
[[6,4,2],[4,2]] => [[6,4,2],[4,2]] => [4,2] => 6
[[2,2,1,1],[]] => [[2,2,2,2],[1,1]] => [1,1] => 2
[[3,3,2,1],[1,1,1]] => [[3,2,2,2],[2,1]] => [2,1] => 3
[[3,3,1,1],[1,1]] => [[3,3,2,2],[2,2]] => [2,2] => 4
[[4,4,2,1],[2,2,1]] => [[4,3,2,2],[3,2]] => [3,2] => 5
[[3,2,1,1],[1]] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 5
[[4,3,2,1],[2,1,1]] => [[4,3,3,2],[3,2,1]] => [3,2,1] => 6
[[4,3,1,1],[2,1]] => [[4,4,3,2],[3,3,1]] => [3,3,1] => 7
[[5,4,2,1],[3,2,1]] => [[5,4,3,2],[4,3,1]] => [4,3,1] => 8
[[4,2,1,1],[2]] => [[4,4,4,2],[3,3,2]] => [3,3,2] => 8
[[5,3,2,1],[3,1,1]] => [[5,4,4,2],[4,3,2]] => [4,3,2] => 9
[[5,3,1,1],[3,1]] => [[5,5,4,2],[4,4,2]] => [4,4,2] => 10
[[4,3,3],[2,2]] => [[4,2,2],[1,1]] => [1,1] => 2
[[5,4,3],[3,3]] => [[5,2,2],[2,1]] => [2,1] => 3
[[5,3,3],[3,2]] => [[5,3,2],[2,2]] => [2,2] => 4
[[6,4,3],[4,3]] => [[6,3,2],[3,2]] => [3,2] => 5
[[3,2,2,1],[1,1]] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 4
[[4,3,3,1],[2,2,1]] => [[4,3,2,2],[3,1,1]] => [3,1,1] => 5
[[4,3,2,1],[2,2]] => [[4,4,2,2],[3,2,1]] => [3,2,1] => 6
[[5,4,3,1],[3,3,1]] => [[5,4,2,2],[4,2,1]] => [4,2,1] => 7
[[4,2,2,1],[2,1]] => [[4,4,3,2],[3,2,2]] => [3,2,2] => 7
[[5,3,3,1],[3,2,1]] => [[5,4,3,2],[4,2,2]] => [4,2,2] => 8
[[5,3,2,1],[3,2]] => [[5,5,3,2],[4,3,2]] => [4,3,2] => 9
[[6,4,3,1],[4,3,1]] => [[6,5,3,2],[5,3,2]] => [5,3,2] => 10
[[3,2,2,2],[1,1,1]] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 3
[[4,3,3,2],[2,2,2]] => [[4,2,2,2],[2,1,1]] => [2,1,1] => 4
[[4,3,2,2],[2,2,1]] => [[4,3,2,2],[2,2,1]] => [2,2,1] => 5
[[5,4,3,2],[3,3,2]] => [[5,3,2,2],[3,2,1]] => [3,2,1] => 6
[[4,2,2,2],[2,1,1]] => [[4,3,3,2],[2,2,2]] => [2,2,2] => 6
[[5,3,3,2],[3,2,2]] => [[5,3,3,2],[3,2,2]] => [3,2,2] => 7
[[5,3,2,2],[3,2,1]] => [[5,4,3,2],[3,3,2]] => [3,3,2] => 8
[[6,4,3,2],[4,3,2]] => [[6,4,3,2],[4,3,2]] => [4,3,2] => 9
[[2,1,1,1,1],[]] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 4
[[3,2,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1,1]] => [2,1,1,1] => 5
[[3,2,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1,1]] => [2,2,1,1] => 6
[[4,3,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1,1]] => [3,2,1,1] => 7
[[3,2,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2,1]] => [2,2,2,1] => 7
[[4,3,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2,1]] => [3,2,2,1] => 8
[[4,3,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2,1]] => [3,3,2,1] => 9
[[5,4,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2,1]] => [4,3,2,1] => 10
[[3,1,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,2]] => [2,2,2,2] => 8
[[4,2,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,2]] => [3,2,2,2] => 9
[[4,2,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,2]] => [3,3,2,2] => 10
[[5,5],[4]] => [[5,1],[]] => [] => 0
[[6,5],[5]] => [[6,1],[1]] => [1] => 1
[[4,4,1],[3]] => [[4,4,1],[3]] => [3] => 3
[[5,5,1],[4,1]] => [[5,4,1],[4]] => [4] => 4
[[5,4,1],[4]] => [[5,5,1],[4,1]] => [4,1] => 5
[[6,5,1],[5,1]] => [[6,5,1],[5,1]] => [5,1] => 6
[[3,3,2],[2]] => [[3,3,1],[1]] => [1] => 1
[[4,4,2],[3,1]] => [[4,3,1],[2]] => [2] => 2
[[5,5,2],[4,2]] => [[5,3,1],[3]] => [3] => 3
[[4,3,2],[3]] => [[4,4,1],[2,1]] => [2,1] => 3
[[5,4,2],[4,1]] => [[5,4,1],[3,1]] => [3,1] => 4
[[6,5,2],[5,2]] => [[6,4,1],[4,1]] => [4,1] => 5
[[3,3,1,1],[2]] => [[3,3,3,1],[2,2]] => [2,2] => 4
[[4,4,2,1],[3,1,1]] => [[4,3,3,1],[3,2]] => [3,2] => 5
[[4,4,1,1],[3,1]] => [[4,4,3,1],[3,3]] => [3,3] => 6
[[5,5,2,1],[4,2,1]] => [[5,4,3,1],[4,3]] => [4,3] => 7
[[4,3,1,1],[3]] => [[4,4,4,1],[3,3,1]] => [3,3,1] => 7
[[5,4,2,1],[4,1,1]] => [[5,4,4,1],[4,3,1]] => [4,3,1] => 8
[[5,4,1,1],[4,1]] => [[5,5,4,1],[4,4,1]] => [4,4,1] => 9
[[6,5,2,1],[5,2,1]] => [[6,5,4,1],[5,4,1]] => [5,4,1] => 10
[[3,3,3],[2,1]] => [[3,2,1],[]] => [] => 0
[[4,4,3],[3,2]] => [[4,2,1],[1]] => [1] => 1
[[5,5,3],[4,3]] => [[5,2,1],[2]] => [2] => 2
[[4,3,3],[3,1]] => [[4,3,1],[1,1]] => [1,1] => 2
[[5,4,3],[4,2]] => [[5,3,1],[2,1]] => [2,1] => 3
[[6,5,3],[5,3]] => [[6,3,1],[3,1]] => [3,1] => 4
[[2,2,2,1],[1]] => [[2,2,2,1],[1]] => [1] => 1
[[3,3,3,1],[2,1,1]] => [[3,2,2,1],[2]] => [2] => 2
[[3,3,2,1],[2,1]] => [[3,3,2,1],[2,1]] => [2,1] => 3
[[4,4,3,1],[3,2,1]] => [[4,3,2,1],[3,1]] => [3,1] => 4
[[4,4,2,1],[3,2]] => [[4,4,2,1],[3,2]] => [3,2] => 5
[[5,5,3,1],[4,3,1]] => [[5,4,2,1],[4,2]] => [4,2] => 6
[[3,2,2,1],[2]] => [[3,3,3,1],[2,1,1]] => [2,1,1] => 4
[[4,3,3,1],[3,1,1]] => [[4,3,3,1],[3,1,1]] => [3,1,1] => 5
[[4,3,2,1],[3,1]] => [[4,4,3,1],[3,2,1]] => [3,2,1] => 6
[[5,4,3,1],[4,2,1]] => [[5,4,3,1],[4,2,1]] => [4,2,1] => 7
[[5,4,2,1],[4,2]] => [[5,5,3,1],[4,3,1]] => [4,3,1] => 8
[[6,5,3,1],[5,3,1]] => [[6,5,3,1],[5,3,1]] => [5,3,1] => 9
[[3,3,2,2],[2,1,1]] => [[3,2,2,1],[1,1]] => [1,1] => 2
[[4,4,3,2],[3,2,2]] => [[4,2,2,1],[2,1]] => [2,1] => 3
[[4,4,2,2],[3,2,1]] => [[4,3,2,1],[2,2]] => [2,2] => 4
[[5,5,3,2],[4,3,2]] => [[5,3,2,1],[3,2]] => [3,2] => 5
[[4,3,2,2],[3,1,1]] => [[4,3,3,1],[2,2,1]] => [2,2,1] => 5
[[5,4,3,2],[4,2,2]] => [[5,3,3,1],[3,2,1]] => [3,2,1] => 6
[[5,4,2,2],[4,2,1]] => [[5,4,3,1],[3,3,1]] => [3,3,1] => 7
[[6,5,3,2],[5,3,2]] => [[6,4,3,1],[4,3,1]] => [4,3,1] => 8
[[2,2,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 3
[[3,3,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1]] => [2,1,1] => 4
[[3,3,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1]] => [2,2,1] => 5
[[4,4,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1]] => [3,2,1] => 6
[[3,3,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2]] => [2,2,2] => 6
[[4,4,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2]] => [3,2,2] => 7
[[4,4,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2]] => [3,3,2] => 8
[[5,5,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2]] => [4,3,2] => 9
[[3,2,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2,1]] => [2,2,2,1] => 7
[[4,3,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2,1]] => [3,2,2,1] => 8
[[4,3,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2,1]] => [3,3,2,1] => 9
[[5,4,3,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,2,1]] => [4,3,2,1] => 10
[[4,3,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3,1]] => [3,3,3,1] => 10
[[4,4,4],[3,3]] => [[4,1,1],[]] => [] => 0
[[5,5,4],[4,4]] => [[5,1,1],[1]] => [1] => 1
[[5,4,4],[4,3]] => [[5,2,1],[1,1]] => [1,1] => 2
[[6,5,4],[5,4]] => [[6,2,1],[2,1]] => [2,1] => 3
[[3,3,3,1],[2,2]] => [[3,3,1,1],[2]] => [2] => 2
[[4,4,4,1],[3,3,1]] => [[4,3,1,1],[3]] => [3] => 3
[[4,4,3,1],[3,3]] => [[4,4,1,1],[3,1]] => [3,1] => 4
[[5,5,4,1],[4,4,1]] => [[5,4,1,1],[4,1]] => [4,1] => 5
[[4,3,3,1],[3,2]] => [[4,4,2,1],[3,1,1]] => [3,1,1] => 5
[[5,4,4,1],[4,3,1]] => [[5,4,2,1],[4,1,1]] => [4,1,1] => 6
[[5,4,3,1],[4,3]] => [[5,5,2,1],[4,2,1]] => [4,2,1] => 7
[[6,5,4,1],[5,4,1]] => [[6,5,2,1],[5,2,1]] => [5,2,1] => 8
[[2,2,2,2],[1,1]] => [[2,2,1,1],[]] => [] => 0
[[3,3,3,2],[2,2,1]] => [[3,2,1,1],[1]] => [1] => 1
[[4,4,4,2],[3,3,2]] => [[4,2,1,1],[2]] => [2] => 2
[[3,3,2,2],[2,2]] => [[3,3,1,1],[1,1]] => [1,1] => 2
[[4,4,3,2],[3,3,1]] => [[4,3,1,1],[2,1]] => [2,1] => 3
[[5,5,4,2],[4,4,2]] => [[5,3,1,1],[3,1]] => [3,1] => 4
[[3,2,2,2],[2,1]] => [[3,3,2,1],[1,1,1]] => [1,1,1] => 3
[[4,3,3,2],[3,2,1]] => [[4,3,2,1],[2,1,1]] => [2,1,1] => 4
[[5,4,4,2],[4,3,2]] => [[5,3,2,1],[3,1,1]] => [3,1,1] => 5
[[4,3,2,2],[3,2]] => [[4,4,2,1],[2,2,1]] => [2,2,1] => 5
[[5,4,3,2],[4,3,1]] => [[5,4,2,1],[3,2,1]] => [3,2,1] => 6
[[6,5,4,2],[5,4,2]] => [[6,4,2,1],[4,2,1]] => [4,2,1] => 7
[[2,2,2,1,1],[1,1]] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[[3,3,3,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1]] => [2,1] => 3
[[3,3,3,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2]] => [2,2] => 4
[[4,4,4,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2]] => [3,2] => 5
[[3,3,2,1,1],[2,2]] => [[3,3,3,1,1],[2,2,1]] => [2,2,1] => 5
[[4,4,3,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2,1]] => [3,2,1] => 6
[[4,4,3,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3,1]] => [3,3,1] => 7
[[5,5,4,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3,1]] => [4,3,1] => 8
[[3,2,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1,1]] => [2,2,1,1] => 6
[[4,3,3,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,1,1]] => [3,2,1,1] => 7
[[4,3,3,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,1,1]] => [3,3,1,1] => 8
[[5,4,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1,1]] => [4,3,1,1] => 9
[[4,3,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2,1]] => [3,3,2,1] => 9
[[5,4,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2,1]] => [4,3,2,1] => 10
[[3,3,3,3],[2,2,2]] => [[3,1,1,1],[]] => [] => 0
[[4,4,4,3],[3,3,3]] => [[4,1,1,1],[1]] => [1] => 1
[[4,4,3,3],[3,3,2]] => [[4,2,1,1],[1,1]] => [1,1] => 2
[[5,5,4,3],[4,4,3]] => [[5,2,1,1],[2,1]] => [2,1] => 3
[[4,3,3,3],[3,2,2]] => [[4,2,2,1],[1,1,1]] => [1,1,1] => 3
[[5,4,4,3],[4,3,3]] => [[5,2,2,1],[2,1,1]] => [2,1,1] => 4
[[5,4,3,3],[4,3,2]] => [[5,3,2,1],[2,2,1]] => [2,2,1] => 5
[[6,5,4,3],[5,4,3]] => [[6,3,2,1],[3,2,1]] => [3,2,1] => 6
[[2,2,2,2,1],[1,1,1]] => [[2,2,1,1,1],[1]] => [1] => 1
[[3,3,3,3,1],[2,2,2,1]] => [[3,2,1,1,1],[2]] => [2] => 2
[[3,3,3,2,1],[2,2,2]] => [[3,3,1,1,1],[2,1]] => [2,1] => 3
[[4,4,4,3,1],[3,3,3,1]] => [[4,3,1,1,1],[3,1]] => [3,1] => 4
[[3,3,2,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1,1]] => [2,1,1] => 4
[[4,4,3,3,1],[3,3,2,1]] => [[4,3,2,1,1],[3,1,1]] => [3,1,1] => 5
[[4,4,3,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2,1]] => [3,2,1] => 6
[[5,5,4,3,1],[4,4,3,1]] => [[5,4,2,1,1],[4,2,1]] => [4,2,1] => 7
[[3,2,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1,1]] => [2,1,1,1] => 5
[[4,3,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1,1]] => [3,1,1,1] => 6
[[4,3,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1,1]] => [3,2,1,1] => 7
[[5,4,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1,1]] => [4,2,1,1] => 8
[[4,3,2,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,2,1]] => [3,2,2,1] => 8
[[5,4,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2,1]] => [4,2,2,1] => 9
[[5,4,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2,1]] => [4,3,2,1] => 10
[[2,2,2,2,2],[1,1,1,1]] => [[2,1,1,1,1],[]] => [] => 0
[[3,3,3,3,2],[2,2,2,2]] => [[3,1,1,1,1],[1]] => [1] => 1
[[3,3,3,2,2],[2,2,2,1]] => [[3,2,1,1,1],[1,1]] => [1,1] => 2
[[4,4,4,3,2],[3,3,3,2]] => [[4,2,1,1,1],[2,1]] => [2,1] => 3
[[3,3,2,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1,1]] => [1,1,1] => 3
[[4,4,3,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1,1]] => [2,1,1] => 4
[[4,4,3,2,2],[3,3,2,1]] => [[4,3,2,1,1],[2,2,1]] => [2,2,1] => 5
[[5,5,4,3,2],[4,4,3,2]] => [[5,3,2,1,1],[3,2,1]] => [3,2,1] => 6
[[3,2,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 4
[[4,3,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 5
[[4,3,3,2,2],[3,2,2,1]] => [[4,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 6
[[5,4,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => 7
[[4,3,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 7
[[5,4,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => 8
[[5,4,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => 9
[[6,5,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => 10
[[1,1,1,1,1,1],[]] => [[1,1,1,1,1,1],[]] => [] => 0
[[2,2,2,2,2,1],[1,1,1,1,1]] => [[2,1,1,1,1,1],[1]] => [1] => 1
[[2,2,2,2,1,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1,1]] => [1,1] => 2
[[3,3,3,3,2,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2,1]] => [2,1] => 3
[[2,2,2,1,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1,1]] => [1,1,1] => 3
[[3,3,3,2,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1,1]] => [2,1,1] => 4
[[3,3,3,2,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2,1]] => [2,2,1] => 5
[[4,4,4,3,2,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,2,1]] => [3,2,1] => 6
[[2,2,1,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => 4
[[3,3,2,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => 5
[[3,3,2,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1,1]] => [2,2,1,1] => 6
[[4,4,3,3,2,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => 7
[[3,3,2,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2,1]] => [2,2,2,1] => 7
[[4,4,3,2,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => 8
[[4,4,3,2,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,2,1]] => [3,3,2,1] => 9
[[5,5,4,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => 10
[[2,1,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => 5
[[3,2,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1] => 6
[[3,2,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1,1]] => [2,2,1,1,1] => 7
[[4,3,3,3,2,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1] => 8
[[3,2,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1,1]] => [2,2,2,1,1] => 8
[[4,3,3,2,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,2,1,1]] => [3,2,2,1,1] => 9
[[4,3,3,2,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,2,1,1]] => [3,3,2,1,1] => 10
[[3,2,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2,1]] => [2,2,2,2,1] => 9
[[4,3,2,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1] => 10
[[7],[]] => [[7],[]] => [] => 0
[[6,1],[]] => [[6,6],[5]] => [5] => 5
[[7,1],[1]] => [[7,6],[6]] => [6] => 6
[[5,2],[]] => [[5,5],[3]] => [3] => 3
[[6,2],[1]] => [[6,5],[4]] => [4] => 4
[[7,2],[2]] => [[7,5],[5]] => [5] => 5
[[5,1,1],[]] => [[5,5,5],[4,4]] => [4,4] => 8
[[6,2,1],[1,1]] => [[6,5,5],[5,4]] => [5,4] => 9
[[6,1,1],[1]] => [[6,6,5],[5,5]] => [5,5] => 10
[[4,3],[]] => [[4,4],[1]] => [1] => 1
[[5,3],[1]] => [[5,4],[2]] => [2] => 2
[[6,3],[2]] => [[6,4],[3]] => [3] => 3
[[7,3],[3]] => [[7,4],[4]] => [4] => 4
[[4,2,1],[]] => [[4,4,4],[3,2]] => [3,2] => 5
[[5,3,1],[1,1]] => [[5,4,4],[4,2]] => [4,2] => 6
[[5,2,1],[1]] => [[5,5,4],[4,3]] => [4,3] => 7
[[6,3,1],[2,1]] => [[6,5,4],[5,3]] => [5,3] => 8
[[6,2,1],[2]] => [[6,6,4],[5,4]] => [5,4] => 9
[[7,3,1],[3,1]] => [[7,6,4],[6,4]] => [6,4] => 10
[[5,2,2],[1,1]] => [[5,4,4],[3,3]] => [3,3] => 6
[[6,3,2],[2,2]] => [[6,4,4],[4,3]] => [4,3] => 7
[[6,2,2],[2,1]] => [[6,5,4],[4,4]] => [4,4] => 8
[[7,3,2],[3,2]] => [[7,5,4],[5,4]] => [5,4] => 9
[[4,1,1,1],[]] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 9
[[5,2,2,1],[1,1,1]] => [[5,4,4,4],[4,3,3]] => [4,3,3] => 10
[[4,4],[1]] => [[4,3],[]] => [] => 0
[[5,4],[2]] => [[5,3],[1]] => [1] => 1
[[6,4],[3]] => [[6,3],[2]] => [2] => 2
[[7,4],[4]] => [[7,3],[3]] => [3] => 3
[[3,3,1],[]] => [[3,3,3],[2]] => [2] => 2
[[4,4,1],[1,1]] => [[4,3,3],[3]] => [3] => 3
[[4,3,1],[1]] => [[4,4,3],[3,1]] => [3,1] => 4
[[5,4,1],[2,1]] => [[5,4,3],[4,1]] => [4,1] => 5
[[5,3,1],[2]] => [[5,5,3],[4,2]] => [4,2] => 6
[[6,4,1],[3,1]] => [[6,5,3],[5,2]] => [5,2] => 7
[[6,3,1],[3]] => [[6,6,3],[5,3]] => [5,3] => 8
[[7,4,1],[4,1]] => [[7,6,3],[6,3]] => [6,3] => 9
[[3,2,2],[]] => [[3,3,3],[1,1]] => [1,1] => 2
[[4,3,2],[1,1]] => [[4,3,3],[2,1]] => [2,1] => 3
[[5,4,2],[2,2]] => [[5,3,3],[3,1]] => [3,1] => 4
[[4,2,2],[1]] => [[4,4,3],[2,2]] => [2,2] => 4
[[5,3,2],[2,1]] => [[5,4,3],[3,2]] => [3,2] => 5
[[6,4,2],[3,2]] => [[6,4,3],[4,2]] => [4,2] => 6
[[5,2,2],[2]] => [[5,5,3],[3,3]] => [3,3] => 6
[[6,3,2],[3,1]] => [[6,5,3],[4,3]] => [4,3] => 7
[[7,4,2],[4,2]] => [[7,5,3],[5,3]] => [5,3] => 8
[[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]] => [2,2,1] => 5
[[4,3,2,1],[1,1,1]] => [[4,3,3,3],[3,2,1]] => [3,2,1] => 6
[[4,3,1,1],[1,1]] => [[4,4,3,3],[3,3,1]] => [3,3,1] => 7
[[5,4,2,1],[2,2,1]] => [[5,4,3,3],[4,3,1]] => [4,3,1] => 8
[[4,2,1,1],[1]] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 8
[[5,3,2,1],[2,1,1]] => [[5,4,4,3],[4,3,2]] => [4,3,2] => 9
[[5,3,1,1],[2,1]] => [[5,5,4,3],[4,4,2]] => [4,4,2] => 10
[[5,3,3],[2,2]] => [[5,3,3],[2,2]] => [2,2] => 4
[[6,4,3],[3,3]] => [[6,3,3],[3,2]] => [3,2] => 5
[[6,3,3],[3,2]] => [[6,4,3],[3,3]] => [3,3] => 6
[[7,4,3],[4,3]] => [[7,4,3],[4,3]] => [4,3] => 7
[[4,2,2,1],[1,1]] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 7
[[5,3,3,1],[2,2,1]] => [[5,4,3,3],[4,2,2]] => [4,2,2] => 8
[[5,3,2,1],[2,2]] => [[5,5,3,3],[4,3,2]] => [4,3,2] => 9
[[6,4,3,1],[3,3,1]] => [[6,5,3,3],[5,3,2]] => [5,3,2] => 10
[[5,2,2,1],[2,1]] => [[5,5,4,3],[4,3,3]] => [4,3,3] => 10
[[4,2,2,2],[1,1,1]] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 6
[[5,3,3,2],[2,2,2]] => [[5,3,3,3],[3,2,2]] => [3,2,2] => 7
[[5,3,2,2],[2,2,1]] => [[5,4,3,3],[3,3,2]] => [3,3,2] => 8
[[6,4,3,2],[3,3,2]] => [[6,4,3,3],[4,3,2]] => [4,3,2] => 9
[[5,2,2,2],[2,1,1]] => [[5,4,4,3],[3,3,3]] => [3,3,3] => 9
[[6,3,3,2],[3,2,2]] => [[6,4,4,3],[4,3,3]] => [4,3,3] => 10
[[3,1,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 8
[[4,2,2,2,1],[1,1,1,1]] => [[4,3,3,3,3],[3,2,2,2]] => [3,2,2,2] => 9
[[4,2,2,1,1],[1,1,1]] => [[4,4,3,3,3],[3,3,2,2]] => [3,3,2,2] => 10
[[5,5],[3]] => [[5,2],[]] => [] => 0
[[6,5],[4]] => [[6,2],[1]] => [1] => 1
[[7,5],[5]] => [[7,2],[2]] => [2] => 2
[[4,4,1],[2]] => [[4,4,2],[3]] => [3] => 3
[[5,5,1],[3,1]] => [[5,4,2],[4]] => [4] => 4
[[5,4,1],[3]] => [[5,5,2],[4,1]] => [4,1] => 5
[[6,5,1],[4,1]] => [[6,5,2],[5,1]] => [5,1] => 6
[[6,4,1],[4]] => [[6,6,2],[5,2]] => [5,2] => 7
[[7,5,1],[5,1]] => [[7,6,2],[6,2]] => [6,2] => 8
[[3,3,2],[1]] => [[3,3,2],[1]] => [1] => 1
[[4,4,2],[2,1]] => [[4,3,2],[2]] => [2] => 2
[[5,5,2],[3,2]] => [[5,3,2],[3]] => [3] => 3
[[4,3,2],[2]] => [[4,4,2],[2,1]] => [2,1] => 3
[[5,4,2],[3,1]] => [[5,4,2],[3,1]] => [3,1] => 4
[[6,5,2],[4,2]] => [[6,4,2],[4,1]] => [4,1] => 5
[[5,3,2],[3]] => [[5,5,2],[3,2]] => [3,2] => 5
[[6,4,2],[4,1]] => [[6,5,2],[4,2]] => [4,2] => 6
[[7,5,2],[5,2]] => [[7,5,2],[5,2]] => [5,2] => 7
[[3,3,1,1],[1]] => [[3,3,3,2],[2,2]] => [2,2] => 4
[[4,4,2,1],[2,1,1]] => [[4,3,3,2],[3,2]] => [3,2] => 5
[[4,4,1,1],[2,1]] => [[4,4,3,2],[3,3]] => [3,3] => 6
[[5,5,2,1],[3,2,1]] => [[5,4,3,2],[4,3]] => [4,3] => 7
[[4,3,1,1],[2]] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 7
[[5,4,2,1],[3,1,1]] => [[5,4,4,2],[4,3,1]] => [4,3,1] => 8
[[5,4,1,1],[3,1]] => [[5,5,4,2],[4,4,1]] => [4,4,1] => 9
[[6,5,2,1],[4,2,1]] => [[6,5,4,2],[5,4,1]] => [5,4,1] => 10
[[5,3,1,1],[3]] => [[5,5,5,2],[4,4,2]] => [4,4,2] => 10
[[3,3,3],[1,1]] => [[3,2,2],[]] => [] => 0
[[4,4,3],[2,2]] => [[4,2,2],[1]] => [1] => 1
[[5,5,3],[3,3]] => [[5,2,2],[2]] => [2] => 2
[[4,3,3],[2,1]] => [[4,3,2],[1,1]] => [1,1] => 2
[[5,4,3],[3,2]] => [[5,3,2],[2,1]] => [2,1] => 3
[[6,5,3],[4,3]] => [[6,3,2],[3,1]] => [3,1] => 4
[[5,3,3],[3,1]] => [[5,4,2],[2,2]] => [2,2] => 4
[[6,4,3],[4,2]] => [[6,4,2],[3,2]] => [3,2] => 5
[[7,5,3],[5,3]] => [[7,4,2],[4,2]] => [4,2] => 6
[[2,2,2,1],[]] => [[2,2,2,2],[1]] => [1] => 1
[[3,3,3,1],[1,1,1]] => [[3,2,2,2],[2]] => [2] => 2
[[3,3,2,1],[1,1]] => [[3,3,2,2],[2,1]] => [2,1] => 3
[[4,4,3,1],[2,2,1]] => [[4,3,2,2],[3,1]] => [3,1] => 4
[[4,4,2,1],[2,2]] => [[4,4,2,2],[3,2]] => [3,2] => 5
[[5,5,3,1],[3,3,1]] => [[5,4,2,2],[4,2]] => [4,2] => 6
[[3,2,2,1],[1]] => [[3,3,3,2],[2,1,1]] => [2,1,1] => 4
[[4,3,3,1],[2,1,1]] => [[4,3,3,2],[3,1,1]] => [3,1,1] => 5
[[4,3,2,1],[2,1]] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[[5,4,3,1],[3,2,1]] => [[5,4,3,2],[4,2,1]] => [4,2,1] => 7
[[5,4,2,1],[3,2]] => [[5,5,3,2],[4,3,1]] => [4,3,1] => 8
[[6,5,3,1],[4,3,1]] => [[6,5,3,2],[5,3,1]] => [5,3,1] => 9
[[4,2,2,1],[2]] => [[4,4,4,2],[3,2,2]] => [3,2,2] => 7
[[5,3,3,1],[3,1,1]] => [[5,4,4,2],[4,2,2]] => [4,2,2] => 8
[[5,3,2,1],[3,1]] => [[5,5,4,2],[4,3,2]] => [4,3,2] => 9
[[6,4,3,1],[4,2,1]] => [[6,5,4,2],[5,3,2]] => [5,3,2] => 10
[[3,3,2,2],[1,1,1]] => [[3,2,2,2],[1,1]] => [1,1] => 2
[[4,4,3,2],[2,2,2]] => [[4,2,2,2],[2,1]] => [2,1] => 3
[[4,4,2,2],[2,2,1]] => [[4,3,2,2],[2,2]] => [2,2] => 4
[[5,5,3,2],[3,3,2]] => [[5,3,2,2],[3,2]] => [3,2] => 5
[[4,3,2,2],[2,1,1]] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 5
[[5,4,3,2],[3,2,2]] => [[5,3,3,2],[3,2,1]] => [3,2,1] => 6
[[5,4,2,2],[3,2,1]] => [[5,4,3,2],[3,3,1]] => [3,3,1] => 7
[[6,5,3,2],[4,3,2]] => [[6,4,3,2],[4,3,1]] => [4,3,1] => 8
[[5,3,2,2],[3,1,1]] => [[5,4,4,2],[3,3,2]] => [3,3,2] => 8
[[6,4,3,2],[4,2,2]] => [[6,4,4,2],[4,3,2]] => [4,3,2] => 9
[[6,4,2,2],[4,2,1]] => [[6,5,4,2],[4,4,2]] => [4,4,2] => 10
[[2,2,1,1,1],[]] => [[2,2,2,2,2],[1,1,1]] => [1,1,1] => 3
[[3,3,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1]] => [2,1,1] => 4
[[3,3,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1]] => [2,2,1] => 5
[[4,4,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1]] => [3,2,1] => 6
[[3,3,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2]] => [2,2,2] => 6
[[4,4,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2]] => [3,2,2] => 7
[[4,4,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2]] => [3,3,2] => 8
[[5,5,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2]] => [4,3,2] => 9
[[3,2,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 7
[[4,3,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,1]] => [3,2,2,1] => 8
[[4,3,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,1]] => [3,3,2,1] => 9
[[5,4,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,1]] => [4,3,2,1] => 10
[[4,3,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,1]] => [3,3,3,1] => 10
[[5,4,4],[3,3]] => [[5,2,2],[1,1]] => [1,1] => 2
[[6,5,4],[4,4]] => [[6,2,2],[2,1]] => [2,1] => 3
[[6,4,4],[4,3]] => [[6,3,2],[2,2]] => [2,2] => 4
[[7,5,4],[5,4]] => [[7,3,2],[3,2]] => [3,2] => 5
[[4,3,3,1],[2,2]] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 5
[[5,4,4,1],[3,3,1]] => [[5,4,2,2],[4,1,1]] => [4,1,1] => 6
[[5,4,3,1],[3,3]] => [[5,5,2,2],[4,2,1]] => [4,2,1] => 7
[[6,5,4,1],[4,4,1]] => [[6,5,2,2],[5,2,1]] => [5,2,1] => 8
[[5,3,3,1],[3,2]] => [[5,5,3,2],[4,2,2]] => [4,2,2] => 8
[[6,4,4,1],[4,3,1]] => [[6,5,3,2],[5,2,2]] => [5,2,2] => 9
[[6,4,3,1],[4,3]] => [[6,6,3,2],[5,3,2]] => [5,3,2] => 10
[[3,2,2,2],[1,1]] => [[3,3,2,2],[1,1,1]] => [1,1,1] => 3
[[4,3,3,2],[2,2,1]] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 4
[[5,4,4,2],[3,3,2]] => [[5,3,2,2],[3,1,1]] => [3,1,1] => 5
[[4,3,2,2],[2,2]] => [[4,4,2,2],[2,2,1]] => [2,2,1] => 5
[[5,4,3,2],[3,3,1]] => [[5,4,2,2],[3,2,1]] => [3,2,1] => 6
[[6,5,4,2],[4,4,2]] => [[6,4,2,2],[4,2,1]] => [4,2,1] => 7
[[4,2,2,2],[2,1]] => [[4,4,3,2],[2,2,2]] => [2,2,2] => 6
[[5,3,3,2],[3,2,1]] => [[5,4,3,2],[3,2,2]] => [3,2,2] => 7
[[6,4,4,2],[4,3,2]] => [[6,4,3,2],[4,2,2]] => [4,2,2] => 8
[[5,3,2,2],[3,2]] => [[5,5,3,2],[3,3,2]] => [3,3,2] => 8
[[6,4,3,2],[4,3,1]] => [[6,5,3,2],[4,3,2]] => [4,3,2] => 9
[[7,5,4,2],[5,4,2]] => [[7,5,3,2],[5,3,2]] => [5,3,2] => 10
[[3,2,2,1,1],[1,1]] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 6
[[4,3,3,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,1,1]] => [3,2,1,1] => 7
[[4,3,3,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,1,1]] => [3,3,1,1] => 8
[[5,4,4,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,1,1]] => [4,3,1,1] => 9
[[4,3,2,1,1],[2,2]] => [[4,4,4,2,2],[3,3,2,1]] => [3,3,2,1] => 9
[[5,4,3,2,1],[3,3,1,1]] => [[5,4,4,2,2],[4,3,2,1]] => [4,3,2,1] => 10
[[4,2,2,1,1],[2,1]] => [[4,4,4,3,2],[3,3,2,2]] => [3,3,2,2] => 10
[[4,3,3,3],[2,2,2]] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 3
[[5,4,4,3],[3,3,3]] => [[5,2,2,2],[2,1,1]] => [2,1,1] => 4
[[5,4,3,3],[3,3,2]] => [[5,3,2,2],[2,2,1]] => [2,2,1] => 5
[[6,5,4,3],[4,4,3]] => [[6,3,2,2],[3,2,1]] => [3,2,1] => 6
[[5,3,3,3],[3,2,2]] => [[5,3,3,2],[2,2,2]] => [2,2,2] => 6
[[6,4,4,3],[4,3,3]] => [[6,3,3,2],[3,2,2]] => [3,2,2] => 7
[[6,4,3,3],[4,3,2]] => [[6,4,3,2],[3,3,2]] => [3,3,2] => 8
[[7,5,4,3],[5,4,3]] => [[7,4,3,2],[4,3,2]] => [4,3,2] => 9
[[3,2,2,2,1],[1,1,1]] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 5
[[4,3,3,3,1],[2,2,2,1]] => [[4,3,2,2,2],[3,1,1,1]] => [3,1,1,1] => 6
[[4,3,3,2,1],[2,2,2]] => [[4,4,2,2,2],[3,2,1,1]] => [3,2,1,1] => 7
[[5,4,4,3,1],[3,3,3,1]] => [[5,4,2,2,2],[4,2,1,1]] => [4,2,1,1] => 8
[[4,3,2,2,1],[2,2,1]] => [[4,4,3,2,2],[3,2,2,1]] => [3,2,2,1] => 8
[[5,4,3,3,1],[3,3,2,1]] => [[5,4,3,2,2],[4,2,2,1]] => [4,2,2,1] => 9
[[5,4,3,2,1],[3,3,2]] => [[5,5,3,2,2],[4,3,2,1]] => [4,3,2,1] => 10
[[4,2,2,2,1],[2,1,1]] => [[4,4,3,3,2],[3,2,2,2]] => [3,2,2,2] => 9
[[5,3,3,3,1],[3,2,2,1]] => [[5,4,3,3,2],[4,2,2,2]] => [4,2,2,2] => 10
[[3,2,2,2,2],[1,1,1,1]] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 4
[[4,3,3,3,2],[2,2,2,2]] => [[4,2,2,2,2],[2,1,1,1]] => [2,1,1,1] => 5
[[4,3,3,2,2],[2,2,2,1]] => [[4,3,2,2,2],[2,2,1,1]] => [2,2,1,1] => 6
[[5,4,4,3,2],[3,3,3,2]] => [[5,3,2,2,2],[3,2,1,1]] => [3,2,1,1] => 7
[[4,3,2,2,2],[2,2,1,1]] => [[4,3,3,2,2],[2,2,2,1]] => [2,2,2,1] => 7
[[5,4,3,3,2],[3,3,2,2]] => [[5,3,3,2,2],[3,2,2,1]] => [3,2,2,1] => 8
[[5,4,3,2,2],[3,3,2,1]] => [[5,4,3,2,2],[3,3,2,1]] => [3,3,2,1] => 9
[[6,5,4,3,2],[4,4,3,2]] => [[6,4,3,2,2],[4,3,2,1]] => [4,3,2,1] => 10
[[4,2,2,2,2],[2,1,1,1]] => [[4,3,3,3,2],[2,2,2,2]] => [2,2,2,2] => 8
[[5,3,3,3,2],[3,2,2,2]] => [[5,3,3,3,2],[3,2,2,2]] => [3,2,2,2] => 9
[[5,3,3,2,2],[3,2,2,1]] => [[5,4,3,3,2],[3,3,2,2]] => [3,3,2,2] => 10
[[2,1,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 5
[[3,2,2,2,2,1],[1,1,1,1,1]] => [[3,2,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 6
[[3,2,2,2,1,1],[1,1,1,1]] => [[3,3,2,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 7
[[4,3,3,3,2,1],[2,2,2,2,1]] => [[4,3,2,2,2,2],[3,2,1,1,1]] => [3,2,1,1,1] => 8
[[3,2,2,1,1,1],[1,1,1]] => [[3,3,3,2,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 8
[[4,3,3,2,2,1],[2,2,2,1,1]] => [[4,3,3,2,2,2],[3,2,2,1,1]] => [3,2,2,1,1] => 9
[[4,3,3,2,1,1],[2,2,2,1]] => [[4,4,3,2,2,2],[3,3,2,1,1]] => [3,3,2,1,1] => 10
[[3,2,1,1,1,1],[1,1]] => [[3,3,3,3,2,2],[2,2,2,2,1]] => [2,2,2,2,1] => 9
[[4,3,2,2,2,1],[2,2,1,1,1]] => [[4,3,3,3,2,2],[3,2,2,2,1]] => [3,2,2,2,1] => 10
[[3,1,1,1,1,1],[1]] => [[3,3,3,3,3,2],[2,2,2,2,2]] => [2,2,2,2,2] => 10
[[6,6],[5]] => [[6,1],[]] => [] => 0
[[7,6],[6]] => [[7,1],[1]] => [1] => 1
[[5,5,1],[4]] => [[5,5,1],[4]] => [4] => 4
[[6,6,1],[5,1]] => [[6,5,1],[5]] => [5] => 5
[[6,5,1],[5]] => [[6,6,1],[5,1]] => [5,1] => 6
[[7,6,1],[6,1]] => [[7,6,1],[6,1]] => [6,1] => 7
[[4,4,2],[3]] => [[4,4,1],[2]] => [2] => 2
[[5,5,2],[4,1]] => [[5,4,1],[3]] => [3] => 3
[[6,6,2],[5,2]] => [[6,4,1],[4]] => [4] => 4
[[5,4,2],[4]] => [[5,5,1],[3,1]] => [3,1] => 4
[[6,5,2],[5,1]] => [[6,5,1],[4,1]] => [4,1] => 5
[[7,6,2],[6,2]] => [[7,5,1],[5,1]] => [5,1] => 6
[[4,4,1,1],[3]] => [[4,4,4,1],[3,3]] => [3,3] => 6
[[5,5,2,1],[4,1,1]] => [[5,4,4,1],[4,3]] => [4,3] => 7
[[5,5,1,1],[4,1]] => [[5,5,4,1],[4,4]] => [4,4] => 8
[[6,6,2,1],[5,2,1]] => [[6,5,4,1],[5,4]] => [5,4] => 9
[[5,4,1,1],[4]] => [[5,5,5,1],[4,4,1]] => [4,4,1] => 9
[[6,5,2,1],[5,1,1]] => [[6,5,5,1],[5,4,1]] => [5,4,1] => 10
[[3,3,3],[2]] => [[3,3,1],[]] => [] => 0
[[4,4,3],[3,1]] => [[4,3,1],[1]] => [1] => 1
[[5,5,3],[4,2]] => [[5,3,1],[2]] => [2] => 2
[[6,6,3],[5,3]] => [[6,3,1],[3]] => [3] => 3
[[4,3,3],[3]] => [[4,4,1],[1,1]] => [1,1] => 2
[[5,4,3],[4,1]] => [[5,4,1],[2,1]] => [2,1] => 3
[[6,5,3],[5,2]] => [[6,4,1],[3,1]] => [3,1] => 4
[[7,6,3],[6,3]] => [[7,4,1],[4,1]] => [4,1] => 5
[[3,3,2,1],[2]] => [[3,3,3,1],[2,1]] => [2,1] => 3
[[4,4,3,1],[3,1,1]] => [[4,3,3,1],[3,1]] => [3,1] => 4
[[4,4,2,1],[3,1]] => [[4,4,3,1],[3,2]] => [3,2] => 5
[[5,5,3,1],[4,2,1]] => [[5,4,3,1],[4,2]] => [4,2] => 6
[[5,5,2,1],[4,2]] => [[5,5,3,1],[4,3]] => [4,3] => 7
[[6,6,3,1],[5,3,1]] => [[6,5,3,1],[5,3]] => [5,3] => 8
[[4,3,2,1],[3]] => [[4,4,4,1],[3,2,1]] => [3,2,1] => 6
[[5,4,3,1],[4,1,1]] => [[5,4,4,1],[4,2,1]] => [4,2,1] => 7
[[5,4,2,1],[4,1]] => [[5,5,4,1],[4,3,1]] => [4,3,1] => 8
[[6,5,3,1],[5,2,1]] => [[6,5,4,1],[5,3,1]] => [5,3,1] => 9
[[6,5,2,1],[5,2]] => [[6,6,4,1],[5,4,1]] => [5,4,1] => 10
[[4,4,2,2],[3,1,1]] => [[4,3,3,1],[2,2]] => [2,2] => 4
[[5,5,3,2],[4,2,2]] => [[5,3,3,1],[3,2]] => [3,2] => 5
[[5,5,2,2],[4,2,1]] => [[5,4,3,1],[3,3]] => [3,3] => 6
[[6,6,3,2],[5,3,2]] => [[6,4,3,1],[4,3]] => [4,3] => 7
[[5,4,2,2],[4,1,1]] => [[5,4,4,1],[3,3,1]] => [3,3,1] => 7
[[6,5,3,2],[5,2,2]] => [[6,4,4,1],[4,3,1]] => [4,3,1] => 8
[[6,5,2,2],[5,2,1]] => [[6,5,4,1],[4,4,1]] => [4,4,1] => 9
[[7,6,3,2],[6,3,2]] => [[7,5,4,1],[5,4,1]] => [5,4,1] => 10
[[3,3,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 6
[[4,4,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2]] => [3,2,2] => 7
[[4,4,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2]] => [3,3,2] => 8
[[5,5,3,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,2]] => [4,3,2] => 9
[[4,4,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3]] => [3,3,3] => 9
[[5,5,2,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,3]] => [4,3,3] => 10
[[4,3,1,1,1],[3]] => [[4,4,4,4,1],[3,3,3,1]] => [3,3,3,1] => 10
[[4,4,4],[3,2]] => [[4,2,1],[]] => [] => 0
[[5,5,4],[4,3]] => [[5,2,1],[1]] => [1] => 1
[[6,6,4],[5,4]] => [[6,2,1],[2]] => [2] => 2
[[5,4,4],[4,2]] => [[5,3,1],[1,1]] => [1,1] => 2
[[6,5,4],[5,3]] => [[6,3,1],[2,1]] => [2,1] => 3
[[7,6,4],[6,4]] => [[7,3,1],[3,1]] => [3,1] => 4
[[3,3,3,1],[2,1]] => [[3,3,2,1],[2]] => [2] => 2
[[4,4,4,1],[3,2,1]] => [[4,3,2,1],[3]] => [3] => 3
[[4,4,3,1],[3,2]] => [[4,4,2,1],[3,1]] => [3,1] => 4
[[5,5,4,1],[4,3,1]] => [[5,4,2,1],[4,1]] => [4,1] => 5
[[5,5,3,1],[4,3]] => [[5,5,2,1],[4,2]] => [4,2] => 6
[[6,6,4,1],[5,4,1]] => [[6,5,2,1],[5,2]] => [5,2] => 7
[[4,3,3,1],[3,1]] => [[4,4,3,1],[3,1,1]] => [3,1,1] => 5
[[5,4,4,1],[4,2,1]] => [[5,4,3,1],[4,1,1]] => [4,1,1] => 6
[[5,4,3,1],[4,2]] => [[5,5,3,1],[4,2,1]] => [4,2,1] => 7
[[6,5,4,1],[5,3,1]] => [[6,5,3,1],[5,2,1]] => [5,2,1] => 8
[[6,5,3,1],[5,3]] => [[6,6,3,1],[5,3,1]] => [5,3,1] => 9
[[7,6,4,1],[6,4,1]] => [[7,6,3,1],[6,3,1]] => [6,3,1] => 10
[[2,2,2,2],[1]] => [[2,2,2,1],[]] => [] => 0
[[3,3,3,2],[2,1,1]] => [[3,2,2,1],[1]] => [1] => 1
[[4,4,4,2],[3,2,2]] => [[4,2,2,1],[2]] => [2] => 2
[[3,3,2,2],[2,1]] => [[3,3,2,1],[1,1]] => [1,1] => 2
[[4,4,3,2],[3,2,1]] => [[4,3,2,1],[2,1]] => [2,1] => 3
[[5,5,4,2],[4,3,2]] => [[5,3,2,1],[3,1]] => [3,1] => 4
[[4,4,2,2],[3,2]] => [[4,4,2,1],[2,2]] => [2,2] => 4
[[5,5,3,2],[4,3,1]] => [[5,4,2,1],[3,2]] => [3,2] => 5
[[6,6,4,2],[5,4,2]] => [[6,4,2,1],[4,2]] => [4,2] => 6
[[3,2,2,2],[2]] => [[3,3,3,1],[1,1,1]] => [1,1,1] => 3
[[4,3,3,2],[3,1,1]] => [[4,3,3,1],[2,1,1]] => [2,1,1] => 4
[[5,4,4,2],[4,2,2]] => [[5,3,3,1],[3,1,1]] => [3,1,1] => 5
[[4,3,2,2],[3,1]] => [[4,4,3,1],[2,2,1]] => [2,2,1] => 5
[[5,4,3,2],[4,2,1]] => [[5,4,3,1],[3,2,1]] => [3,2,1] => 6
[[6,5,4,2],[5,3,2]] => [[6,4,3,1],[4,2,1]] => [4,2,1] => 7
[[5,4,2,2],[4,2]] => [[5,5,3,1],[3,3,1]] => [3,3,1] => 7
[[6,5,3,2],[5,3,1]] => [[6,5,3,1],[4,3,1]] => [4,3,1] => 8
[[7,6,4,2],[6,4,2]] => [[7,5,3,1],[5,3,1]] => [5,3,1] => 9
[[2,2,2,1,1],[1]] => [[2,2,2,2,1],[1,1]] => [1,1] => 2
[[3,3,3,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1]] => [2,1] => 3
[[3,3,3,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2]] => [2,2] => 4
[[4,4,4,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2]] => [3,2] => 5
[[3,3,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 5
[[4,4,3,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,1]] => [3,2,1] => 6
[[4,4,3,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,1]] => [3,3,1] => 7
[[5,5,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1]] => [4,3,1] => 8
[[4,4,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2]] => [3,3,2] => 8
[[5,5,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2]] => [4,3,2] => 9
[[5,5,3,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,2]] => [4,4,2] => 10
[[3,2,2,1,1],[2]] => [[3,3,3,3,1],[2,2,1,1]] => [2,2,1,1] => 6
[[4,3,3,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,1,1]] => [3,2,1,1] => 7
[[4,3,3,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,1,1]] => [3,3,1,1] => 8
[[5,4,4,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,1,1]] => [4,3,1,1] => 9
[[4,3,2,1,1],[3,1]] => [[4,4,4,3,1],[3,3,2,1]] => [3,3,2,1] => 9
[[5,4,3,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,2,1]] => [4,3,2,1] => 10
[[4,4,3,3],[3,2,2]] => [[4,2,2,1],[1,1]] => [1,1] => 2
[[5,5,4,3],[4,3,3]] => [[5,2,2,1],[2,1]] => [2,1] => 3
[[5,5,3,3],[4,3,2]] => [[5,3,2,1],[2,2]] => [2,2] => 4
[[6,6,4,3],[5,4,3]] => [[6,3,2,1],[3,2]] => [3,2] => 5
[[5,4,3,3],[4,2,2]] => [[5,3,3,1],[2,2,1]] => [2,2,1] => 5
[[6,5,4,3],[5,3,3]] => [[6,3,3,1],[3,2,1]] => [3,2,1] => 6
[[6,5,3,3],[5,3,2]] => [[6,4,3,1],[3,3,1]] => [3,3,1] => 7
[[7,6,4,3],[6,4,3]] => [[7,4,3,1],[4,3,1]] => [4,3,1] => 8
[[3,3,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 4
[[4,4,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1]] => [3,1,1] => 5
[[4,4,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1]] => [3,2,1] => 6
[[5,5,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1]] => [4,2,1] => 7
[[4,4,2,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,2]] => [3,2,2] => 7
[[5,5,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2]] => [4,2,2] => 8
[[5,5,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2]] => [4,3,2] => 9
[[6,6,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2]] => [5,3,2] => 10
[[4,3,2,2,1],[3,1,1]] => [[4,4,3,3,1],[3,2,2,1]] => [3,2,2,1] => 8
[[5,4,3,3,1],[4,2,2,1]] => [[5,4,3,3,1],[4,2,2,1]] => [4,2,2,1] => 9
[[5,4,3,2,1],[4,2,2]] => [[5,5,3,3,1],[4,3,2,1]] => [4,3,2,1] => 10
[[3,3,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 3
[[4,4,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1]] => [2,1,1] => 4
[[4,4,3,2,2],[3,2,2,1]] => [[4,3,2,2,1],[2,2,1]] => [2,2,1] => 5
[[5,5,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1]] => [3,2,1] => 6
[[4,4,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2]] => [2,2,2] => 6
[[5,5,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2]] => [3,2,2] => 7
[[5,5,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2]] => [3,3,2] => 8
[[6,6,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2]] => [4,3,2] => 9
[[4,3,2,2,2],[3,1,1,1]] => [[4,3,3,3,1],[2,2,2,1]] => [2,2,2,1] => 7
[[5,4,3,3,2],[4,2,2,2]] => [[5,3,3,3,1],[3,2,2,1]] => [3,2,2,1] => 8
[[5,4,3,2,2],[4,2,2,1]] => [[5,4,3,3,1],[3,3,2,1]] => [3,3,2,1] => 9
[[6,5,4,3,2],[5,3,3,2]] => [[6,4,3,3,1],[4,3,2,1]] => [4,3,2,1] => 10
[[5,4,2,2,2],[4,2,1,1]] => [[5,4,4,3,1],[3,3,3,1]] => [3,3,3,1] => 10
[[2,2,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 4
[[3,3,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 5
[[3,3,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1]] => [2,2,1,1] => 6
[[4,4,3,3,2,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,2,1,1]] => [3,2,1,1] => 7
[[3,3,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1]] => [2,2,2,1] => 7
[[4,4,3,2,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,2,1]] => [3,2,2,1] => 8
[[4,4,3,2,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,2,1]] => [3,3,2,1] => 9
[[5,5,4,3,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1]] => [4,3,2,1] => 10
[[3,3,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2]] => [2,2,2,2] => 8
[[4,4,2,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,2]] => [3,2,2,2] => 9
[[4,4,2,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,2]] => [3,3,2,2] => 10
[[3,2,1,1,1,1],[2]] => [[3,3,3,3,3,1],[2,2,2,2,1]] => [2,2,2,2,1] => 9
[[4,3,2,2,2,1],[3,1,1,1,1]] => [[4,3,3,3,3,1],[3,2,2,2,1]] => [3,2,2,2,1] => 10
[[5,5,5],[4,4]] => [[5,1,1],[]] => [] => 0
[[6,6,5],[5,5]] => [[6,1,1],[1]] => [1] => 1
[[6,5,5],[5,4]] => [[6,2,1],[1,1]] => [1,1] => 2
[[7,6,5],[6,5]] => [[7,2,1],[2,1]] => [2,1] => 3
[[4,4,4,1],[3,3]] => [[4,4,1,1],[3]] => [3] => 3
[[5,5,5,1],[4,4,1]] => [[5,4,1,1],[4]] => [4] => 4
[[5,5,4,1],[4,4]] => [[5,5,1,1],[4,1]] => [4,1] => 5
[[6,6,5,1],[5,5,1]] => [[6,5,1,1],[5,1]] => [5,1] => 6
[[5,4,4,1],[4,3]] => [[5,5,2,1],[4,1,1]] => [4,1,1] => 6
[[6,5,5,1],[5,4,1]] => [[6,5,2,1],[5,1,1]] => [5,1,1] => 7
[[6,5,4,1],[5,4]] => [[6,6,2,1],[5,2,1]] => [5,2,1] => 8
[[7,6,5,1],[6,5,1]] => [[7,6,2,1],[6,2,1]] => [6,2,1] => 9
[[3,3,3,2],[2,2]] => [[3,3,1,1],[1]] => [1] => 1
[[4,4,4,2],[3,3,1]] => [[4,3,1,1],[2]] => [2] => 2
[[5,5,5,2],[4,4,2]] => [[5,3,1,1],[3]] => [3] => 3
[[4,4,3,2],[3,3]] => [[4,4,1,1],[2,1]] => [2,1] => 3
[[5,5,4,2],[4,4,1]] => [[5,4,1,1],[3,1]] => [3,1] => 4
[[6,6,5,2],[5,5,2]] => [[6,4,1,1],[4,1]] => [4,1] => 5
[[4,3,3,2],[3,2]] => [[4,4,2,1],[2,1,1]] => [2,1,1] => 4
[[5,4,4,2],[4,3,1]] => [[5,4,2,1],[3,1,1]] => [3,1,1] => 5
[[6,5,5,2],[5,4,2]] => [[6,4,2,1],[4,1,1]] => [4,1,1] => 6
[[5,4,3,2],[4,3]] => [[5,5,2,1],[3,2,1]] => [3,2,1] => 6
[[6,5,4,2],[5,4,1]] => [[6,5,2,1],[4,2,1]] => [4,2,1] => 7
[[7,6,5,2],[6,5,2]] => [[7,5,2,1],[5,2,1]] => [5,2,1] => 8
[[3,3,3,1,1],[2,2]] => [[3,3,3,1,1],[2,2]] => [2,2] => 4
[[4,4,4,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2]] => [3,2] => 5
[[4,4,4,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3]] => [3,3] => 6
[[5,5,5,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3]] => [4,3] => 7
[[4,4,3,1,1],[3,3]] => [[4,4,4,1,1],[3,3,1]] => [3,3,1] => 7
[[5,5,4,2,1],[4,4,1,1]] => [[5,4,4,1,1],[4,3,1]] => [4,3,1] => 8
[[5,5,4,1,1],[4,4,1]] => [[5,5,4,1,1],[4,4,1]] => [4,4,1] => 9
[[6,6,5,2,1],[5,5,2,1]] => [[6,5,4,1,1],[5,4,1]] => [5,4,1] => 10
[[4,3,3,1,1],[3,2]] => [[4,4,4,2,1],[3,3,1,1]] => [3,3,1,1] => 8
[[5,4,4,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,1,1]] => [4,3,1,1] => 9
[[5,4,4,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,1,1]] => [4,4,1,1] => 10
[[3,3,3,3],[2,2,1]] => [[3,2,1,1],[]] => [] => 0
[[4,4,4,3],[3,3,2]] => [[4,2,1,1],[1]] => [1] => 1
[[5,5,5,3],[4,4,3]] => [[5,2,1,1],[2]] => [2] => 2
[[4,4,3,3],[3,3,1]] => [[4,3,1,1],[1,1]] => [1,1] => 2
[[5,5,4,3],[4,4,2]] => [[5,3,1,1],[2,1]] => [2,1] => 3
[[6,6,5,3],[5,5,3]] => [[6,3,1,1],[3,1]] => [3,1] => 4
[[4,3,3,3],[3,2,1]] => [[4,3,2,1],[1,1,1]] => [1,1,1] => 3
[[5,4,4,3],[4,3,2]] => [[5,3,2,1],[2,1,1]] => [2,1,1] => 4
[[6,5,5,3],[5,4,3]] => [[6,3,2,1],[3,1,1]] => [3,1,1] => 5
[[5,4,3,3],[4,3,1]] => [[5,4,2,1],[2,2,1]] => [2,2,1] => 5
[[6,5,4,3],[5,4,2]] => [[6,4,2,1],[3,2,1]] => [3,2,1] => 6
[[7,6,5,3],[6,5,3]] => [[7,4,2,1],[4,2,1]] => [4,2,1] => 7
[[2,2,2,2,1],[1,1]] => [[2,2,2,1,1],[1]] => [1] => 1
[[3,3,3,3,1],[2,2,1,1]] => [[3,2,2,1,1],[2]] => [2] => 2
[[3,3,3,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1]] => [2,1] => 3
[[4,4,4,3,1],[3,3,2,1]] => [[4,3,2,1,1],[3,1]] => [3,1] => 4
[[4,4,4,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2]] => [3,2] => 5
[[5,5,5,3,1],[4,4,3,1]] => [[5,4,2,1,1],[4,2]] => [4,2] => 6
[[3,3,2,2,1],[2,2]] => [[3,3,3,1,1],[2,1,1]] => [2,1,1] => 4
[[4,4,3,3,1],[3,3,1,1]] => [[4,3,3,1,1],[3,1,1]] => [3,1,1] => 5
[[4,4,3,2,1],[3,3,1]] => [[4,4,3,1,1],[3,2,1]] => [3,2,1] => 6
[[5,5,4,3,1],[4,4,2,1]] => [[5,4,3,1,1],[4,2,1]] => [4,2,1] => 7
[[5,5,4,2,1],[4,4,2]] => [[5,5,3,1,1],[4,3,1]] => [4,3,1] => 8
[[6,6,5,3,1],[5,5,3,1]] => [[6,5,3,1,1],[5,3,1]] => [5,3,1] => 9
[[3,2,2,2,1],[2,1]] => [[3,3,3,2,1],[2,1,1,1]] => [2,1,1,1] => 5
[[4,3,3,3,1],[3,2,1,1]] => [[4,3,3,2,1],[3,1,1,1]] => [3,1,1,1] => 6
[[4,3,3,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,1,1]] => [3,2,1,1] => 7
[[5,4,4,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,1,1]] => [4,2,1,1] => 8
[[5,4,4,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,1,1]] => [4,3,1,1] => 9
[[6,5,5,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,1,1]] => [5,3,1,1] => 10
[[4,3,2,2,1],[3,2]] => [[4,4,4,2,1],[3,2,2,1]] => [3,2,2,1] => 8
[[5,4,3,3,1],[4,3,1,1]] => [[5,4,4,2,1],[4,2,2,1]] => [4,2,2,1] => 9
[[5,4,3,2,1],[4,3,1]] => [[5,5,4,2,1],[4,3,2,1]] => [4,3,2,1] => 10
[[3,3,3,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[[4,4,4,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1]] => [2,1] => 3
[[4,4,4,2,2],[3,3,2,1]] => [[4,3,2,1,1],[2,2]] => [2,2] => 4
[[5,5,5,3,2],[4,4,3,2]] => [[5,3,2,1,1],[3,2]] => [3,2] => 5
[[4,4,3,2,2],[3,3,1,1]] => [[4,3,3,1,1],[2,2,1]] => [2,2,1] => 5
[[5,5,4,3,2],[4,4,2,2]] => [[5,3,3,1,1],[3,2,1]] => [3,2,1] => 6
[[5,5,4,2,2],[4,4,2,1]] => [[5,4,3,1,1],[3,3,1]] => [3,3,1] => 7
[[6,6,5,3,2],[5,5,3,2]] => [[6,4,3,1,1],[4,3,1]] => [4,3,1] => 8
[[4,3,3,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,1,1]] => [2,2,1,1] => 6
[[5,4,4,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,1,1]] => [3,2,1,1] => 7
[[5,4,4,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,1,1]] => [3,3,1,1] => 8
[[6,5,5,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,1,1]] => [4,3,1,1] => 9
[[5,4,3,2,2],[4,3,1,1]] => [[5,4,4,2,1],[3,3,2,1]] => [3,3,2,1] => 9
[[6,5,4,3,2],[5,4,2,2]] => [[6,4,4,2,1],[4,3,2,1]] => [4,3,2,1] => 10
[[2,2,2,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 3
[[3,3,3,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1]] => [2,1,1] => 4
[[3,3,3,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1]] => [2,2,1] => 5
[[4,4,4,3,2,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,2,1]] => [3,2,1] => 6
[[3,3,3,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2]] => [2,2,2] => 6
[[4,4,4,2,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,2]] => [3,2,2] => 7
[[4,4,4,2,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,2]] => [3,3,2] => 8
[[5,5,5,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2]] => [4,3,2] => 9
[[3,3,2,1,1,1],[2,2]] => [[3,3,3,3,1,1],[2,2,2,1]] => [2,2,2,1] => 7
[[4,4,3,2,2,1],[3,3,1,1,1]] => [[4,3,3,3,1,1],[3,2,2,1]] => [3,2,2,1] => 8
[[4,4,3,2,1,1],[3,3,1,1]] => [[4,4,3,3,1,1],[3,3,2,1]] => [3,3,2,1] => 9
[[5,5,4,3,2,1],[4,4,2,2,1]] => [[5,4,3,3,1,1],[4,3,2,1]] => [4,3,2,1] => 10
[[4,4,3,1,1,1],[3,3,1]] => [[4,4,4,3,1,1],[3,3,3,1]] => [3,3,3,1] => 10
[[3,2,2,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,1,1]] => [2,2,2,1,1] => 8
[[4,3,3,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,1,1]] => [3,2,2,1,1] => 9
[[4,3,3,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,1,1]] => [3,3,2,1,1] => 10
[[4,4,4,4],[3,3,3]] => [[4,1,1,1],[]] => [] => 0
[[5,5,5,4],[4,4,4]] => [[5,1,1,1],[1]] => [1] => 1
[[5,5,4,4],[4,4,3]] => [[5,2,1,1],[1,1]] => [1,1] => 2
[[6,6,5,4],[5,5,4]] => [[6,2,1,1],[2,1]] => [2,1] => 3
[[5,4,4,4],[4,3,3]] => [[5,2,2,1],[1,1,1]] => [1,1,1] => 3
[[6,5,5,4],[5,4,4]] => [[6,2,2,1],[2,1,1]] => [2,1,1] => 4
[[6,5,4,4],[5,4,3]] => [[6,3,2,1],[2,2,1]] => [2,2,1] => 5
[[7,6,5,4],[6,5,4]] => [[7,3,2,1],[3,2,1]] => [3,2,1] => 6
[[3,3,3,3,1],[2,2,2]] => [[3,3,1,1,1],[2]] => [2] => 2
[[4,4,4,4,1],[3,3,3,1]] => [[4,3,1,1,1],[3]] => [3] => 3
[[4,4,4,3,1],[3,3,3]] => [[4,4,1,1,1],[3,1]] => [3,1] => 4
[[5,5,5,4,1],[4,4,4,1]] => [[5,4,1,1,1],[4,1]] => [4,1] => 5
[[4,4,3,3,1],[3,3,2]] => [[4,4,2,1,1],[3,1,1]] => [3,1,1] => 5
[[5,5,4,4,1],[4,4,3,1]] => [[5,4,2,1,1],[4,1,1]] => [4,1,1] => 6
[[5,5,4,3,1],[4,4,3]] => [[5,5,2,1,1],[4,2,1]] => [4,2,1] => 7
[[6,6,5,4,1],[5,5,4,1]] => [[6,5,2,1,1],[5,2,1]] => [5,2,1] => 8
[[4,3,3,3,1],[3,2,2]] => [[4,4,2,2,1],[3,1,1,1]] => [3,1,1,1] => 6
[[5,4,4,4,1],[4,3,3,1]] => [[5,4,2,2,1],[4,1,1,1]] => [4,1,1,1] => 7
[[5,4,4,3,1],[4,3,3]] => [[5,5,2,2,1],[4,2,1,1]] => [4,2,1,1] => 8
[[6,5,5,4,1],[5,4,4,1]] => [[6,5,2,2,1],[5,2,1,1]] => [5,2,1,1] => 9
[[5,4,3,3,1],[4,3,2]] => [[5,5,3,2,1],[4,2,2,1]] => [4,2,2,1] => 9
[[6,5,4,4,1],[5,4,3,1]] => [[6,5,3,2,1],[5,2,2,1]] => [5,2,2,1] => 10
[[2,2,2,2,2],[1,1,1]] => [[2,2,1,1,1],[]] => [] => 0
[[3,3,3,3,2],[2,2,2,1]] => [[3,2,1,1,1],[1]] => [1] => 1
[[4,4,4,4,2],[3,3,3,2]] => [[4,2,1,1,1],[2]] => [2] => 2
[[3,3,3,2,2],[2,2,2]] => [[3,3,1,1,1],[1,1]] => [1,1] => 2
[[4,4,4,3,2],[3,3,3,1]] => [[4,3,1,1,1],[2,1]] => [2,1] => 3
[[5,5,5,4,2],[4,4,4,2]] => [[5,3,1,1,1],[3,1]] => [3,1] => 4
[[3,3,2,2,2],[2,2,1]] => [[3,3,2,1,1],[1,1,1]] => [1,1,1] => 3
[[4,4,3,3,2],[3,3,2,1]] => [[4,3,2,1,1],[2,1,1]] => [2,1,1] => 4
[[5,5,4,4,2],[4,4,3,2]] => [[5,3,2,1,1],[3,1,1]] => [3,1,1] => 5
[[4,4,3,2,2],[3,3,2]] => [[4,4,2,1,1],[2,2,1]] => [2,2,1] => 5
[[5,5,4,3,2],[4,4,3,1]] => [[5,4,2,1,1],[3,2,1]] => [3,2,1] => 6
[[6,6,5,4,2],[5,5,4,2]] => [[6,4,2,1,1],[4,2,1]] => [4,2,1] => 7
[[3,2,2,2,2],[2,1,1]] => [[3,3,2,2,1],[1,1,1,1]] => [1,1,1,1] => 4
[[4,3,3,3,2],[3,2,2,1]] => [[4,3,2,2,1],[2,1,1,1]] => [2,1,1,1] => 5
[[5,4,4,4,2],[4,3,3,2]] => [[5,3,2,2,1],[3,1,1,1]] => [3,1,1,1] => 6
[[4,3,3,2,2],[3,2,2]] => [[4,4,2,2,1],[2,2,1,1]] => [2,2,1,1] => 6
[[5,4,4,3,2],[4,3,3,1]] => [[5,4,2,2,1],[3,2,1,1]] => [3,2,1,1] => 7
[[6,5,5,4,2],[5,4,4,2]] => [[6,4,2,2,1],[4,2,1,1]] => [4,2,1,1] => 8
[[4,3,2,2,2],[3,2,1]] => [[4,4,3,2,1],[2,2,2,1]] => [2,2,2,1] => 7
[[5,4,3,3,2],[4,3,2,1]] => [[5,4,3,2,1],[3,2,2,1]] => [3,2,2,1] => 8
[[6,5,4,4,2],[5,4,3,2]] => [[6,4,3,2,1],[4,2,2,1]] => [4,2,2,1] => 9
[[5,4,3,2,2],[4,3,2]] => [[5,5,3,2,1],[3,3,2,1]] => [3,3,2,1] => 9
[[6,5,4,3,2],[5,4,3,1]] => [[6,5,3,2,1],[4,3,2,1]] => [4,3,2,1] => 10
[[2,2,2,2,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[[3,3,3,3,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1]] => [2,1] => 3
[[3,3,3,3,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2]] => [2,2] => 4
[[4,4,4,4,2,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,2]] => [3,2] => 5
[[3,3,3,2,1,1],[2,2,2]] => [[3,3,3,1,1,1],[2,2,1]] => [2,2,1] => 5
[[4,4,4,3,2,1],[3,3,3,1,1]] => [[4,3,3,1,1,1],[3,2,1]] => [3,2,1] => 6
[[4,4,4,3,1,1],[3,3,3,1]] => [[4,4,3,1,1,1],[3,3,1]] => [3,3,1] => 7
[[5,5,5,4,2,1],[4,4,4,2,1]] => [[5,4,3,1,1,1],[4,3,1]] => [4,3,1] => 8
[[3,3,2,2,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,1,1]] => [2,2,1,1] => 6
[[4,4,3,3,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,1,1]] => [3,2,1,1] => 7
[[4,4,3,3,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,1,1]] => [3,3,1,1] => 8
[[5,5,4,4,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,1,1]] => [4,3,1,1] => 9
[[4,4,3,2,1,1],[3,3,2]] => [[4,4,4,2,1,1],[3,3,2,1]] => [3,3,2,1] => 9
[[5,5,4,3,2,1],[4,4,3,1,1]] => [[5,4,4,2,1,1],[4,3,2,1]] => [4,3,2,1] => 10
[[3,2,2,2,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,1,1,1]] => [2,2,1,1,1] => 7
[[4,3,3,3,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1] => 8
[[4,3,3,3,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,1,1,1]] => [3,3,1,1,1] => 9
[[5,4,4,4,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,1,1,1]] => [4,3,1,1,1] => 10
[[4,3,3,2,1,1],[3,2,2]] => [[4,4,4,2,2,1],[3,3,2,1,1]] => [3,3,2,1,1] => 10
[[3,3,3,3,3],[2,2,2,2]] => [[3,1,1,1,1],[]] => [] => 0
[[4,4,4,4,3],[3,3,3,3]] => [[4,1,1,1,1],[1]] => [1] => 1
[[4,4,4,3,3],[3,3,3,2]] => [[4,2,1,1,1],[1,1]] => [1,1] => 2
[[5,5,5,4,3],[4,4,4,3]] => [[5,2,1,1,1],[2,1]] => [2,1] => 3
[[4,4,3,3,3],[3,3,2,2]] => [[4,2,2,1,1],[1,1,1]] => [1,1,1] => 3
[[5,5,4,4,3],[4,4,3,3]] => [[5,2,2,1,1],[2,1,1]] => [2,1,1] => 4
[[5,5,4,3,3],[4,4,3,2]] => [[5,3,2,1,1],[2,2,1]] => [2,2,1] => 5
[[6,6,5,4,3],[5,5,4,3]] => [[6,3,2,1,1],[3,2,1]] => [3,2,1] => 6
[[4,3,3,3,3],[3,2,2,2]] => [[4,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 4
[[5,4,4,4,3],[4,3,3,3]] => [[5,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 5
[[5,4,4,3,3],[4,3,3,2]] => [[5,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 6
[[6,5,5,4,3],[5,4,4,3]] => [[6,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => 7
[[5,4,3,3,3],[4,3,2,2]] => [[5,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 7
[[6,5,4,4,3],[5,4,3,3]] => [[6,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => 8
[[6,5,4,3,3],[5,4,3,2]] => [[6,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => 9
[[7,6,5,4,3],[6,5,4,3]] => [[7,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => 10
[[2,2,2,2,2,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1]] => [1] => 1
[[3,3,3,3,3,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2]] => [2] => 2
[[3,3,3,3,2,1],[2,2,2,2]] => [[3,3,1,1,1,1],[2,1]] => [2,1] => 3
[[4,4,4,4,3,1],[3,3,3,3,1]] => [[4,3,1,1,1,1],[3,1]] => [3,1] => 4
[[3,3,3,2,2,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,1,1]] => [2,1,1] => 4
[[4,4,4,3,3,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,1,1]] => [3,1,1] => 5
[[4,4,4,3,2,1],[3,3,3,2]] => [[4,4,2,1,1,1],[3,2,1]] => [3,2,1] => 6
[[5,5,5,4,3,1],[4,4,4,3,1]] => [[5,4,2,1,1,1],[4,2,1]] => [4,2,1] => 7
[[3,3,2,2,2,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => 5
[[4,4,3,3,3,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,1,1,1]] => [3,1,1,1] => 6
[[4,4,3,3,2,1],[3,3,2,2]] => [[4,4,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => 7
[[5,5,4,4,3,1],[4,4,3,3,1]] => [[5,4,2,2,1,1],[4,2,1,1]] => [4,2,1,1] => 8
[[4,4,3,2,2,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => 8
[[5,5,4,3,3,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,2,2,1]] => [4,2,2,1] => 9
[[5,5,4,3,2,1],[4,4,3,2]] => [[5,5,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => 10
[[3,2,2,2,2,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1] => 6
[[4,3,3,3,3,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,1,1,1,1]] => [3,1,1,1,1] => 7
[[4,3,3,3,2,1],[3,2,2,2]] => [[4,4,2,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1] => 8
[[5,4,4,4,3,1],[4,3,3,3,1]] => [[5,4,2,2,2,1],[4,2,1,1,1]] => [4,2,1,1,1] => 9
[[4,3,3,2,2,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,2,2,1,1]] => [3,2,2,1,1] => 9
[[5,4,4,3,3,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,2,2,1,1]] => [4,2,2,1,1] => 10
[[4,3,2,2,2,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1] => 10
[[2,2,2,2,2,2],[1,1,1,1,1]] => [[2,1,1,1,1,1],[]] => [] => 0
[[3,3,3,3,3,2],[2,2,2,2,2]] => [[3,1,1,1,1,1],[1]] => [1] => 1
[[3,3,3,3,2,2],[2,2,2,2,1]] => [[3,2,1,1,1,1],[1,1]] => [1,1] => 2
[[4,4,4,4,3,2],[3,3,3,3,2]] => [[4,2,1,1,1,1],[2,1]] => [2,1] => 3
[[3,3,3,2,2,2],[2,2,2,1,1]] => [[3,2,2,1,1,1],[1,1,1]] => [1,1,1] => 3
[[4,4,4,3,3,2],[3,3,3,2,2]] => [[4,2,2,1,1,1],[2,1,1]] => [2,1,1] => 4
[[4,4,4,3,2,2],[3,3,3,2,1]] => [[4,3,2,1,1,1],[2,2,1]] => [2,2,1] => 5
[[5,5,5,4,3,2],[4,4,4,3,2]] => [[5,3,2,1,1,1],[3,2,1]] => [3,2,1] => 6
[[3,3,2,2,2,2],[2,2,1,1,1]] => [[3,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => 4
[[4,4,3,3,3,2],[3,3,2,2,2]] => [[4,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => 5
[[4,4,3,3,2,2],[3,3,2,2,1]] => [[4,3,2,2,1,1],[2,2,1,1]] => [2,2,1,1] => 6
[[5,5,4,4,3,2],[4,4,3,3,2]] => [[5,3,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => 7
[[4,4,3,2,2,2],[3,3,2,1,1]] => [[4,3,3,2,1,1],[2,2,2,1]] => [2,2,2,1] => 7
[[5,5,4,3,3,2],[4,4,3,2,2]] => [[5,3,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => 8
[[5,5,4,3,2,2],[4,4,3,2,1]] => [[5,4,3,2,1,1],[3,3,2,1]] => [3,3,2,1] => 9
[[6,6,5,4,3,2],[5,5,4,3,2]] => [[6,4,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => 10
[[3,2,2,2,2,2],[2,1,1,1,1]] => [[3,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => 5
[[4,3,3,3,3,2],[3,2,2,2,2]] => [[4,2,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1] => 6
[[4,3,3,3,2,2],[3,2,2,2,1]] => [[4,3,2,2,2,1],[2,2,1,1,1]] => [2,2,1,1,1] => 7
[[5,4,4,4,3,2],[4,3,3,3,2]] => [[5,3,2,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1] => 8
[[4,3,3,2,2,2],[3,2,2,1,1]] => [[4,3,3,2,2,1],[2,2,2,1,1]] => [2,2,2,1,1] => 8
[[5,4,4,3,3,2],[4,3,3,2,2]] => [[5,3,3,2,2,1],[3,2,2,1,1]] => [3,2,2,1,1] => 9
[[5,4,4,3,2,2],[4,3,3,2,1]] => [[5,4,3,2,2,1],[3,3,2,1,1]] => [3,3,2,1,1] => 10
[[4,3,2,2,2,2],[3,2,1,1,1]] => [[4,3,3,3,2,1],[2,2,2,2,1]] => [2,2,2,2,1] => 9
[[5,4,3,3,3,2],[4,3,2,2,2]] => [[5,3,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1] => 10
[[1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1],[]] => [] => 0
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [[2,1,1,1,1,1,1],[1]] => [1] => 1
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => [[2,2,1,1,1,1,1],[1,1]] => [1,1] => 2
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [[3,2,1,1,1,1,1],[2,1]] => [2,1] => 3
[[2,2,2,2,1,1,1],[1,1,1,1]] => [[2,2,2,1,1,1,1],[1,1,1]] => [1,1,1] => 3
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [[3,2,2,1,1,1,1],[2,1,1]] => [2,1,1] => 4
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => [[3,3,2,1,1,1,1],[2,2,1]] => [2,2,1] => 5
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [[4,3,2,1,1,1,1],[3,2,1]] => [3,2,1] => 6
[[2,2,2,1,1,1,1],[1,1,1]] => [[2,2,2,2,1,1,1],[1,1,1,1]] => [1,1,1,1] => 4
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [[3,2,2,2,1,1,1],[2,1,1,1]] => [2,1,1,1] => 5
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => [[3,3,2,2,1,1,1],[2,2,1,1]] => [2,2,1,1] => 6
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [[4,3,2,2,1,1,1],[3,2,1,1]] => [3,2,1,1] => 7
[[3,3,3,2,1,1,1],[2,2,2,1]] => [[3,3,3,2,1,1,1],[2,2,2,1]] => [2,2,2,1] => 7
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [[4,3,3,2,1,1,1],[3,2,2,1]] => [3,2,2,1] => 8
[[4,4,4,3,2,1,1],[3,3,3,2,1]] => [[4,4,3,2,1,1,1],[3,3,2,1]] => [3,3,2,1] => 9
[[5,5,5,4,3,2,1],[4,4,4,3,2,1]] => [[5,4,3,2,1,1,1],[4,3,2,1]] => [4,3,2,1] => 10
[[2,2,1,1,1,1,1],[1,1]] => [[2,2,2,2,2,1,1],[1,1,1,1,1]] => [1,1,1,1,1] => 5
[[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => [[3,2,2,2,2,1,1],[2,1,1,1,1]] => [2,1,1,1,1] => 6
[[3,3,2,2,2,1,1],[2,2,1,1,1]] => [[3,3,2,2,2,1,1],[2,2,1,1,1]] => [2,2,1,1,1] => 7
[[4,4,3,3,3,2,1],[3,3,2,2,2,1]] => [[4,3,2,2,2,1,1],[3,2,1,1,1]] => [3,2,1,1,1] => 8
[[3,3,2,2,1,1,1],[2,2,1,1]] => [[3,3,3,2,2,1,1],[2,2,2,1,1]] => [2,2,2,1,1] => 8
[[4,4,3,3,2,2,1],[3,3,2,2,1,1]] => [[4,3,3,2,2,1,1],[3,2,2,1,1]] => [3,2,2,1,1] => 9
[[4,4,3,3,2,1,1],[3,3,2,2,1]] => [[4,4,3,2,2,1,1],[3,3,2,1,1]] => [3,3,2,1,1] => 10
[[3,3,2,1,1,1,1],[2,2,1]] => [[3,3,3,3,2,1,1],[2,2,2,2,1]] => [2,2,2,2,1] => 9
[[4,4,3,2,2,2,1],[3,3,2,1,1,1]] => [[4,3,3,3,2,1,1],[3,2,2,2,1]] => [3,2,2,2,1] => 10
[[2,1,1,1,1,1,1],[1]] => [[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 6
[[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => [[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => [2,1,1,1,1,1] => 7
[[3,2,2,2,2,1,1],[2,1,1,1,1]] => [[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => [2,2,1,1,1,1] => 8
[[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => [[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => [3,2,1,1,1,1] => 9
[[3,2,2,2,1,1,1],[2,1,1,1]] => [[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [2,2,2,1,1,1] => 9
[[4,3,3,3,2,2,1],[3,2,2,2,1,1]] => [[4,3,3,2,2,2,1],[3,2,2,1,1,1]] => [3,2,2,1,1,1] => 10
[[3,2,2,1,1,1,1],[2,1,1]] => [[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [2,2,2,2,1,1] => 10
[[8],[]] => [[8],[]] => [] => 0
[[7,1],[]] => [[7,7],[6]] => [6] => 6
[[6,2],[]] => [[6,6],[4]] => [4] => 4
[[6,1,1],[]] => [[6,6,6],[5,5]] => [5,5] => 10
[[5,3],[]] => [[5,5],[2]] => [2] => 2
[[5,2,1],[]] => [[5,5,5],[4,3]] => [4,3] => 7
[[4,4],[]] => [[4,4],[]] => [] => 0
[[4,3,1],[]] => [[4,4,4],[3,1]] => [3,1] => 4
[[4,2,2],[]] => [[4,4,4],[2,2]] => [2,2] => 4
[[4,2,1,1],[]] => [[4,4,4,4],[3,3,2]] => [3,3,2] => 8
[[3,3,2],[]] => [[3,3,3],[1]] => [1] => 1
[[3,3,1,1],[]] => [[3,3,3,3],[2,2]] => [2,2] => 4
[[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]] => [2,1,1] => 4
[[3,2,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,1]] => [2,2,2,1] => 7
[[3,1,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 10
[[2,2,2,2],[]] => [[2,2,2,2],[]] => [] => 0
[[2,2,2,1,1],[]] => [[2,2,2,2,2],[1,1]] => [1,1] => 2
[[2,2,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 4
[[2,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 6
[[1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1],[]] => [] => 0
[[9],[]] => [[9],[]] => [] => 0
[[8,1],[]] => [[8,8],[7]] => [7] => 7
[[7,2],[]] => [[7,7],[5]] => [5] => 5
[[6,3],[]] => [[6,6],[3]] => [3] => 3
[[6,2,1],[]] => [[6,6,6],[5,4]] => [5,4] => 9
[[5,4],[]] => [[5,5],[1]] => [1] => 1
[[5,3,1],[]] => [[5,5,5],[4,2]] => [4,2] => 6
[[5,2,2],[]] => [[5,5,5],[3,3]] => [3,3] => 6
[[4,4,1],[]] => [[4,4,4],[3]] => [3] => 3
[[4,3,2],[]] => [[4,4,4],[2,1]] => [2,1] => 3
[[4,3,1,1],[]] => [[4,4,4,4],[3,3,1]] => [3,3,1] => 7
[[4,2,2,1],[]] => [[4,4,4,4],[3,2,2]] => [3,2,2] => 7
[[3,3,3],[]] => [[3,3,3],[]] => [] => 0
[[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => [2,1] => 3
[[3,3,1,1,1],[]] => [[3,3,3,3,3],[2,2,2]] => [2,2,2] => 6
[[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]] => [1,1,1] => 3
[[3,2,2,1,1],[]] => [[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => 6
[[3,2,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2,1]] => [2,2,2,2,1] => 9
[[2,2,2,2,1],[]] => [[2,2,2,2,2],[1]] => [1] => 1
[[2,2,2,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1]] => [1,1,1] => 3
[[2,2,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 5
[[2,1,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => 7
[[1,1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1,1],[]] => [] => 0
[[10],[]] => [[10],[]] => [] => 0
[[9,1],[]] => [[9,9],[8]] => [8] => 8
[[8,2],[]] => [[8,8],[6]] => [6] => 6
[[7,3],[]] => [[7,7],[4]] => [4] => 4
[[6,4],[]] => [[6,6],[2]] => [2] => 2
[[6,3,1],[]] => [[6,6,6],[5,3]] => [5,3] => 8
[[6,2,2],[]] => [[6,6,6],[4,4]] => [4,4] => 8
[[5,5],[]] => [[5,5],[]] => [] => 0
[[5,4,1],[]] => [[5,5,5],[4,1]] => [4,1] => 5
[[5,3,2],[]] => [[5,5,5],[3,2]] => [3,2] => 5
[[5,3,1,1],[]] => [[5,5,5,5],[4,4,2]] => [4,4,2] => 10
[[5,2,2,1],[]] => [[5,5,5,5],[4,3,3]] => [4,3,3] => 10
[[4,4,2],[]] => [[4,4,4],[2]] => [2] => 2
[[4,4,1,1],[]] => [[4,4,4,4],[3,3]] => [3,3] => 6
[[4,3,3],[]] => [[4,4,4],[1,1]] => [1,1] => 2
[[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => [3,2,1] => 6
[[4,3,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,1]] => [3,3,3,1] => 10
[[4,2,2,2],[]] => [[4,4,4,4],[2,2,2]] => [2,2,2] => 6
[[4,2,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,2]] => [3,3,2,2] => 10
[[3,3,3,1],[]] => [[3,3,3,3],[2]] => [2] => 2
[[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => [1,1] => 2
[[3,3,2,1,1],[]] => [[3,3,3,3,3],[2,2,1]] => [2,2,1] => 5
[[3,3,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 8
[[3,2,2,2,1],[]] => [[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1] => 5
[[3,2,2,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,1,1]] => [2,2,2,1,1] => 8
[[2,2,2,2,2],[]] => [[2,2,2,2,2],[]] => [] => 0
[[2,2,2,2,1,1],[]] => [[2,2,2,2,2,2],[1,1]] => [1,1] => 2
[[2,2,2,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 4
[[2,2,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 6
[[2,1,1,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => 8
[[1,1,1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1,1,1],[]] => [] => 0
[[6,5],[]] => [[6,6],[1]] => [1] => 1
[[5,5,1],[]] => [[5,5,5],[4]] => [4] => 4
[[5,4,2],[]] => [[5,5,5],[3,1]] => [3,1] => 4
[[5,4,1,1],[]] => [[5,5,5,5],[4,4,1]] => [4,4,1] => 9
[[5,3,3],[]] => [[5,5,5],[2,2]] => [2,2] => 4
[[5,3,2,1],[]] => [[5,5,5,5],[4,3,2]] => [4,3,2] => 9
[[5,2,2,2],[]] => [[5,5,5,5],[3,3,3]] => [3,3,3] => 9
[[4,4,3],[]] => [[4,4,4],[1]] => [1] => 1
[[4,4,2,1],[]] => [[4,4,4,4],[3,2]] => [3,2] => 5
[[4,4,1,1,1],[]] => [[4,4,4,4,4],[3,3,3]] => [3,3,3] => 9
[[4,3,3,1],[]] => [[4,4,4,4],[3,1,1]] => [3,1,1] => 5
[[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]] => [2,2,1] => 5
[[4,3,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1] => 9
[[4,2,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,2]] => [3,2,2,2] => 9
[[3,3,3,2],[]] => [[3,3,3,3],[1]] => [1] => 1
[[3,3,3,1,1],[]] => [[3,3,3,3,3],[2,2]] => [2,2] => 4
[[3,3,2,2,1],[]] => [[3,3,3,3,3],[2,1,1]] => [2,1,1] => 4
[[3,2,2,2,2],[]] => [[3,3,3,3,3],[1,1,1,1]] => [1,1,1,1] => 4
[[6,6],[]] => [[6,6],[]] => [] => 0
[[6,4,2],[]] => [[6,6,6],[4,2]] => [4,2] => 6
[[5,5,2],[]] => [[5,5,5],[3]] => [3] => 3
[[5,4,3],[]] => [[5,5,5],[2,1]] => [2,1] => 3
[[5,4,2,1],[]] => [[5,5,5,5],[4,3,1]] => [4,3,1] => 8
[[5,3,3,1],[]] => [[5,5,5,5],[4,2,2]] => [4,2,2] => 8
[[5,3,2,2],[]] => [[5,5,5,5],[3,3,2]] => [3,3,2] => 8
[[4,4,4],[]] => [[4,4,4],[]] => [] => 0
[[4,4,3,1],[]] => [[4,4,4,4],[3,1]] => [3,1] => 4
[[4,4,2,2],[]] => [[4,4,4,4],[2,2]] => [2,2] => 4
[[4,4,2,1,1],[]] => [[4,4,4,4,4],[3,3,2]] => [3,3,2] => 8
[[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]] => [2,1,1] => 4
[[4,3,3,1,1],[]] => [[4,4,4,4,4],[3,3,1,1]] => [3,3,1,1] => 8
[[4,3,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1] => 8
[[3,3,3,3],[]] => [[3,3,3,3],[]] => [] => 0
[[3,3,3,2,1],[]] => [[3,3,3,3,3],[2,1]] => [2,1] => 3
[[3,3,2,2,2],[]] => [[3,3,3,3,3],[1,1,1]] => [1,1,1] => 3
[[3,3,2,2,1,1],[]] => [[3,3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => 6
[[2,2,2,2,2,2],[]] => [[2,2,2,2,2,2],[]] => [] => 0
[[5,5,3],[]] => [[5,5,5],[2]] => [2] => 2
[[5,4,4],[]] => [[5,5,5],[1,1]] => [1,1] => 2
[[5,4,3,1],[]] => [[5,5,5,5],[4,2,1]] => [4,2,1] => 7
[[5,4,2,2],[]] => [[5,5,5,5],[3,3,1]] => [3,3,1] => 7
[[5,3,3,2],[]] => [[5,5,5,5],[3,2,2]] => [3,2,2] => 7
[[4,4,4,1],[]] => [[4,4,4,4],[3]] => [3] => 3
[[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [2,1] => 3
[[4,4,3,1,1],[]] => [[4,4,4,4,4],[3,3,1]] => [3,3,1] => 7
[[4,4,2,2,1],[]] => [[4,4,4,4,4],[3,2,2]] => [3,2,2] => 7
[[4,3,3,3],[]] => [[4,4,4,4],[1,1,1]] => [1,1,1] => 3
[[4,3,3,2,1],[]] => [[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1] => 7
[[3,3,3,3,1],[]] => [[3,3,3,3,3],[2]] => [2] => 2
[[3,3,3,2,2],[]] => [[3,3,3,3,3],[1,1]] => [1,1] => 2
[[5,5,4],[]] => [[5,5,5],[1]] => [1] => 1
[[5,4,3,2],[]] => [[5,5,5,5],[3,2,1]] => [3,2,1] => 6
[[4,4,4,2],[]] => [[4,4,4,4],[2]] => [2] => 2
[[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [1,1] => 2
[[4,4,3,2,1],[]] => [[4,4,4,4,4],[3,2,1]] => [3,2,1] => 6
[[3,3,3,3,2],[]] => [[3,3,3,3,3],[1]] => [1] => 1
[[5,5,5],[]] => [[5,5,5],[]] => [] => 0
[[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1] => 10
[[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1] => 1
[[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => [] => 0
[[4,4,4,4],[]] => [[4,4,4,4],[]] => [] => 0
[[3,3,3],[1]] => [[3,3,2],[]] => [] => 0
[[3,3,3,1],[1,1]] => [[3,3,2,2],[2]] => [2] => 2
[[4,4,1],[1]] => [[4,4,3],[3]] => [3] => 3
[[3,3,2,1],[1]] => [[3,3,3,2],[2,1]] => [2,1] => 3
[[2,2,2,2,1],[1]] => [[2,2,2,2,1],[1]] => [1] => 1
[[3,3,3,1],[2]] => [[3,3,3,1],[2]] => [2] => 2
[[3,3,3,1],[1]] => [[3,3,3,2],[2]] => [2] => 2
[[3,3,3,2],[1,1,1]] => [[3,2,2,2],[1]] => [1] => 1
[[4,4,2],[1,1]] => [[4,3,3],[2]] => [2] => 2
[[4,4,4],[2,2]] => [[4,2,2],[]] => [] => 0
[[5,5],[2]] => [[5,3],[]] => [] => 0
[[4,4,3],[2,1]] => [[4,3,2],[1]] => [1] => 1
[[3,3,3,3],[2,1,1]] => [[3,2,2,1],[]] => [] => 0
[[4,3,3],[1,1]] => [[4,3,3],[1,1]] => [1,1] => 2
[[3,3,3,3],[1,1,1]] => [[3,2,2,2],[]] => [] => 0
[[4,4,3],[1,1]] => [[4,3,3],[1]] => [1] => 1
[[4,4,4],[3,1]] => [[4,3,1],[]] => [] => 0
[[5,4],[1]] => [[5,4],[1]] => [1] => 1
[[4,4,4],[2,1]] => [[4,3,2],[]] => [] => 0
[[5,5],[1]] => [[5,4],[]] => [] => 0
[[4,4,4],[1,1]] => [[4,3,3],[]] => [] => 0
[[3,3,2,2],[1,1]] => [[3,3,2,2],[1,1]] => [1,1] => 2
[[4,4,2],[2]] => [[4,4,2],[2]] => [2] => 2
[[3,3,3,2],[2,1]] => [[3,3,2,1],[1]] => [1] => 1
[[4,3,2],[1]] => [[4,4,3],[2,1]] => [2,1] => 3
[[3,3,3,2],[1,1]] => [[3,3,2,2],[1]] => [1] => 1
[[4,4,2],[1]] => [[4,4,3],[2]] => [2] => 2
[[2,2,2,2,2],[1,1]] => [[2,2,2,1,1],[]] => [] => 0
[[3,2,2,2],[1]] => [[3,3,3,2],[1,1,1]] => [1,1,1] => 3
[[3,3,2,2],[2]] => [[3,3,3,1],[1,1]] => [1,1] => 2
[[3,3,2,2],[1]] => [[3,3,3,2],[1,1]] => [1,1] => 2
[[2,2,2,2,2],[1]] => [[2,2,2,2,1],[]] => [] => 0
[[3,3,3,2],[2]] => [[3,3,3,1],[1]] => [1] => 1
[[3,3,3,2],[1]] => [[3,3,3,2],[1]] => [1] => 1
[[3,3,3,3],[2,2]] => [[3,3,1,1],[]] => [] => 0
[[4,3,3],[2]] => [[4,4,2],[1,1]] => [1,1] => 2
[[4,4,3],[3]] => [[4,4,1],[1]] => [1] => 1
[[4,4,3],[2]] => [[4,4,2],[1]] => [1] => 1
[[3,3,3,3],[2,1]] => [[3,3,2,1],[]] => [] => 0
[[4,3,3],[1]] => [[4,4,3],[1,1]] => [1,1] => 2
[[3,3,3,3],[1,1]] => [[3,3,2,2],[]] => [] => 0
[[4,4,3],[1]] => [[4,4,3],[1]] => [1] => 1
[[4,4,4],[3]] => [[4,4,1],[]] => [] => 0
[[4,4,4],[2]] => [[4,4,2],[]] => [] => 0
[[4,4,4],[1]] => [[4,4,3],[]] => [] => 0
[[3,3,3,3],[2]] => [[3,3,3,1],[]] => [] => 0
[[3,3,3,3],[1]] => [[3,3,3,2],[]] => [] => 0
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,1 3,3,2,1 5,5,6,6,3,2,1 7,9,12,14,13,11,9,6,3,2,1
$F_{1} = 1$
$F_{2} = 2 + q$
$F_{3} = 3 + 3\ q + 2\ q^{2} + q^{3}$
$F_{4} = 5 + 5\ q + 6\ q^{2} + 6\ q^{3} + 3\ q^{4} + 2\ q^{5} + q^{6}$
$F_{5} = 7 + 9\ q + 12\ q^{2} + 14\ q^{3} + 13\ q^{4} + 11\ q^{5} + 9\ q^{6} + 6\ q^{7} + 3\ q^{8} + 2\ q^{9} + q^{10}$
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.
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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.
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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inner shape
Description
The inner shape of a skew partition.
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